Astro.pdf

  • Uploaded by: Tanushree Bezbaruah
  • 0
  • 0
  • July 2020
  • PDF

This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA


Overview

Download & View Astro.pdf as PDF for free.

More details

  • Words: 192,064
  • Pages: 194
Scanned by CamScanner



O b s e r v a t io n

p le x p t o c e s s

a co m

th e c ir c u m

W

e

tim e w

w

s ta n c e s u n

h ic h p re s e n ts de r

s h a ll th e r e fo re

h e n b o th

d itio

s an

m an

d

p t io

a ssu m

y p ro b le m

s

p e c te d to o c c u s ta r t p u r s u in g th e e v o lu tio n w

h ic h it is

ex

f th e d e fin itio

ns

th a t a r e s till u n der

in te ı

ı ıiy e

r

o

f

a

s ta f

h a v e b e e n fu lĥ lle d

fr o m

th e e a r ti

e st w e sh a ı ls ùo w h e n a t le a s t o n e c o n d itio n h a s c e a s e d to b e s a tis fie d c o m p , p le te ly a n d ir r e v e r s ib F in a ı ly w e s h a ll c o n s id e r th e lif f l ll y e c yc e o s te a r p o p u la tio n s a n d th e e « ect s te lla r e v o lu ti ol o n o n th e e v o lu tio n o f a la x ie s w ith in w h i h c g s ta r s r e s id e G al a r e la r e s s te a x ie " g m s o f s ta r s (u s y t 1 0 h i h o o r l s o w c a s o c o n ta in in te r s t p , e lla r c l o f ga s a n d du o u d st M a n s y o f th e s ta r s in a g a la x y a r e a g g r e g a te d in c lu s te la r g e s t a m o n th r s th , 5 e e m c o n ta in in g g m o r e th a n 10 s ta r s T h e o b e c t o f r e f e re n c s te lla r e in p h y s ic s is , n a tu r a lly , th e S u n a n d in a la c tic h , g p y s ic s , th e G a la x y to it b e lo n s a ls o k w h ic h g , n o w n a s th e M ilk y W a y g a la x y co n

ns o

n

,

an

d

)

j

ı2 A

W ha t

ca n

w e

le a

rn

fr o

m

bse

o

rv a

t io n s ?

p h y s ic s (th e p h y s ic s o f s ta r s d o e ) s n o t le n d its e lf to e x p e r im e n ta l s tu d th e o th e r fie ld s f y a s do o p h y s ic a l s c ie n c e W e c an n o t de i v se a n d c o n d u t c e x p e r im e n t i o r d e r to te s t a d s n n v a lid a te th e o r ie s o r h y o th e s e s V p a lid a tio n o f a th e o r y is a c h i b y a c c u m u la tin e ve d g o b s e r v a tio n a l e v id e n c e th a t s u p p o r ts it a n d its p r e d ic tio n s in fe r e n c e s T h e e v id or e n c e is d e r iv e d f r o m e v e n ts th t h a a v e o c c u rr e d i are c o m t h n e e te ly b e o n d o pa st an d pı u r c o n tr o l T h e t y a s k is r a th e r s i m ila r to th a t o f d A s a r u le o f th u m b a e te c tiv e a th e o r y is a c c e p te d a s v a lid o ( r a t le a s t M g h ly r o b a b le if it w ith s ta n d s tw o p ) r a d ic a ll d iff e r e n t a itd in d y e pe n de n t o b s e r v i a t c o u r s e s o lo n o n a l te s ts a n d o f g a s n o c o n tr a d ic to r e v id e n c e ha s be y e f n o u d n T h e in fo r m a tio n w e can g a th e r fr o m a n in d iv id u a l s ta r is p r im a r y c h a r a c te r is tic th a t c q u ite r e s tr ic te d T he an be m e a s u r e d is th e a pp a ren t br i ì is th e a m o u n t o f d i ra g z» ıe s s w hic h a tio n fr o m th e s ta r fa lli n e g p r u n it tim e o n u n it a r e a o f a c o lle c to r (u s u a ll y a te le s c o p e ) T h is r a d ia tio n fl u x is n o t, h o w e v e r a n i w h ic h w e s h ll d a e n o te n tń n s ic , p r o p e r ty o f th e o b s e r v e d s ta d is ta n c e o f th e s ta r f r fo r it d e e n d s o n th e ro m th e o b s e r v p e r T he st e lla r d e ń n e d a s th e a m o u p r o p e r ty is th e lı n t o f en er u?ı iı ı piı y1 g y r a d ia te d e r u i p n t tim e e n g in e S in c e L i th e p o w e r o f th e s oe lla ı s a ls o th e a m ou nt of en er Ï g y c r o s s in g p e r u n it tim e a s p h e ń c a b r ig h tn e s s is s tr o

,

,

,

,

,

,

,

,

,

,

ム钿 an

d L

ex

p re



4 7r 4 2

y b e in fe r r e d fr o m l o b s if d is k now s s e d r e la tiv e to th a t o f th e S u n , th e s o la

(I 1

'

m a

n r

T he ı ll u m in o s it y o f a s ta r is u s u a 1 o s iı y L o - 3 8 5 × 10 2 6 1 s

lu n ıin

Scanned by CamScanner

ı2

F ig u

I

re

N

S k e tc h

T he

o te

o n

b o d ie s ) is b a s e d o

f

fr o m

s ta r

a

o

a

(

'

p o s itio

s

n

y ie ld in g

,

) T h u s th e

is

ith

d

v e r y n e a r ly

a

B

a se

(O

d

w e

hav e

s a te

llite

o

on

° ,

a t an

s p e c ia

Bc

,

w

,

com m on

,

p

m e

×

-

3

ba se

×

a

O " 7 6) C

ı 5

m

ho

11

m

,

E

ye ar

EiJiia

tw

ic a l u n it fo r

q u ir e d fo o n

r

a r th

E

a r th s o r b it '

ve n

p o s itio

'

a s ta r s

so

,

th e tr ia n

n re la

e gı

o

tiv e

b ta in e d

h ile th e p a r a lla x p d e fin e d a s s te lla r p a r a lı a x is th a t o f P r o x iı ı ı a

n

o n se

,

q u e n tly , to

g o o d a p p r o x im

a

ce

m e a s u r in

a

a tio n

y b e d ir e c tly

tra v e lle d in o n e y e a r a t th e

g d is ta n c e s

c a 1ı ed

pa

r se c

,

is

th o d : a s its n a m e in d ic a te s , it is th e d is ta n c e c o rr e s p o n d in to a g

g to

a fte r th e

a

b o u t 3 lig h t y e a r s R n

a

c a ta lo

h u n d r e d fo ld

f w hic h

ıc o s

tly , th e n u m b e r o f s ta r s fo r a s a r e s u lt o

m e a s u re a 】e

d

ba se d

illio a re

llite H ip lìa

n n e a 】b y s ta r s

q u ite

Ņ

,

s a te

t th e

w

h ic h

a c tiv ity o

f th e

(H ig h P re c is io n P a i a lla x C o lle c tin g

no m er o

g u e T he

o n m o re th a n a m

d is ta n c e s th a t c a ll b e d ire c tly

ecen

f a n tiq u ity t ı ?p W c e le s tia l p o s itio n s a n d b r ig h m e s s e s

g r e a te s t a s tr o

m e a s u r e d th e

s o īn e o

re

a s s ho w n

ic e th e E a r th S u n d is ta n c e

w

is th e d is ta n

,

,

d

so

10

d th e lin e

an

la r s y s te m d is ta n t p o in ts

g le s ,

an

f s ig h t

o

f s ig h t

th e lin e s o

een

s ta r a t th e

b ta in e d b y d e te r m in in g

o

-

10

d is ta n c e s h a s g r o w

,

w e sha

f

in te r v a l o f h a lf

a s tr o n o m

d p r o d u c e d th e firs t s ta r

d e v is e d ,

o

th e r c e le s tia l

T h is is p r o v id e d b y th e E

n e e de d

l b a s e lin e

o

id e r th e b a s e lin e

w

,

ith in th e

w

g le b e tw

ith th e

w

,

la n d

to s ta r s

b s e r v e r T h e lin e s

b je c t th e

o

lly d e s ig n e d fo r th is ta s k H ilìp a

n am e

)

b je c ts

o

th e a n

tr ia n g le

a

a lm o s t r ig h t

lig h t y e a r 9 4 6

19 89 9 3 g a th e r e d d a ta to b e

lltt t

tu

s ta r s

th is m e th o d , d is ta n c e s o f u p to a b o u t 5 0 0 lig h t y e a r s m

a m o u n tin

a c c u ].A te

,

s ta r s a n

d

n e

f1

S a te llite ) c e n tu ry

g d is ta n c e s to

,

p a r a ll?

o n th e

p a ra lla x

r m e trs u r in

g le Î s Iės s th a n V (th e la ľ g e s t k n o w

f lig h t ) A

sp e e d o

w

,

r o

th e s ta r c lo s e s t to o u r S u n

/p

m e a s u re

ba se d

is o s c e le s

a p e x in

e lz la u r i H

rm

lla r p a ra ı 1a x is

s te

,

,

C

b ııp v ıt ı o n ıf

f th e

s o

fo

ns

a m a x im a

to v e r y d is ta n t Fix e d s ta ls

h a lf th e

pt o f p a

la rg e r b a s e lin e is

s ta r s , a m u c h

d th e S u

1 A U

=

co nce

d fo

o

m

f d e te rm in in g d is ta n c e s

th o d o

d is c e r n ib le p a r a lla x : fo

a

ffic e ; fo r

a ro u n

th o

m e

d iffe r e n t p o s itio n

b se rv e r

o

ld

e

ı ıa p n fr o

w e

1 I T h e la rg e r th e d is ta n c e to th e

re

b ta in in g

su

th e o

o n

ca n

f th e p a r a lla x

ly tlir e c [ m

tw o

c o n n e c tin g th e

in Ħ g u

o

W ha t

sm a

)

rco s , w

s o lı

o

f a lm

h ic h

B u t o n th e

o

o s t a th o u s a n

f s te lı . s tr u c tu ıe aı

ic a l s c a le

c t m e th o an

d

p e r a te d d u r in g

a s tr o n o m

ll a n d h e n c e in d iıe

o n th e th e o ry o

f N ic e a (s e c o n d

d

ds h av e

e v o lu tio n

,

as

ll s e e in C h a p te r 9

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

p t ıo n S a s s u rrı

B a s ic

ı3 .

d d s e v e r a l fu n d a m e n ta ıa łs u ı T rity a np w e ı h t i h o b a s e th e c w n o r l a s ta , d lin ilio n o e n e ra l e

ev aı ih c o b s c r v a lio n

id e n c e

G u id e d b y n s ) to ih c g lio n s (o r a x io ı d e v o lu tio n o l s te lla r s lľ u c tu r e a n

,

is o la t io R e g a r d in g its s tru c tu r e

an

d

e v o lu tio n

,

n

s ta r m a y

g le

a s in

be r

be

c o n s id e r e d

is o la te d

in la r g e g ro u p a g a la x y W l d e x c e u f r e e t ( ro m th c lu s

o

f

a

em r ia b ly a m g h it is in v a lla r e h i a g a la x y a s te o r e v e n a d e n s e r g ro u p w it n d b n u s o t s a e f m rm t h o t h y atw e rs t a a p a ir o f s ta ľs p re s e n t d is c u s s io n b in a t y s ta il i l i d t n w s o e x c lu s iv h in itia l c o n e ly C s e q u e n tly t e s h a ll a d ? e s s in c h a p te r 1 1 ) o n i r r a l n o c t o e s u s f o v o a s ta y p T h u s th e e r d e te r m in e th e c o u r s e o f a s ta r s e v o lu tio n h l t t s r e u e a tt a f e c i l e e f v r b o t i h t a e ng (m e ta p h o r ic a lly te ľ m e d te ) d ifre r s fio m T t b i e n m o o n t r e t e r g ra s h ir e n v in flu e n c e d to a la r g e e x te n t b y in te r a c tio n w ith t e p i P S C n o x m n a u r u ( e o t t n t o a l e s u r i) th e is o la tio n o f s ta ľ s c o n s id e r th e s ta r c o s l h i t r a r e s a h n t e s o la r T h is d is ta n c e g w h ic h is a t a d is ta n c e o f 4 3 lig h t y e a f s 7 d ia m e te r b y a fa c to r o f 3 × 10 S u c h a s itu a tio n w o u ld b e s im ila r to n e a re s t 10 7 tim e s th e ir h e ig ht n e ig h b o u r s o n E a r th b e in g s e p a r a te d b y a d is ta n c e 3 × T h is is fo u r tim e s th e E a r th d ia m e te r o r w h ic h ro u g h ly a m o u n ts to 5 0 0 0 0 k m em

p ty

s pa c e

,

a lth o u

,

'

,

,

,

,

o n e se v e n

th

o

f th e d is ta n c e to th e M

W

oon

e w ou

g r a v ita tio n a l ń e ld a n d th e r a d ia tio n flu x , w h ic h d im in is h e d b y a fa c to r o f a t le a s t İ /(3 × 10 7 )2 _

U n ifo A

s ta r

is b o r n

ith

w

g iv e n

a

p o s itio n T h e la tte r d e p e n d s

in it ia ıc o

rm

m a ss a n on

d

g iv e n

T he

ca

ll th is ¡ s o la tio n ! B o th the

2 ry in p r o p o r tio n to V d a re IO 15 fr o m o n e s ta r to a n o the r

va

p o s it io

,

n

p re s u m a b ly h o m o g e n e o u s c o m o f fo r m a tio n a n d o n th e lo c a tio n w ith in

a

th e tim e

th e g a la x y w h e r e th e s ta r is fo r m e d

m

ld

,

,

p o s itio n o f s ta r s h a s b e e n a q u e s tio tì e It tu r n e d o u t fi n a lly th a t m o s t o f th e m a ı e r ia r o f a n e w ly fo r m e d s ta r a b o u t 7 0 % o f its m a s s c o n s i t s s o f h y d r o g e n T h e se c o n ? m o s t im p o r ta n t e le m e n t is h e liu m a m o u n tin g to 2 5 3 0 % o f th e m a s s a n d th e rt a r e tr a c e s o f h e a v ie r e le m e n t s o f w h ic h th e m o s t a b u n d a n t a re o x ı y g e n c a rb o r a n d n itr o g e n (in th a t o rd e r ) k n o w n c o lle c tiv l e y a s th e C N O g r o u p In th e ó m fu i ex a m pł e fo r e v e r y 10 0 0 0 h d r o y g e n a to m s th e r e a re a b o u t 10 0 0 h e liu m a to M s 8 o x y g e n a to m s a lm o s t 4 c a r b o n a to m s o n e a to m o f n it ro g e n o n e o f n e o n a n d le s s th a n o n e a to m o f e a c h o f th e o th e r s e i p c e s T h e c o m o s itio n o f s te lla r m a te ria l p is u s u a lly d e s c r ib e d b y th e m a s s 加 c tio n s o f d ift h e r e n t e le m e n t s th e m a s s o f e a c e le ln e n t p e r u n it m a s s o f m a te r ia l It i s c o n 】m o of n to d e n o te th e m a s s fr a o tio n h y d r o g e n b y X th a t o f h e liu m by Y a n d th e to t he r a l m a s s fr a c ti o n o f a ll th e o t e le m e n ts b y Z s o th a t X + Y + Z = l o

f in te n

se

d e b a te fo r

com

lo n g tim

a

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

ı0

7

a m 0 J

甑 爆 一



F ig u r e ı3 T h e H

ru n s sequ

f s ta 】s in th e

ne

ig h b o

u rho o

d

o

,

no

th e r p o p u la te d a r e a o

f th e d ia g r a m

is fo

u n

d to

f th e S u n

s tf ip

is

ca

lle d t/ze

q u e n c e s ta th e r ig h t a n d se

m a in

rs

a b o v e the

h t a r e b rig h te r th a n m a in s e q u e n c e s ta rs o f q u e n c e : it r e p re s e n ts s ta r s t a L , m e a n in g th a t th e ir s p e c tr u m is s h ifte d e T tt o r o f lo w e r f f fo r th e s a m e L a n d lo w e r T íĹ i h a r d lo n g e r w a v e le n g th s a n d th e ir c o lo u r is r e d d is h A h g e r

m a in

to w

o

l e T h is d ia g o n a lly th r o u g h th e (lo g i f lo g L ) p a n d in g s ta r s a r e k n o w n a s t?za in e n c e a n d th e c o rr e s p o n

A

są m

R d ia g r a m

se

,

ï H

A

n o th e r r e

is lo c a te d

g io n

a t th e

lo w

o

f th e

er

le ft

İ



(lo g ï e ff lo g L ) p la n e th a t is ,

co m

er

tiv

e

ly

r ic

h in p o in ĺ ç

d h ig h e fr e c tiv e te m pe ra ou a s m a ll r a d iu s a n d a b lu is h w h ite c o ı d ljs W n ite d w a r f r a d ii a r e o f th e o rd e r

lo w lu m in

tu r e s S ta r s th a t fa ll in th is r e g io n h a v e

r e la

o s itie s a n

g ly th e y a r e n a m e d w lżite d w a th e E a r th s a lth o u g h th e ir m a s s e s a r e c lo s e to th e S u n s T h e t ic a l d e n s itie s yp a te ria s u c h s ta r s a r e th e r e fo r e tr e m e n d o u s ; o n e c u b ic c e n tim e tr e o f w h ite d w a rf m w o u ld w e ig h m o r e th a n a to n o n E a r th T h e r e a r e p o in ts o u ts id e th e s e th r e e m a in r e i o u s l) g o n s a n d th e r e a re c o n s p ic u n o te e m p ty s p o ts w ith in d e n s e ly p o p u la te d a r e a s o f th e d ia r a m b u t w e s h a ll ig g th e m fo r th e m o m e n t a n d c o n c e n tr a te o n th e th th in g r e e m a in o n e s W h a t if a n y fs fr o m th e m ? W e r e c a ll th a t i c a n w e te a m s s ta n v ie w o f o u r b a s ic a s s u m p tio n , a c c o r d in

,

'

'

,

,

,

,

Scanned by CamScanner

Scanned by CamScanner

ı 2

ı O b s e r v a t io

F ig u o

ld g lo b u la r

v a to r y

w

I 4 S te lla r c lu s te r s : (a ) th e

re

ith

m a in

D

c lu s te r

47 T ucan ae

yo u n g

,

se

qu

g in g b e tw

een

3

an

d

N

M

5

e n c e s ta r th e r e la ti , o n can

s ta r s

d

p e n (m

(c o p y r ig h t A

E d in b u r g h p h o to ra h s b D g p y

u ra n

o

n s a n

a ssu m

p t io

o rp h o u s s h a

g lo A

u s tr a

o v e r m o st o

f th e

a lin

be

n

ns

)

c a lib r a te

d to

p e ) p le ia d e s

c lu s te r (b )th e lia n O b s e r v a to r /R o a l O b se r y y

m a s s ra n

ge A

s th e

S u n iH

re a d

le a v e th e

m a in s e u e q n c e to b e c o m e tu ĺ r e d g ia n ts ? D o th e in to w h ite d w a r fs ? O r d o s o y la te r , m e s ta r s b e c o m e re d g ia n ts a n d o th e r s w h ite W h y a r e th e r e a lw a y s in a ll H R d ia r a g m s lo w e r m a in s e u e n c e s ta r s ? W n q o

\

d

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

ı 8

The

2

Ww

d e n o te b ô a y f a s s e le m e n t ov er e

m

c

n a ll p e r io a sı

,

th e c h a n

d

h e re

a ln o u n t o

g e in th e internal e n e r g y

hav e

w e

w o rk m a y

be

ı f s te ı ar

s o

,

f tim

o

e v o lu

e

f h e a t a b s o r b e d (ÕQ

d n ıõ u

u

ex

c o n se rv a ū o n o

pre sse d

e n o te th a t com

an

d he n

ôQ + ôW

-

,

.

O)

is g iv e n b y

,

fm

ass

in

a ssu m

p e n se o

m e a n s s h r in

a d d itio n o

f th e

in g d m

be

to

c o n st an t

as

p r e s s io n

c e e n ta ils a n

an

0 ) o r e m itte d (õ Q

>

U 2) s e d th e

W

if a v a ila b le

h w i itt h in t he an E 111e ria tl

g to th e fir s t la w

dn z

a t th e e x

t io n

f a n y q u a n tit y ff õ r (a L a g r a n g ia n r a th e r t h

a c c o r d in

ò (u d n t ) = w

t io n

th a t o c c u r s in th e v a lu e o

ha n \

h a n g e ) T h e n if ô i h Q st e

c

equ a

e le m e n

ť

d (b ) th e b a la n

f e n e rgy

(2 3 1

p

k in g ,

w

o

f th e

h ile

ex

e le m e n

p a n s io n

T he

'

t s v o lu m e

(ô d v

>

s ow n en er gy

,

or

O ) is

òd v

.

a c h ie v

O

,

ed

f th e h e a t flu x e s s tr e a m in g in to th e e le m e n t an d e n e r g y r e le a s e e r p u n it m a s s is d e n o te d b h e a t flo w in y q a n d th e g p e rp e n d ic u la r ly th r o u h g a s p h e ń c a l s u r fa c e b F d im e n s io n o f m ) T hu s F h ( y a s th e p o w e r (n o t to b e c o n fu s e d w ith th e s tr i t d c e fin itio n o f P o w e r p e r u n it a r e a ) a n d b a he at ūu x o v io u s l F M y ( ) = L A c c o r d in l g y, o u t o

,

f it T h e

r a te o

ce o

f n u c le a r

,

S u b s titu tin la tte r

g E q u a tio

(2 3 ) a n d (2 4 ) in t o E u a tio q n (2 2 )

ns

as

,

P an

d in th e lim it ô t

O

w e o

h e re

w e

ha v e

In tlze n

na

u se

d th e

,

w

w

ń te th e

(2 5 )

b ta in

n o ta tio n

l e q u itib r i um

y

?m

P w

w e m a

he n

j

am

(2 6 )

'

fo r th e t em p o r a l (p a r tia l) d e i r v a tiv

te m

q

p o r a l d e iiv a ti =

X

ves v ani h s , w e

e

a f ta l o f

hav e

(2 7 )

Scanned by CamScanner

2 3

T ha

e

o n q u a tı

f

o

ı 9

tı o n

m o

秒 画

画 ( l 一

F ig u

2 2 C y lin d r ic a l m

re

ı n te g r a tin g

a s s e le m e n t w

ith in

a s ta r

o v e r th e m a s s , M

qdm

fo

h e a t flo

r th e

d e n o te d b y L

dF

=

m u s t v a n is h a t th e c e n tr e to a v o

w

is th e to ta l p o w

p p lie d in th e s ta r b y h t e n u c le a r lu m in o s ity ,

e r su

nuc

,

医 置

M _

L

id

s in

n u c le a r

(2 8 )

,

p ro



g u la r ity T h e le ft h a n d s id e c e s s e s w h ic h is c o m m o n ı y ,

M

L

an

d th u

l e q u ilib ń u

m

T he

2 3

fo

' to n s s e c o n d la w

ew

r c e a c tin

g

a

o n

o

bo dy

fm o

ec

w

ith

f fix e d

o

a n a x is o

m a ss

w

p

ra

,

r c e s a c tin

g

o n

th e

sp he

ńcalm

m a ss

m

-

A

p re s s u r e

e x e r te d

ll e x te r io r to

b y th e g a s



o tio n

s u tT o u n

r

s ta te s th a t th e n e t

th a t is e q u a l

c o n s e r v a tio n

e n tu m

m e e le m e n t w

e e n r a d ii r a n

?

tw o k in d s :

van

,

a c c e le r a tio n

an

s ta r a t

d

x im a te

la w fo

ith in r

a s ta r ,

+ dr

ly

r a

u n

,

ifo

an

d

)

rm

is g iv e n b y

m

p dr ds

f

y b y th e

4 召

in F ig u r e 2 2 If th e (a p p r o

th is e le m e n t a r e o

a s s she

it

aw a

n

fm

ll c y lin d ń c a l v o lu

e x e r te d b y th e m a s s o f th e s p h e r e in te r io r to

b y th e

t io

o

m

d ia l d ir e c tio n , b e tw

its A

T h e fo

f

im p a r ts to T h is is th e m o m

a s sho w n

e le m e n t is

o

n

o r th e e q u a tio n o

,

o n s id e r a s m a

la re a d s ,

ith in th e

q u a t io

m a ss

a ss

f le n g th d r in th e

a c r o s s s e c tio n a

d e n s ity

C

m

e

h a n ic s

f fix e d

to th e fo r c e d iv id e d b y th e

bo dy

(2 9 )

,

im p lie s th a t e n e r g y is r a d ia te d L nuc it is p r o d u c e d in its ¡ n te ń o r l L -

s th e r m a

th e s a m e r a te a s

N

qdm

=

nuc

r

(th e

n e

w

(a ) th e g r a v ita tio n a l fo r c e t g r a v ita tio n a l fo r c e

is h e s ) a n d

d in g th e

(2 10 )

a

(b ) fo r c e s

e le m e n t

e x e r te

,

d

r e s u ltin

T h e g r a v ita tio n

g fr o m a l fo r c e

Scanned by CamScanner

l = ・»

e lla r

2

st s of ıtio n

ew

lu tio n

ı e qı

T he

20

re Th ę p r e s s u

a s su m e d

es l th e p r nd o n y b a la n c e d a

e e le m e n t a r

m ay en t w e o f th e e le m

řA



=

r

to

ha v e

an d

G m 八n ł ı= ïł

r

a,

2

dr

dm

-

e th e in d e p e n d e n t s p a c

/(4 Jr r

z

p )is

u s e d,

4 rr r

T

th a n r a n d th e tra n sfo r

2

le t F . b e

es

ðP

3) (2 ı

ðm

E q u a tio n s (2 12 )a n d (2 13 ) d e s c ń b e

n e n a c c e le ra tio n s a re n e g lig ib le ,

W

v a r ia ble r a th e r

m

-

div id e by Ą n ı

(2 12)

E q u a tio n (2 12 ) b e c o m

G r

e m ay n o w

l ap

G nï

m a tio n

T he

P

0 W E q u a tio n (2 1 )

ıfro m tı

A s u b s titu te d

as

y ie ld in g

he n c e

o b ta in

If m is c h o se n

(2 11)

2

ŕh

w e

ds P (r + d r )

ds + p (r )

?r )d r p (r )+ (a p /

B u t p (r + tlr ) =

h e re

t tı

pre s s u re

fo rm

he tio n ın t o fm o

io n he e q u a t uv rite t

Gm A

w

ng a c tı

Fo rc e s

id e o f th e c y lin d ri to th e s c al dic u la r ly e rp e n dic u la r ly oo i n t p c g in fo t c e s a s u r1e

en pe rp

hy d m s ta lic e q u ilib riıa ıı w ith gr a v ita tio n a l a n d p re s s rıre fo rc e s

dP

G P

=

dr

e x a c tly in

a s ta te o f

b a la n c e

m

(2 14)

三厂,

r

m

or

dP

G

;

m

(2 ı51

4ï r r 4 s th e

ń g h t h a n d s id e o f E u a tio n 2 1 q ( 4 )o r (2 ı5)is a lw a s n e a tiv e h dro M ti. y y g , e q u ilib riu m im p lie s th a t th e p re s s u r e d e c re a se s o u tw a rd T h e p re s s u r e gra die r v a n is h e s a t th e c e n tre s i n c e o n the ri h g t h a n d s id e o f E u a tio n 2 14 n ł r z te ı 1. q 6 ) / to z e ro i h A



,

w

W

t

0

r

m

e m a y e s tim a te

th e pre s su re a t the e e n e o f a s ta r in by in te gra tin g E u a h o n 2 q ( 15)fro m th e c e s ïr e to th e

b

h y d ro sta tic e qu i\ibńt su r fäc e o f th e s ta r T h e le ft

O n the le ft h a n d s id e m a y re p la c e r

w e a re l e ft w

b y the s te il a r ra ?

ith the

us

R

c e n tra l

p re s s u r e p c

> r , to o b t a in

a

lo w

er

=

h p (0 ) sin c e ıt t ,

lim it fo r th e

tra c e rı



Scanned by CamScanner

2 4

p re s s u

re

Thı v ı r lıl t h e o

U ı

t

r* m

t

=r

17 ) y ie ld in g

8 tr R th

p re

e

Ex

s s u re a t

e r c is e

d e n s ity

va

an

M

For lid ity

a s ta r o o

f

i

.

f in e q u a lity

n

im p o r ta n

b e tw

een

a s y s te m

(2 1 5 ) b y

o

an

d

r a diu s

R

,

in E

x e r c is e

The

t c o n se q u e n c e o

f hy?

v ir ia

fin d th e

c e n tr a l c a se s :

!

pre ssu re

(a ) a

u n

an

ifo

d

rm

12

l th e o

o s ta tic e q u

(2 18 )

n a tm o s p h e r e s

(2 18 ) fo r th e fo llo w in g as

2

m

R

ŢYï Yīī 2 4

A

M

m a ss

d (b ) a d e n s ity p r o file

£ X

N

th e c e n tr e o f th e S u n e x c e e d s 4 5 0 m illio

2 l

c h e c k th e

4

is p c

a t th e c e n tr e a n

d

re m

ilib ń u

is

m

a

lin k th a t it

e s ta b lis h e s

g r a v ita tio n a l p o te n tia l e n e r8 y a n d internal e n e r g y (o r k in e tic e n e rg y in o f fre e p a r tic le s ) M u ltip ly in g th e e q u a tio n o f h y ? o s ta tic e q u ilib ń u m th e v o lu m e

v

-

7r

r

P (R

3

an

d in te g r a tin g

)

o v e r th e w

h o le

ģ

-

(2 19 )

T h e in te g r a l o n th e ń g h t h a n d s id e o f E q u a tio n (2 19 ) is g r a v ita tio n a l p o te n tia l e n e r8 y o f th e s ta r , th a t is , th e e n e qg y th e s ta r b y b ń n g in g m a tte r fr o m

s id e o

f E q u a tio n

o th e r th a n

th e

r e q u ir e d to a s s e m

b le

no ne

in fin ity , M

T h e le ft h a n d

b ta in

"

V dp

n

s ta r , w e o

1 Ëe

=

G

m

dm

(2 2 0 )



(2 19 ) c a n b e in te g r a te d b y p a r ts

P (R )

Vdp

=

[pv]

v (R

,

)

pd v

(2 2 1)

Ą

Scanned by CamScanner

T h e fır s t

tre n n o n th e r i h t g

th e s u r fa c e p

=

o c

o m

ha n d

s

a t th e c e n tr e

v a n is h e s , s in c e

id e

b in in g E q u a tio

ns

(2

2 1),

192

w e

fin a lly

V o

=

O

an

d

al

b ta in

V (R )

pD V

3 留

s in c e



dv

山n



lp

Q

=

(2 2 2 )

,

.

,

T h is is th e g e n e r a l lo b a l fo w h ic h w ill p r o v e e x tr e r m o f th e v ir ia l th e o r e m g m e ly v a lu a b le in m a n y la te r d is c u s s io n s A s im ila r re la tio n a p p lic a b le to p a r t o f th e s ta r M a b y e o b ta in e d b y c a iT y in g th e in te g r a tio n o f E q u a tio n (2 1 9 ) u p to a r a d iu s ,

,

,

R

P

M

イm

Ą H

Q

įn

-

(2 24 )

.

is th e g r a v ita ti n a l o te n tia l e n e q p rg y o f th e s p h e r e w h o s e b o u n d a r y is a t R s w h ic h is u n a ffe c te d b th e h ll s e o u ts id e it (b e tw e e n R y d R ), w h ile P is th e s an s r e s s lı r e t R a p e x e r te d b y th e w e i h t o f th e o v s e r ly in g s h e ll g C o n s id e r th e p a r tic u la r c a s e o f a n id e a l g a s o f d e n s it y p a n d te m p e r a tu r e T (to b e tneated in m o r e d e ta il in th e n e x t c h a te r le t th e m a ss o f a ); p g a s p a r tic le b e n z T h e a s r e i s s u r h e s t i g e n g v e n by P _ p g (p /m g )k T w h e r e k is th e B o ltz m a n n c o n s ta n t T h e k in e tic e n e r g y p e r p a r tic le is k T a n d s in c e fo r a n id e a l g a s th e internal e n e r g y is th e k in e tic e n e r gy o f its p a r tic le s , th e internal e n e r8 y p e r u n it m ass i e re

,

.

,

,

,

ĝ

s

3 kT U

=

2 C

3 P =

m

(2 2 5 )

2 p

g

b in in g E q u a tio n (2 2 5 w ith ) th e v ir ia l th e o r e m (2 2 3 ), w e h a v e u dm Q T h e in te g r a l o n th e le ft h d an s id e is s im p ly th e to ta l internal e n e qg y U a n d he n c e o m

ģ

U W

e

c an

u se

th is r e s u lt to



_

e s tim

a te th e a v e r a g e internal te m p e r a tu r e o f a s ta r in g th a t s te lla r m a te ń l a be ha v e s a s a n id e a l a s ll a n a s su m g b e ju s tifie d la te r o n T h p tio n th a t w i ) e g r a v ita tio n a l p o te n tia l e n e r g y E u a tio n 2 2 0 o f a s ta r q ( ) o f m a ss M a n d r a d iu s R is g iv e n b y

(

assu m

,

Q

G M R

w

h e re

m

a tte r w

ce

is

a c o n s ta n t o

ith in th e

f th e

s ta r , th a t

o rd e r o

Ł

ol

=

f

,

'

2 2 7)

u n ity ,

d e te r m in e d b th d i t ib u ı io n o f e s r y is b y th e d e n s ity p r o file B y th e v ir ia l th e o re m w e ,

,

Scanned by CamScanner

2 5

ha v e

th e o n e h a n

o n

d u

T h e t o t a ıe n e r g y

ģce G

=

2

M

w

h e re Ť is th e

r e s u lts , w e o

p e r a tu r e

te m

a v e ra

is

a ]s o

2 /3

M

p

m

(2 2 5 )

n

,

(2 2 8 )

,

g

lla r

o v e r th e s te

C

m a ss

b in in g th e tw

o m

o

ď M g

" 3

3

12

29)

R

k

3 tio n (2 2 9 ) w e o b ta in g e d e n s ity p = 3 M /4 7r R in E q u a d er o ne in g th a t b e tw e e n tw o s ta r s o f th e s a m e m a s s th e e n s

a v e ra m ean

,

G M

=

,

,

th e h o tte r

Ex

e r c is e

2 3

ex

p r e s s io

n

d e n s ity

T a k in g

ď

=

a v e r a g e te m

ľ d

an

For

a s ta r o

f

M

m a ss

an

r a d iu s

d

th e g r a v ita tio n a ıp o te n tia l

ģand

in g th e g a s to b e

a ssu m

p e r a tu r e

o

fa

s ta r

fo

v a lu e

fin d th e

,

c a se s :

f tw o

o

f

in th e

a

(a ) a

u n

ifo

rm

12

a to m

ic h y d r o g e n

,

fin d th a t th e

w e

is

4

w

R

e n e rgy

e a s in E x e l c is e (b ) a d e n s ity p r o fiı

Ť

×

10

6

( )(f )

(2 3 o )

K

f

te m

e r a tu r e

p Ť is m u c h h ig h e r th a n th e s u r a te m p e r a tu r e s im p ly in g th a t internal o b s e f v a tio n s )

W e n o te th a t

fr o

E q u a tio

b ta in

S u b s titu tin g th e oc

2

9,

ge d

Ť

Ť

m

ŤM

=

23

lb

s ta r

3 k

dm

=

2

fa

; o n th e o th e r h a n d , fr o m

/R

M

U

o

ce

(a s

T e fF

m u s t re a c

h

o

b ta in e d

s till

h ig h e r

a n d h e liu m h y d rw v in f d e g re e s K e ı A t v a lu e s m in g a s e o u s h ig h ly e n ts a r e fo n h e a v ie r e le m e v d e n d a i l io n z e n u c le i i a r e c o m p le te y a m ix tu r e o f o n s ?ta f o r e a p la s ı h r e e t i l s i a r e t l m a io n iz ń i fo r m S te l a r

m

,

te m p e r a tu r e s o

f

m

illio

ns o

,

,

,

,

s tr ip

T h e t o ta l e n

2 S

W

e s ta r t

by

in te g r a tin

g th e

ene

rg y

q u a tio

M

M

"

S in

e

p

"

n

e rgy o

s ta r

(2 6 ) o v e r th e

)

."

L

nuc

en

tir e s ta r

L

(2 3 1)

d n tia tio n a n h o r d e r o f d ifr e r e e n de n t t e d e i n p t and h n d s id e is th e v a f ia b le s n th e le ft a h e fir s t te r m o t e c H n e d c ha n ge io n m a y b e in te r n ? a re

ce

fa

,

in te g r a t

M

dm lł

=

u

dnı-

Ů

0 3 2)

Scanned by CamScanner



岱 ベ







į%14l

歹 シ 罗

(

ゴ 日





= 區 冒

n 到

習 、



# 侧

目 罾







吕 '

-



.

目 眉

,

需. ,



.



吕 . 回











:



/

.

習- 智 卫

爰 惡勇

. 月





》 制

¥ 势-

署ıa 智



.

-\

k

.





目 層











岩 专谷

- 署



H



召 憂

名 4 ł

n

習+ 召 (

.

7

召4l

n n

褐U+ 售 신V 慰

召 回

-

四 喟



-

咽 胃 吕 凸 o

9



昌i 習 層妇 層





-

身. 剧 層



;

勇 習 J 心 手,

售 暮

)





岧Ų 岧



N

b 弓

慰 勇 段 ì 可+ . 剧 钍 回



*

)



'



曾 、 朻



省 習



(



唇 F

打 耗

島 Scanned by CamScanner

2 6

If

a

a

d d itio

q

e

is in th e r m

s ta r

s ta n t If in

co n

The

a

u a

tı o n

ıe q u ilib r iu

th e s ta r is in

n

o n tı p o ıı

n g co m go v e r n ı

s

m

,

o w it fo lı

s

h y d r o s ta t ic

È

th a t

equ

c

O

=

ilib r iu

25

ha n ge ı

m

,

an

/c

e n e r g y Is

d th e

is h e s v a rı

In th is

, i es i h e r o f th e m d e te r m n d b y th e v ir ia l th e o r e m , a n d h e n c e e t ı t e a a re re c a se t o n ly h m is c o n s e f v e d n o n tly e a c h o n e o f t e th e to ta ıe n e r g y o f th e s ta r C o n s e q u e ib r iu m c a n n o t c o o l ic e q u iı h i e r m a l a n d h y d r o s ta t t l t n a r a e s F a m e x r o m u i s r p h e t s io n he e n e fgy a n d e x p a n h o lin g d e c r e a s e s t c o l h d t o u d a n a x e a n ( t h u g o p th ro u g tio n a l n d th e g r a v ita h e r m a l) e n e r g y a t internal ( h t e e r v e t n s i c o t m u s i t in c r e a s e s ); a s ta r c lu s io n is th a t n tly p u z z lin g c o n i e n e r8 y s e p a r a te ly A n o th e r a p p a f e t aı n t e o p th a t it b e c o m e s i h e a t c a p a c ity m e a n in g in h y d r o s ta tic e q u ilib ń u m h a s a n e g a t v e fo r a n id e a l in fr o m th e v ir ia l th e o r e m h o tte r u p o n lo s in g e n e rg y ! T h is fo llo w s a g a h ga s w e av e ,

U an d Q

,

,

,

,

,

,

,

E

び十口







(2 4 4 )





d b y a c o n s ta n t o f th e o r e r d i d e is m u ltip lie d s h h n i a t h r e t l e s c a r a e n h e g a n d in t e g th e a v e r a g e u a tio n (2 2 8 )) a n d w ith it (b y E q h È O t en u f < i o f u n ity H e n c e m u s t c o n tr a c t m e tim e th e s ta r u s t in c r e a s e A t th e s a te m p e r a tu r e o f th e s ta r m im p ly v io la tio n o f o t n e c e s s a f ily h l t a t c o n tr a c tio n d o e s n t h r o s l e e l s h a y s W ( e In fa c t t is n o t conadictory ) h t a t th e la s t a r g u m e n o s ń m b i l i u u i e t c t a h y d fo s q b o th th e e n e rg y le a s e d in c o n tr a c tio n s u p p lie s i n a l p o te n tia l e n e r8 y r e t i o th e g f a v ta t r e to r is e th a t c a u s e s th e te m p e r a u n d th e th e r m a l e n e r g y th a t is lo s t (r a d ia te d ) ü o f a n id e a l g a s in e q u a l a m o u n ts in th e c a s e ,

,

,

,

,

,



°"

"

"

The

2 6 A

s w e

hav e

e n tir e ly b a r e

be

o fi

se e n ,

"

"

c

e

it L if it m a in ta in s a c o n s ta n t lu m in o s y " o n o f its r a d iu s ,

q u a t io

th a t s te lla 】 m a te

h e m ic a lly

c h e m ic a l

n a tu r e

i

cur c o n s t tu e n ts c a n o c n u c le a r r e a c

tio n s

T he

ic

g o v e r n in g

n s

by

ń a l is

co m

co m

po

d

se

p o s it io o

c

n

ha

n

ge s d

e le c tro n s a n

f fr e e

(a ım

)

o st

c an n o t if a n y p o s itio n c h a n g e s in th e a b u n d a n c e o f th e T h e o n ly p o s s ib le c h a n g e s i b f n e e le m e n t in to a n o th e r th a t s , y tr a n s fo r m a tio n s o o

u n

bo

u n

d

n u c le

i

,

co m

,

in te r a c tio

n s

b e tw

e e n n u c le

i

ll tiv e ly c a lle d f p r o to n s a n d n e u tr o n s c o e c ' a m e d b a ıy o n s ( b a r y o n ì f i e a w p a r tic le s n o l s s a c h t e t b e lo n g o n u c le o n s w h ic h f h a s a p o s itiv e e le c tr ic c h a r g e o G r e e k ) T h e p r o to n i n e n o v h e a y m e a n in g e T he se th e n e u tr o n h a s z e r o c h a r g n ta r y c h a f g e e ); e m l e e h e t f u n ity (in u n its o be r A a n d n u m b e rs b a ry o n n u m a c te ń z e d b y tw o f h a c b e f e r o p a r tic le s m a y th e r e h n e u tr o n E le c tr o n s lik e p r o to n s to n a n d (1 0 ) fo r t e c h arge Z (1 + 1 ) fo r th e p r o i O m e a n in g th a t e l e c o n s a r e n o t T h e ir b a r y o n n u m b e f s a r e c h a r g e d p a r tic le s i s s m a lle r th a n th e s is a lm o s t 2 0 0 0 t m e h e e le c tr o n m a s t d d e e i n l s i e ( c he av t ar a to m

n u c le u s

is

m a

de

o

,

'

,

'

'

,

,

,

,

,

,

,

y p

,

Scanned by CamScanner

ll C lh c iW lltr iN u Ý o l h i\r y o n n u c c tı{t n « ı P T u lo n M tı+i8 ) A s « w ln lc d w llh ï h o c ı m be r l i o i h » « e 0 (lh ų 11o\11 In tl m ł\ Ñ i # llı n s n r t l o l u g ht t g nl[houh l c (»n ır o v c lR u ı , o be l l i > s o l t l [ o a c i a h t zeı o n r n )ł c c l rı ncuttlno ı \ l t h n r g e o ıı p e n g s caı c t 11o n H n d le d i i i /ť p ır)n v ( llR h ıo ł1c )i In ( lre c k ) 1 o 1 c n c h p l\r lic ı ı t £ t l c u m v s u m m ech c rc tl q ani ,

,

,

'

J

,

'

'

,

s lu ı n ïc N

Pu

be r

nu m

,

,

lı rc

c

x ls le n e c o

tin t ı t hm

' ł {lllrlp {lr fi( /t ,

N v c I s c ĹıT

gc u N

c lo t lı n n s u n ti n ılic lc p

l łm

Ib

s ig n s o

h ic h th c

r w

h c h c >il k n o w

n tm tip a r tic le

d //w

,

bo

v llu ı l# llllť

u m

ılo g c lh c r in lh c

/}lte

tp m

r c h a r g e th ıtl s u r ı\łis e s lh c rc u ı p p s iv c C ı c n g lh s c a le s bw a ı ıı b i= I m iv

u

,

/

P ľ o to n s a n

d

n

is th c p n s itr o n the

,

n s n n d n e u lr o n s u r c

n llr a c llo n c t\llc

cs

n o r le p to ,

'

P ro to

f b Łiry o

(

'

is th c

rı n

T h is is ı o

ı 5

m

n u c le u s

a s h o r t ra n

b fo

o u lo ı n

ic

a to m

b e tw

re G

) A

no

g e fo

een

th e r fo

rc e

by ,

1x )rc e

of

in d e p e n d

ent

a

p r o to n s a t n u c le a r rc e th a t c a n a cton

g e is e s tim a te d to b e s till s h o r te r (< 10 m ) T h e w e a k in te r a c tio n is r e s o n s ib le r th e c o n v e r s io n o f r o t p p o ns in to n c u tro n s (o r v ic e v e ıv u ) In a n u c le a r r e a c tio n (in te r a c tio n b y m e a n s o f th e s lıo n g o r th c w e a k Ib r e c ) th e c h a i e a s w e ll a s th e b a r o n a n d le t g y p o n n u m b e r s a re c o n s e r v e d H e n c e in il w e a k in te l a c tio n a n e ı e c tr o n o r a p o s itr o n m u s t b e in v l o ved in o r d e r to c o n s e r v e c h a ig e a n d a n e u tr in o o r a n tin e u tr in o s o a s to c o n s e r v e th e le p to n m im b e r C o n s e r v a tio n o f le to n n u m b e r m e a n s e l p u a b n u m e r f s o le p to n s q a n d a n tile to n s h e n c e a p o s itro n (a n tile to n w ill b p ; e ) a c c o m p a n ie d b p y a n e u tr in o a n d a n e le c tr o n b y a n a n tin e u tr in o If th e b u lk d e n s it in s o m e p a r t o f a s ta r is y p a n d th e p a r tia l d e n s ity o f th e ith n u c le a r s p e c ie s is p i th e m a s s fr a c tio n o f th is s e c ie s is iv e b n p g y n c u lıo n s

w eu

7 ı

k lb r c e

,

w

ho se

ra n

,

,

,

,

d th e

b e r d e n s ity n u m b e r o f n u c le i p e r u n it v o lu m e is g iv e n b y th e p a r tia l d e n s ity d iv id e d b y th e m a s s o f o n e n u c le u s T h e m a s s o f a n a to m ic n u l c eu s is s lig h tly le s s th a n th e s u m o f m a s s e s o f its c o n s titu e n t r o to n s d an p n e u tr o n s a s fr e e p a r tic le s H o w e v e r t o a go o d a p p r o x im a tio n w e m a y w r ite an

n u m

,

w

h e re

m

H

is th e

to m ic m a s s u n it r e p r e s e n tin g th e m a s s o a s a tw e lfth o f a c a rb o a

f a (b o u n d ) n u c le o n lly d e fin e d n n u c le u s m a s s D e s ite th e n o ta tio n m H p is s lig h tly d iffe r e n t b o th f r o m th e p r o to n m a s s a n d fr o m th e m a s s o f a h d ro e n a to m C o m b in in g E u a tio n s 2 4 g y q ( 5 ) a n d (2 4 6 ) w e o b ta i n th e r e la tio n s u su a

,

,

,

n

j

=

? H

T he

n u m

be r

o

f

n u c le

i in

a

A

an i

g iv

d

X

˜

i

=

t

n i

M

P en

v o lu m e m a

(2 4 7 )

H

h

y c a n g e a s a r e s u lt o f n u c le a r tio n s th a t c r e a te it a n d o th e r s th a t d e s t r o y it T h e c r e a tio n o r d e s tr u c tio n o f a n u c le u s ta k e s p la c e b y fu s io n o f lig h te r n u c l i e o r b y b r e a k u p o f a h e a v ie r n u c le u s a n d m a y in v o lv e c a tu r e a n d r e le a s e p o f lig h t p a r tic le s s u c H d

re a c

,

as

p o s itr o

n s an

Scanned by CamScanner

1 6

etrons

tr in o s

n eu

,

n a c t io n s w

Tı ı *

ill b e

u a tı o n s m ı

«

(a n d

ł n g

m

a n tin c u tr in o s ) a n

d

«o m

c h ın

tı o n p* sł

e n e r ge

tic

p h o to n s S w ific a y o f d e s c r ib in g a

th e n

c o n s id e re

b y tw

,

de n o

,

,

b y th e e ith e r

b o ls

sym

d ir e c tio

c e s ses

p a r tic le s

K (

Z

d

An

b je c t to tw

fo

c

Z i) A

ı

h e m ic a l

b e d e sc ń be d

re

Z i ) + J (A j Z ) j la w

e c tr o n s a r e o r e ı

n u c le a r r e a c tio n

re a c tio n s

sym

K (A

k

an

(k in e tic

th e te m p e r a tu r e

o c o n s e r v a tio n

If p o s itr o n s w e ll: fo r th e

d L (A

an

to

o n

c a n th e r e

i

k)

(s im ila r ly

n

) D e p e n d in g

l iA

su

e « n uc ı

n u c le a r d in C h a p te r 4 A g e n e r a l w S in c e o d ifr e r e n t n u c le i c o m b in in g to p r o d u c e tw o o th e r n u c le i ı Z i w e u c e u s o f a n y e le m e n t is u n i u e l d e fin e d b q y y th e tw o in te g e r s A t a n d te th e r e a c ta n ts b y th e s m b o ls / (A Z j ) a n d th e p r o d u c ts y ı Z i ) a n d J (A j

te a c tio n is

p ro

17

m

,

d io e n e

p ro c e e d in t e c o m b in a t io n

c an

n iz a tio n

rg y )

an

d d e n s ity

o

f th e

b o lic a lly b y

Z t ) + L (A

ı,

(2 4 8 }

Z t)

,

s

a ls o

in v

lv e d , th e y

o

m u st

b e ta k e n in to

acc o u n t as

fı e p to n n u m b e r m u s t b e e i in v o lv e d in th e r e a c tio n u n iq u e ly o b e y e d T h e r e fo r e A n y th r e e o f th e fo u r n u c ı d e te r m in e th e fo u r th T h e r e a c tio n r a te s a y fr o m le ft to r ig h t c a n b e id e n tifie d b y th r e e in d ic e s : tw o fo r th e r e a c ta n t s a n d o n e fo r o n e o f th e p r o d u c ts d u a te th e r a te a t w h ic h n u c le i o f ty p e / a r e d e s tr o y e L e t u s n o w a tte m p t to e v a ı l b y r e a c tio n s o f ty p e (2 4 8 ) w ith th e h e lp o f a s im p lifie d p ic tu r e C o n s id e r a u n it v o ith in it h a s a c r o s s s e c tio n a l a re a ç m e a n in g l u m e a n d a s s u m e th a t e a c h I n u c e u s w A s s u m e fu r th e r i th a t a n y J n u c le u s s tr ik in g th is a r e a w ill c a u s e a r e a c t o n to o c c u r e i w ith re s p e c t to l n u c le i is u s o th a t I n u c le i th a t th e r e la tiv e v e lo c ity o f I n u c ı t w h ile J n u c le i flo w to w a r d th e m a t v e lo c ity m a y b e c o n s id e r e d a s ta r g e ts a t r e s i h e fo r e n i ç ; th e n u m b e r o f p a r tic le s c p o s s in g a u n it u T h e e fr e c tiv e ta f g e t a r e a s t e r th e n u m b e r o f r e a c tio n s th a t o c c u r p e r u n it ū m e in a e a p e r u n it tim e is n j u H e n c e h a v in g th e d im e n s io n R ij k = g u h th is u n it v o lu m e is n in j ç u o r n i n j R ij k w e re ı e In th e c a s e o f p a r tic le s is c a lı e d th e r e {ï c lio r z iT ł o f v o lu m e d iv id e d b y tim e is r e p la c e d b y d k in d s a 1 in te r a c tin g w ith e a c h o th e r th e p ro u c t n i n j f m

A

O

-

an

d ź

_

1 1

d

an

c o n s e r v a t io n

o

,

,

,

,

,

,

o

o ne

y v e lo c ity ,

,

,

th is is f g a s p a r tic le s in th e s ta r is th e th e r m a l v e lo c ity in s ta r s a r e c a lle d rlï e r n ıtm łłc le a r r e a c tim s i w h y n u c le a r r e a c tio n s o c c u r r n g d o n th e p r o p e rt ie s o f th e r e a c tin g n u c le i (s u c h a s a n d th e c r o s s s e c tio n d e p e n s

ģn ?

T he

th e ir c h a

W

fr o

m

rg e s ) a s

e m a

a

ll p o

y

now

o

w e

lıa s

o n

e p r o d u c ts ı th e p r o p e r tie s o t tı

s s ib le n u c le a r re a c

ńi



ıc h a n g e

w r ite th e r a te o

n i

(l jk

+

o

f th e ith

e le m e n t s a b u n

da n ce

tio n s , b o th d e s tr u c tiv e a n d c o n s tr u c tiv e



山j )

ij

・。 +

E tk



・!:t



,

r e s u ltin

in th e fo

g

rm

(2 5 "

,

,

Scanned by CamScanner

\ ı Th e

* °n 1 o



ew

ı ar f ıta ı

ı u tlq



n ųyc\ \ w h e j 1 dt tı o 1 ur t i p y o s l e i ) lh lu a t o n (2 5 ı ı w \n lc c uı tn tlN lt h ł t h l r l w g t \ N t tc ľ m ,

\t tw tc th ł d e lta ) W e \\o irs t ı h 1 + 山)in t e th e fa c to r (

tro c ke r

Km

he n c e

d N lic ity w e m a y e n e lb ıe q u a tio n s d e sc r

im

s p tio n s F o ı m i\s s ť ıa c f r th c tìth e r o s i n o t t a u e he s o a n d s im ila T e q x .. ) s o th rtt t x . x : b i n w cM r y a c o m p o s it o

(

com

p o n e n ts

fo r e a c h c le m

one

ent

In

i

ï w ı tilib r u ı ıc le a r e q ı nı

fr o m

s th e s e t o f e q u a tio n

27

島 酽

T he

J}

0

=

Th e

O th e

=

ILl iLs s

,

se t o

G

ı ı ı

C) =

ic

e q u a tio n s

d e s c ıib in g th e

u a tio n s

4 7r r

=

'"

re a d ily o b ta in e d

e v o lu tio n a ry



s ta r is

internal s tľ u c tu re o f a i

X i a re

c tio n s ı ł

Ĥ

u t io n f ev o ı

lin e a r p a r tia l d iffe re n tia l e q

se t o f n o n

c o u r s e o f th e

he n

Řf

(2 53)

f(p T X )

=

2 ,

ðııı

(2 54 )

I)F

q

..

£ tp T X )

_

,

,



,

(1 5 ) A s it s ta n d s th e se t is n o t t p (m t) T (m t) a n d X i(m t) th a c o m p le te be s ide s th e s tr u c tu re fu n c tio n s fo rm the se t o f u n k n o w n s it c o n ta in s a d d itio n a ıfu n c tio n s : (a ) P a n d ıt (b) F to g e the r w ith th e tim e

in de pe n d e n t

re la tio n

,

,

,

,

,

,

,

an d

(c ) q

f

an d

,

w

hic h h a v e to be

s u p p lie d

in te rLn

s of

th e u n k n o w n s

T o this

l h a v e to in v o ke d ifre re n t b ra n c h e s o f p h y s ic s : th e rLï to d y n a m ic s p u rp o s e , w e s h a ı a n d s ta tis tic a l m e c h a n ic s in c a s e (a ); a to m ic ph y s ic s a n d th e th e o r y o f ra dia tio n

(b); a n d

tra n s fe r in c a s e

T h is is in fa c t

,

,

w

n u c le a r a n d e le m e n ta ıy

h a t d is tin g u is h e s

a ș tro p h y s ic s

p a rtic le fro m o the r

:

p h y s ic s in c a se (c ) p h y s ic a l d isc ip lin e s

A s tro p hy s ic s do e s n o td e a lw ith a s p e c ia l d is tin c t c la s s o f e ffe c ts a n d ro c e s s e s a s p d o the ba s ic ńe ld s o fp hy s ic s N u c le a r p h y s ic s , h ıe x iım le d e a ls e x c lu s iv e l w ith p , y ,

,

th e a to m ic n u c le u s ; the re a 】e m a n y ıa m

iĥ c a tio n s to this fie ld o f re s e u c h s u c h a s n u c le a f fo rc e s n u c le a r s tr u c tu re a n d n u c le iu re a c tio n s b u t th e y m e a ll in tim a te ly c o n n e c te d N u c le ar p h y s ic s h a s v e ry little to d o s a , y w ith h y d ro d y n a m ic s th e ,

e

,

c an e

sta r a s a

W 心 田a y

,

,

,

Scanned by CamScanner

1, Ĥ

rı \e e h ır ıt tır ls tlc t ı m e s ca ı os

N \\\\y \\l \lw n \\\lin n

u

Ų\\\\\p b \

,

'

M

¢ı \urn ent

o

f s te lla r

Z9

t io n

e v o lu

p h y s ic s d e a ls w ith o f m a n y d iffe r e n t k in d s It h a s to a n d th is m a k e s fo r its s p e c ia l b e a u ty

ıUnllnuuus m c d iłr B y w illL II In v u ı v e p ro c e s s e s

c o n tr a s t, a s tr o

\\t\\\A HN # ı \W W ł\\\lh c b ru n c h e s o l h s ic s p y \\w \lw i w y n l th e m rll? lu re lin d e v o lu tio n o f s ta r s r e s e n ts a u n i u e o p p o r tu n ity q p m b ï in p n a t e eenilngı y u n c o n n e c te d h s ic a l th e o r ie s u n d e r o n e ro o f In th e '

,

,

p y f th e

,

W \ \ ų h\ \m

ľ w w N lu ll in tc ľ ľ u t o u l p

htr h \ ų }itra ť t th

tn \ tlin b re n l



p u rs u it o

e v o lu tio n a r y c o u r s e o

p h y s ic a l th e o r ie s th e in fo

f s ta r s , in

th a t w ill e tıa b le

r m a tio n

N t\a lly \n \\l\ lc ľ tb t th e s e t o f d iffe re n tia l e u a tio n s to b e s o lv e d b o u n d a ry q * \\\\ ln ltlt\\ wn n tllllu n # In w e to b e s u p p lie d T h e tw o s p a c e d e r iv a tiv e s fe q u ir e \tw \ b \wu n \la ı y Ľ o T\u ltitm s Ł\n d th e /ı4 3 tim e d e r iv a tiv e s r e q u ir e n + 3 in itia l \\ltïlt\utlnn# u l p h y s lc t\l p ln p e ľ lie s T h e b o u n d a f y c o n d itio n s a fe s tr a ig h tfo f w a r d P {A+ t ) = O ļ \n d in o \d e l [o ilv o id a s in g u la r ity a t th e c e n tr e F (O t ) 0 T h e In ltlu l \ x \n d lllo n s c o u ld b e p (N Ł O ) T (m O ) í (m O ) a n d X i (m O ) o r f e la te d h n ť tlu n ķ ıł ı it s e e tn s w e r u n in to s e r io u s d iffic u ltie s : a s m e n tio n e d b e fo re cw # k r nnt\llon ls s till a s u b je c t o f s tu d y T h e in itia l s ta te o f a s ta r is th e re fo f e ,

,

'

,

,

,

,

,

,

,

,

,

,

,

=

,

,

,

,

,

,

\* lh e r o lw

Ľ

u\

F itr lu n iï tc ly

,

1 8 Ilw '

Ľ

itn « ł

f a s ta r is d e s c r i

\ t t lu tio \t o

\ tı ca ťM Ľı

ı l\

u s w e s ha

ll s e e s h o r tly th is p r o b le m ,

e s o c t lm e s c a ı c h a r a c t e r ls t ı

The

.

,

b y th e th r e e tim

f s t e lı a r

e

can

be

o v e rc o m e

,

u t io n evo ı

d e p e n d e n t E q u a tio

ns

(2 5 4 )

,

dilìrent ty p e o f c h a n g e : th e fir s t in v o lv e s d y n a m ic a l o r Th c s e c o n d d e s c r ib e s th e r m a l c h a n g e s a n d th e th ir d d e a ls w ith

wit h a

tu ľ t\l c h a n g e s

.

g to c h a n g e s in c o m p o s itio n (a n d in th e r e s t m a s s e n e r g y ) B łk h Ľ h t\trg c , o t ptc ess h a s its c h a r a c te ii s tic tim e s c a le T w h ic h c a n b e d e fin e d ' d b y th e p ro c e s s h i h & Į Į tlw r a tio o t th e q u u ì tity (o r p h y s ic a l p ro p e r ty ) ¢t a t s c a n g e i a \\u th c r a te o r c h a n g e o f th is q u a n t ty nuc ı e a ıp \x w '

s s e s le a d in

,

,

d

ti

h a r a c te r is tic

f m o tio n w o s e u r a o n p le s t e x a m p le w o u ld b e o a is g iv ć n b y d is ta n c e d iv id e d b y v e lo c ity O b v io u s ly a f a p id p fo c e s s tlı n e s c a le tim a te a n d t ti i ) h a s a s h o łt tim e s c a le a n d v ic e v e r s a It is n s tr u c v e o e s (h\\\ t ro c e s s e s th a t o c c u r in s ta r s if c o m p a iĘ th e tim e s c a le s o f th e d r e r e n p

T h«

s im

h

,

or c

,

T he dyn a

W e w e

ha n ge

m iı y tł\k e

ic a l t im

e e sc a ı

h a n g e in th e s tr u c tu r e o f a s p h e r ic a lly s y m m e tr ic in its c h a f a c te ń s tic d im e n s io n th e r a d iu s R ; h e n c e in th is c a s e l t f 尺 A s g ra v ity is th e b in d in g fo r c e o f a s ta r th e ty p ic a r a e o

a c o n s id e r a b le c

c a n e ï \ų is a \

M ať as a c

m

,



=

,

Scanned by CamScanner

\u tlo t\ *tQ l\a ľ e w t\o \\8 姥荏 ı 神奈瞳业島 30

N'

A' lh n

'

=

M

\2 M

N lc n slly /$ = NI / in R n ils u ltlw Įw ţ ľ tŅc \ ・

tm

(2 5 ) ,

'

' ,

n e g lc ? tln g

thť l\\tN o tthe o tde r '

ť tm itv

t}

.

(2 57) ,

n b \\

It ł\d {o thc \c l] n lı l ln \c s? ł\lc , bu t lı \in lh« \lyn n m lç n l tt\\? w a ys to u btı n \ł n lç u ltln \c w n lt o [ thc \ı it ' T ht\ tı yn Ł u t thc u \\leť u l u n j, sa m le \Ę su lt w ithin lhc l\w \\\tı gt nc ma lly \n tu tu t). Ł ł i\ tlu iuw ľ o ı Su n is a bo u t 1000 S ( ľ hi lų alx

xìthly \\ n

、一

° iw w w

,

眃ıマ Ýla o

iho rlo ľ cł in )◆u li lt s u ln iı Ņ n itlıtı ņ n rc ly s httľ t m ł t hc dyn n n ıic a ltin icsc u lc is c x tı thų S u n Ib r e x a n tplc ls ¢\6 h illio n ttc u I W o ı \ľ a ges T hc e stim ı tha n typic a ls tc llı ' 17 h n ln u l this re su lt? A ycarn o ıN l 5 × 10 s a hm t 10l Ttvn W ha t is [ t m e u g b tľ e is n o l hn lı m ce tl n ec ss o c c \11,s in a s lur w hc n cv e ľ ihc gra v iln lio n n lı d yn +m ìic a lpı by thc ptssure tbtcs (sec E qu a tio n (2 ı2 S u c h u s itu a tio n c ł\n Łlt v o lo p tither lc l gľ ł in to c o n tıa c tio n It thct is in s u n ic ic l\l pı w ily o t In to ţ tisut 1o co u n te ıł .

四 国

.

il thc prssu\ is lo o high Il c ı \n c n tlc ilhc l in ı \ t lllł uitro ph iç e v e n t lı o r in ť e sto ru ti\m o r hyŁ o r c x plo s io rr n s ta tic c tlu ilibtiu m w he n the

e x pa n s io n , co lla pse

,

Ib rr e s łu a gı l stilte s w ill b c Łlc h ic v c d w ithin rin in ha lł m e c Eithe r o r the se c n Ł

pe ľ io d o r tim e o l thc ollcľ o r thc Łlyn n m it a l tim {b llo w in g c o n c lu sio n s a

¢sc ł \lc

T his lc ł ls \Ł

u s to

the

1 ï la s ta r c im

n o t ľ c c o v c Ľ ťto m a dyn ł tm ic ł tlpľ o ec s s (hy lsloring hydľ o s ta tic i i ı c qu briu m ) thc en su in g c o lla pse o ıe x plo s io n s ho u ltl hc o bs e ľ v a b ı e in its cntilly In tlc c d s u c h ev e n ts hav e be e n kn o w n I o o c c u r the a ľ c y c a lle d s tip ( /Tı c)v ele W c s hı rlllu tu rn to the m in C ha ter IO p 2 R a pid c ha n ge s tı w t a rc so m e tim e s o bs cľ v c«l in s t ł \ľ s tLìı ty in d ic tı tc tha ı dyn u m ic ttı pto c e sses a le ta kin g pla ce bu t o n a s m a lle t sc trlc n o t in v l i o v ng ' the e n tire s ta r F ro m lhc lim e sc a ı c o l s u c H c ha n e s u su a ı ly o sc illa tio n s g w ilh a c hı u a c lc ľ is lic pc rio d W C m u ro u hl y g y o s lim tllo thc łwcl llgc de n s it y o lthc s ta r T hc S u n has bee n o b)ie lv o d Io o sc iı la lc w ith a c Ľio d o l i p m n u te s O sc illa tio n s wih pc Rio ds o l" a lbw le n s o l 5 0 m i n d ic H te thı \t thc s ttw d bc a co m pac t o n c stı s ho u ı c h n s ll w hile dw u tI 3 A s il Iu le , s tilrs m u y be assu m c tlto bc in a s lŁllc o l h d y lo s [tltic e qu iı ih,iu m " h thľ o ţ ı A t o u n r b l llio n o l this s ln lc is im m c dim l g y pe u r ł c y q u c n c hc d T hii ł ,

ł

,

,

,

Scanned by CamScanner

2 8

do

Th e

n o t m ean

e s

hara

c

f

t e r is d t d

c

c ıı es

ııı«

o

f

e vo

lu t io

31

n

ife d u ń n g th e ir e n tiï e ı r th a t th e v e q tttıs i s ira tic a lly c o n s ta n tly a d ju s tin g th e ir y evo ı internal s M ıc tu r e s o a s to m a in t i d a n y n a m ic a l b a la n c e C o n s e q u e n tly th e le ft h a u ld s id e o f E u a tio n 2 2 q ( 1 ) m a y b e a s s u m e d to v a n is h A n d th e v iń a l th e o r e m (S e c tio n 2 4 ) m a y b e a s s u m e d to h o ld a t a ll tim e s T h is m e a n s th a t th e g r a v ita tio n a l o te n ti ı a e n e r g y a n d th e th e r m a l e n e rg y o f th e s ta r p e a c h fo llo w s th e b e h a v io tır o f th e to ta l e n e r g y o

th a t s ta r s a r e

c o u rs e

T h e th e

T hem a

m

U

la

l p ro

a

fr e c t th e internal

ıt im

r a d ia te d

b e th e r e fo

aw

re e

a y b y th e s ta r th u s tim a te d b y

e n e r gy

s w e m a

r

Su

th e

ı

n

10

T tlı H

,

"

s

o r a

,

bo

have

f u is th e

n ce

in th is

se e n

,

is

r a te a t w a l tim

T h e th e r m

L

=



w e

c a se

p p lic a b le ) h ic h e n e r8 y

a

,

e s c a le m

a

y

エ ロ

2

G M

(2 5 9 )





R L

L

t 3 0 m illio n y e a r s ,

u

he

s ta r

as w e o

ロ ヒ

ı e

f th e

o

se t

y

U T tıı =

Fo

e sca

=

H

is

c e s se s a

rm

¢ U B y th e v ir ia l th e o r e n ı (w h ic h 2 / R T h e c h a r a c te ń s ū c r a te o f c h a n g e

y ta k e G M

s ta tic

B u t r a th e

spa n



g e n e r a lly

d a iı

团 团

T h e th e tin ıe s c a le

life s p a n o

f

a

o

,

n n a

l tim

e s c a le

b u t it s till

fa

T hu

s ta r

is

y

an

m

o

c o n s t itu te s o n

s

,

rd e r s

ly

a sm

gh w e w o s ta r (in fa c t

a lth o u

th e r m a l p r o c e s s in a

,

u

ld

w e

fm a

ag n

itu d e lo

ll fr a c ū o

n o t

be

hav e

\

r

abo u t

n

1%

o

b se rv

y

o

f kn

w a

e th e

o w

a ssu m

o r

le

ss

o



ic a l

th a n th e d y n a m

b le to

n o

)

o r n o t

a

n

f th e

d e v e lo p m

en t

in g w h e th e r a n y e th a t th r o u g h o u t

m ay If a s ta r m a in ta in s ib i i is in a s ta te o f th e r m a l e q u l r u m m o s t o f its life a s ta r l ilib ń u m d u ń n g a n e v o lu tio n a r y p h a s e its to ta b o th th e r m a l a n d h y ? o s ta t ic e q u h t h a s e a n d b y th e v ir ia l h a n g e s v e r y s lo w ly ) d u ń n g t a p e n e r g y is c o n s e r v e d (o r c l e n e r g y , s e p a r a te ly a r e tia l e n e r g y a n d th e th e r m a th e g r a v ita tio n a l p o te n th e o r e m t f th e s ta r s i s ta tic a 11y ) in s o m e p a r o t a c tio n o c c u r s (q u a c o n s e r v e d T h u s if c o n r Q S im ila r ly if th e ld e x p a n d s o a s to c o n s e r v e it fo llo w s th a t o th e r p a r ts s h o u i a n o th e r s o a s to k e e p U la c e it s h o u ld d e c r e a s e n e

o

bse rv e d

s ta r

is in th e

rm

a

l e q u ilib ń u

o

m

,

w e

亡 歹 一

。 乙

,



,



,

,

,

,

,

,

te m p e r a tu r e r is e s in s o m c o n s ta n

t L a te r o n w e

p s h a ll m

a

ke

u se o

f

su c

h

a r g u m e n ts

it w o u ld ta k e a s ta r to r te d a s th e tim e y b e in te r p e h a v e s h o w n in n c o n tr a c tin g (a s w e f th e r m a l e n e r g y u p o e m it its e n tir e r e s e r v e o it T h is w a s in fa c t th e w a y i i s a c o n s ta n t lu m n o s y S e c tio n 2 5 ) p f o v id e d it ï ń a in ta n lv in ) a n d in d e p e n d e n tly H e r m a n n a s L o rd K e W illia in T h o m s o n (b e tte r k n o w n a n d fo r th is a go r o r e th a n a c e n tu y S u n s age m h e t d t e v o n H e lm h o ltz e s tim a l d th e K e lv iï z H e lm h o ltŁ tim e s c a e le is o fte n c a lle r e a s o n th e th e r m a l tim e s c a

T h e th e r m

a

l tim

\

,

e s c a le m a

,

,

,

,

,

'







,

-

,

Scanned by CamScanner

\

32

la r 2 The e qu a tı o n s o f sto ı

ovo lu tı on

H is to r ic a lN o te K e ]v in s (1862)e stim łılc iın po sctlŁ\n u PPE R lim it o 11 lh h c E a r th w hic h w a i s n m a rke d c o n nic t w ith thc nc w the o ry pu t lb rw w d b c y (in 1859) T his the o r re u ired tha t co lo ic tlltim e be ınu c h lo n c t s g y q g o g '

'

,

hurllı \ ņ

'

tls tu , (\cen unt the s lo w e v o ıti fb j ı i ı ı u o n o fco u n tle ss s ec ies o l ı ı m m t ļ n s i m n s t ( v ng nnd ı b >ix iı pu p )by ı\u p tur se le c tio n A l o n g an d in te n se dc btlte ensu e d be tw e en thc tw o e m in e n t ı ı ı sc lc m i stx I h lı e n d D a rw in re lc m a in e d co n v in c e d tlm t, in tiin c phys ic ists w o u ı d c ha n ge the i .

'

,

r

.

c ritic ism

o F K e lv in s e s tim a te cam e to w a rd '

ge o lo g is t T ho m

as

mind þ lı t

c n d c»l thc n in e te e n th c e n tu '

thc

C C ha m be rlin

,

ı y

[\o m '

.

n l,

the

Is pre se n t kn o w le d e re l tiv a e to the be ha v io u r o rm a tte r u n d e r s u c H e x t' g "rdinmy c o n ditio n s a s o bt i i a n n the in te rio r o l the su n slı f{ic ic n tı y e x ha u s tiv e Io w arr ł lm the a ssertio n tha tn o u n rec o gn ize d so u rc es o Fhea tre s ide the tc ? W ha t th c im c m nl c o n s titu e n ts o f th e a to ı n s m a y be is yc t an o pe n qu e s tio n It is no t i m pı o bu bı c tha t the y a re c o m le x o r i i h d a t n l t za o s n an e se a ls o e n o r】 L1o u s en e i i p g ・

,

g

cs

T C C ha m be rlin A n n u a į R e o rt o rtł itı le Sïł ı ı so tlia lłIn s tilllrio lı p 1899 .

,

A n d tw

tha t the so u r

ce ol

O n ly the in e rtia o f tra ditio n ke e s the p n o t a liv e bu t a n u n bu ı ie d c o rpse ,

.

A sta r is dra w in g us

T his

is kn o w

co n tra c tio n

o n so m e v a st rese rv o ir o f e n e r gy

re se r v o ir c an sc a rc e l y

be o the r tha n the

,

su ba to m ic e n e r gy in

the ir gre a t fu rn ac e s it se e m s to ,



.

by

m e a n s u n kn o w n to

su ba to m ic e n e r gy w

T he re is

its o u tpu t o f he a t fo r 15 billio n e ar y s

If in de e d , the

or ı a ther,

.

n , e x ists a bu n da n tl in a ]1 m a tte r y

m a in ta in

hypo the sis a liv e

su ffic ie n t in thc

.

SŁm

to

.

the sta rs is be in * e e l u se d to g y

brin g a little

hic h Il

n e are r to

c o n tro llin g this la te n t o w e r fo r the p w e ll be in g o f th e

fu lĥ llm hu m

m a in ta in

e n t o u r d re am o f

a n ra c e

o r Ior its "

su ic ide

Sir Ar ur S Eddin to n : O b se r va ï o r y 43, 1920 g F in a lly, a fte r a bo u t te n

q u a n tu m

a n d n u c le ar

m o re

ye ars the ,

c o n tro v e rs

yw

a s se ttle d

physic s, w hic h so lv e d the pu z z le o f the

(in D a rw in s fav o u r!)b) '

e n e rgy so u rc e o Fstiu s

Scanned by CamScanner

2 8

a s s u m e th e r m a

The

c

ha

r a c t e r is t ic

l e q u ilib r iu m

t im

es o e sca ı

w e m a y ta k e

L

=

M

c

ı f s te ı ar

=

nuc

L

H

Z

s o la r u n its ,

g

T nu c -

F o r th e S u n th is is ,

a ge o

en ce

(2 6 1)

てn u c 榴

o r u s in

33

o n u tı evo ı

f th e

u n iv e r s e

m an

A

n

4 5

10 2o

*

y tim e s its im m e d ia te

a ge

( )( ) ,

is ı a r g e r th a n th e e s ū m a te o to th a t e m e rg e s is th a t s ta r s s e e m

; in fa c t,

c o n c lu s io n

(2 6 2 )

Tnuc

ly a s m a ll fr a c tio n o f th e ir a v a ila b le n u c le a r e n e r g y , la r m a s s h a s c h a n g e d its in itia l c o m p o s itio n m e a n in g th a t o n ly a fr a c tio n o f th e s te ı A n o th e r is th a t g e n e r a lly n u c le a r e q u ilib r iu m is n o t to b e e x p e c te d T o s u m m a r iz e o u r r e s u lts ha v e

a c tu a lly c o n s u m e d o n

,

,

,

Td

C

o n s e q u e n tly ,

s te

an

lla r

e v o lu

tio n

d h y d r o s ta tic

re d u c e s

it is th e ,

equ

iı ib ń u m

T th

«

(2 6 3 )

Tnuc

f m in e th e p a c e o p r o c e s s e s th a t d e te r m a in ta in th e r m a l t w h ic h th e s ta r m a y b e a s s u m e d to lu tio n e q u a tio n s (2 5 4 ) a t e a c h s ta g e T h e s e t o f e v o

r a te s o

th r o u g h o u

«

yn

f

n u c le a r

to

ar, w e n e e d f h e o ń g in a ıs e t In p a r tic u ı p liń c a tio n o t t a c e its e v o lu tio n t r in o rd e r to b e a b le to r t r u c tu r e o f th e s a l i s i t i a h n t e w k o not n b itio n w h ic h w e s h a ll a s s u m e to e h t e in itia l c o m p o s i s w k o n t d o A ll w e n e e d h i is p re c is e ly w h a t w e d o d th r o u g h o u t th e s ta r , a n t s h o m o g e n e o u s ly d is tr ib u te f ta r s n o w d iv id e s ti a tin g th e e v o lu tio n o s O u r ta s k o f in v e s g l l e l w b a n o s a e y r kn o w f c le a r i n s : (a )W n a t is th e s e q u e n c e o n u t w o m a in q u e s t o r o t s r a t n f f r e i , p in to tw o d e i b G iv e n th e c o m p o s itio n w h a t s ll a r in te ń o r s ? ( ) t e s i n e l c a k t ta e p tic p r o c e s s e s th a o f a s ta r in h y d ro s ta i

T h is is

im a c o n s id e r a b le s

,

,

t re a n d d e n s ty d is tr ib u tio n o f te m p e r a u e a r a te d n u c le a r b s tio n s c a n n o t e s p l C e a r ly th e se q u e ? ń m u b i l i u a n d th e r m a l e q d d th e s tn ıc tu r e o f a s ta r d e p e n s a n d d e n s ity a n e r t u a r e m t e p nd on p ro c e s s e s d e p e d th e a n s w e r s m a y th e n e r e d in tu m a n h e y c a n be a n sw t t B u i n i t o s o n its c o m p o ti n t re o f s te lla r e v o lu o r e h e n s iv e p ic u b e c o m b in e d in to a c o m p d th e s e c o n d in C h a p te r s 5 i n C h a p te r 4 a n i n o t s e u t i f s r q W e s h a ll a d d r e s s th e f s te lla r l m a n n e r w ith th e p h y s ic s o i l n g in a g e n e r a d a e r t e h a p a n d 6 T he n e x t c ith th e p h y s ic s o f g a s e o u s h o a r e fa m ilia r w w s d r e a e r b d y in te r io f s m a y b e s k ip p e d ia tio n s y s te m s a n d o f ra th e s tr u c tu r e

,

,

,

,

Scanned by CamScanner

ı= = d = =

«

a Th e e q u

2

* f st

o ns tı

ar ı ıı

32

i \a 86 2) c s t n

1 K e lv in s (

te u s to r ic a ıN o ı

o c v o lu titn ı

th e s lo w

ie s s fc o u n tle s s p

te im

ı

r

po s e

n it w R ļ iı d a n u pı

s (liv in g {\n d d n n im i\ı lm ĺ s t\n t}f p ı

ı¢ ı

ı q o = \ u m c II

ťìsiı )by n ntū

h\

o u ltl c h trn gc the ir m in d\ ĺ ï rı h s ic is ts w nh In tiīn e p y t a h t d n th c e n tu r f e t e i e c e i n n n v h r c ı t r r y co d om o d e i n a n m e re i the hc c n d D a rw n to w a td t ' te c a in e a i m t s e K e lv in s c r itic is m o f C h iın rbe rlin lo g is t T ho r n s C ı 1 v \o u ıu ı ıı th c b c h a a tiv e to pe ı e d t o xhaustivc l w e w a o g r k r n a nt ls p re se n t h e :+u n sufficiently in te rio r o f t W h h t a in in th e t b ? t a i e o h n t rc e s t a e s i d r i n i e o t d niı ı co n f he a t re s iz e d sou\es o u n æc o g n i t i n ï o s m t b r o i n b ı ı t o the a ss e rtio n th a t n o ı p c e n qu e s h is ye t łLn o p L1s m a y e he a to ı i r s n e e e u s o c o n s titu e n ts o f t m r g s e a ts o f e n o s a n d the l o rgiın iz a tio n th iıt th e y a re c o m p e x T C C ham

o r U R in g



-

A n d tw

o

a te r E dd in g to n de c a d e s ı

ld e n e r gy in s ta rs s h o u

be

,

ic

su b a to m

,

s ta r is

is k n o w

E x is ts a bu n d a n tly

n

m a in ta in

i[s

su ba to m

,

ic

be

R

ļ a te n t po w

n a lly, a fte r a b o u t te n m o re

q u a n tu m

a n d n u c le a r

phy sic s

w

e n e lgy in

fra c tio n

o f the





s o u rec o f

by

su

; :

o r ra the r

m s u n k n o w n to m eı

ic

e n e rg y w

hic h it

ltic ic n t in th e Su n to

the s ta rs is b e in g fre e ly u s e d to m a in ta in

little

u c r to neı

b e in g o f th e e r fo r th e w e lı

fu ı ĥ 1lm hu m

c o m 】o v c ľ s y w n s s e ttle d

h ic h s o lv e d th c u z z le o r th c p

The

T he q u a n tity tha t is c ha n



15 b illio n ye a rs

ye a rs The ,

T he re is

a tte r

th e ir g r e a t fu rn a c e s it se e m s to b r in g a c o n tro llin g th is

h y p o th e s is a liv e

th e s u b a to m

m o the r th ł

in a ll m

o u tp u t o f h e a t fo r

If in d e e d th e

c o n tra c tio n

ir o f e n e rgy o n s o m e v a s t re s e t v o

re s e rv o ir c an sc a rc e ly

t his

us

d ra w in g



'

th e O n ly th e in e 】t ia o f u tıd itįo n k e e p s iv e bu t a n u n b u ıie d c o ıp s e n o t ilı

A

is s u e P re d ic te d tlm t thc

th e s a n te a d d te s s in g



n u cı ear

en t ou r

d re a m

of

o r fo r its

ace Įı n ı

(in D a rw in

\ s fa LTo u rl

by

e n e rgy 5o \ı æ c o l s talh

tlm e s c a ı e

ge d by n u c lc a t p ro c e ss e s

re s t m a ss e n e ı g

,

be s id e s ł\hu n d t\n e e s is ł1(s11 ,

y g iv e n by E in s te in s lh ıE = m o u s rc lt\lio ı T h is frac tio n w h ic h m ł ty bc lu ln c d in to o the r I" iu te o m s o l cnet n u c le a r po te n tia le lle i g y c o n st t gy lence w o m a tu k ì e qb y 8 M ť 2 w h c ı8 c 1111 he e stin by the ty pic ztıbin din e n g e rgy o I *\ n u c l c o n d iv ld c st 11 c LI b y th c n u c lc o n s ı e n e ig y w hic h a ĺ 11o u n ts I o tl W 3 10 T hc ľ a te o l c hn n g e o l°lhe n u v lc ł oli\1 lľ p e n e rg y is o bv io u s l ih y c n u c lc ıu lu l m in o s i[ L lo w c\ y nu c ı\n d s in c e w c a ıe a ı '

,

,

_

,

'

,

,

,

,

,

X

Scanned by CamScanner

ı8

a s s u tıī e th e m

la

Th e

c

ha

l e q u iı ib r iu

ra c

m

,

ı a r f s te ı

te rı s t ic t im e s c a le s o

y ta k e

w e m a

L

=

M

e

H

L

=

nuc

evo

33

ı o n u tı

en ce

ż

c

(2 6 ı)

てn u c 划

u s in

n r

g

so

lu T

u n

its

rn

F o r th e S u

n

T h is

iv e

a ge o

f th e

u n

ha\

a c tu a

lly

is

rs e

n la n

A

n

c o n su m e

4 5

°

uc

y t im

e s

in

d ia te

d

m

ie

o n

ly

o

( )( )

(2 6 2 )

,

i h h g e ; in fa c t T n u c is la r g e r t a n t e e s t m c o n c lu s io n th a t e m e rg e s is th a t s ta r s s e e

its

sm

a

10 2

*

a

a

,

ll fr a c tio

o

n

f th e ir

av a

n

in g th a t o n ly a fr a c t io n o f th e s te lla r m a s s h a s c h a n g e d its in it ia l c o o th e r is th a t G e n e r a lly N u c le a r e q u ilib r iu m is n o t to b e e x p e c te d T u s u m m a r iz e o u r re s u lts «

td n y

C

o n se

s te an re

qu

lı ar

e n t ly

ev o

d h y d ro

du

It is

th e

r a te s

o

f

T th

n u c le a r

n

,

to

m

p o s itio

,

n

(2 6 3 )

«

T

p ro

c e s se s

n u c

g h o u t w h ic h th e s ta r m a y b e a t e a c h s ta g e T h e s e t s ta tic e q u ilib r iu m lu t io

m

d

n u c le a r e n e r g y

ila b le

m ean

A

a te

th r o u

in

th a t d e te r m a ssu m e

o

f

ev o

d to

lu tio

n

th e

pac e a in ta in th e r m

m e

e

q u a tio

n s

o

a

f

l

(2 5 4 )

c e s to

G

d p =

i

m

4 7r r 4

'

dF

(2 6 4 )

dm

文 T h is is n o t

kn

a c o n s id e r a

tlıe

o w

s im

b le

in itia l s tr u

c tu



K

p

,

T 夏) ,

p liń c a tio n o f th e o ń g in a l s e t In p a r tic u la r w e n e e d r e o f th e s ta r in o rd e r to b e a b le to tr a c e its e v o lu tio n ,

p o s itio n w h ic h w e s h a ll a s s u m e to b e h o m o g e n e o u s ly d is tr ib u te d th r o u g h o u t th e s ta r , a n d th is is p r e c is e ly w h a t w e d o k n o w r e a s o n a b ly w e u O u r ta s k o f in v e s tig a tin g th e e v o lu tio n o f s ta r s n o w d iv id e s in to t w o d ifï e r e n t p a r ts o r tw o m a in q u e s tio n s : (a )W n a t is th e s e q u e n c e o f n u c le m i t lla r in te ń o r s ? (b ) G iv e n th e c o m p o s itio n , w h a t is p r o c e s s e s th a t ta k e p la c e n s e o f a s ta r in h y ? o s t a tic d is tr ib u tio n o f te m p e r a tu r e a n d d e n s ity th e s tr u c M r e tio n s c a n n o t b e s e p a r a te d n u c le a r h a n d th e r m a l e q u ilib ń u m ? C le a r ly , t e s e q u e s d d e n s ity a n d th e s tn ıc tu r e o f a s ta r d e p e n d s p r o c e s s e s d e p e n d o n te m p e r a tu r e a n d in tu m a n d th e a n s w e r s m a y th e n o n its c o m p o s it io n B u t th e y c a n b e a n s w e r e A ll

w e

n ee

d to k n

is th e in itia ıc o

o w

m

,

,

,

p r e h e n s iv e p ic tu r e o f s te lla r e v o lu tio n W e s h a ll a d d r e s s th e fir s t q u e s tio n in C h a p te r 4 a n d th e s e c o n d in C h a p te r s 5 ith th e p h y s ic s o f s te lla r l a n d 6 T h e n e x t c h a p te r d e a lin g in a g e n e r a m a n n e r w in te ń o r s m a y b e s k ip p e d b y r e a d e r s w h o a r e fa m ilia r w ith th e p h y s ic s o f g a s e o u s s y s te m s a n d o f r a d ia tio n

be

co m

b in e d in to

a co m

l

,

Scanned by CamScanner

Scanned by CamScanner

3 ı The v ic io u s

p ro p e n s ity to b e h id d e n fr o

q u a t io

e

35

f s t a te

o

n

th e p u b lic e y e N e e d le s s to s a y th e p h y s ic is t

m

if c h a lı e n g e d b e p re a r e d to d e fe n d th e u s e o f h is d s c e m m e n t; b u t u n le s s p il h th e d e fe n c e in v o lv e s s o m e s u b tı e p o in t o f d iffic u lty it m a y w e lıb e le ft u n t t e c h a lle n g e is m a d e m u st

S ir A r th u r S E d d in g to

n :

3 ı The A

r e la tio n

p o s itio

b e tw

an

n

e q n a tio n o

d th e

b ie n t

am

e

q u a t io

s s u re e x e r te

p e r a tu r e

te m

rs

19 2 6

,

f s ta t e

o

n

S ta

d b y a s y s te m a n d d e n s ity P

f p a r tic le s

o

P (p

=

,

,

o

T X ,

f kn o

) is ,

w n co m ca

lle d

f s t a te

In p r e v io u s s e c tio w h ic h im p lie s a

ga s t h e tim ,

th e p r e

een

e

f tlt e

o n s titu tio n o

T h e ln te 17 tđl C

has

co m

n s w e

re

ju s tify

to

e

ix tu

m

hav e o

re

p e a te d ly

f fre e

a s su m e

d th e

s te

lla r g a s to b e

an

an

id e a l

t as g p a r tic le s (a p e lje c g ) A t th e te m p e r a tu r e s p r e v a ilin g in i s c a n b e e x e c te d to o c c u r W e

n o n in te r a c tin

,

th is a s s u m

p tio

n

t on p g a s e s a r e io n iz e d a n d C o u lo m b in te r a c i m a ll c o m p a r e d w ith th a t th e e n e r g y in v o lv e d in s u c h in te ra c tio n s s s s h a ll s h o w F o r a n a v e r a g e d e n s ity p a n d a g a s l th e k in e tic (th e r m a l) e n e r g y o f th e p a r tic e s s ta r s ,

o a r tic le m a s s

,

M

H

,

th e

m

in te r p a r tic le d is ta n c e is

e an

h e r e p h a s b e e n e x p r e s s e d in d e n o tin g th e c h a r g e is Z e (e s tim a te d a s p a r tic le m a y b e e

te r m s o

w

f s te lla r

e le c tr o n

c

Ť fr o m E q u a tio n

M

an

d

ra

d iu

h a r g e ) th e ty p ic a l C

(p e r p a r tic le ) is o f th e (2 2 9 )

T h e k in e tic e n e r g y

m a ss

s

o m o u ı

,

o rd e r



an

R If th e p a r tic le

d he n c e

b

e n e rg y

a fte r s u

,

pe r

b s titu tin g

,

Z

c

4 7r e o



2

e

2

AĄ/3nĄ G 3

M

2 /3

(3 3 )

'

d M = M o th is it F o r Z = 1 A = 1 a n h e o rd e r o f u n y t f o s r t o f c a ig n o r in g be f l m b in te r a c tio n s m a y th e r e o r e i h s a c c u ra c y C o u o t t o d n a % 1 r a tio is a b o u t h ic h v a r ie s a s 2 2 , a n d th e r a tio (3 3 ), w v e A H h a e w Z h r e i h g n e g le c te d F o r W e s h o u ld i fo r a c o m p o s itio n o f p u r e r o n b 3 2/ e lo w u n ity e v e n l l e w s i n a m re ź t 10 3 M o A lth o u g h s ta r s d o n o 1 fo r m a s s M Ť k t h a / t 3 c r e n o te , h o w e v l 10 M o h m a s s o f J u p ite r is r o u g h y e p la n e ts d o : t e n o z s u o r e d n b e lo n g to th is a g f fr e e b d e s c ń b e d b y a m ix tu r e o l f a n e ts c a n n o t e o e r t u c p u t r C o n s e q u e n tly th e s k e d S in c e c / k Ť > 1 i f s ta te m u s t b e n v o i o s n t o a u d e t q c o m p lic a e a s s th e c lo s e r g a s e s ; m o re h t th e s m a lle r a p la n e t s m a y c o n c lu d e t a m e w d li s o s s i c h a r a c te r z e tu r e to a s o lid is its s tr u c «

,

,

,

,

,

,

,

,

,

'

,

,

Scanned by CamScanner

\

\ l

Eı o m

3

36

F ig u

3 ıB

re

ith th e

w

n o m n a

l to th e

A g e n e r a l th e o

by

s y s te m

w

o

c* o t* r y p h y * ı

f p łlr tic le s im p in g in g

o

e im

・n

nm

ln t ı on ıľ a tı

hct rı c n ıH \ı ì o th c lı hy ı

u

,

\m \n ł n \Į\k ln g 【

ı ¢a

nG e s u r ti

re m

e n llb le s ih e c a lc u ln lio n o n i\s [h c

f n n in te g ra l k n o w

m ean s o

tm

f H il l

p lv

ıth c p rc N # u t e v v llr p

b ite w ・

o

l t\ IIc e p u r tlc ı e

y l/

is th e p a r tic le v e lo c ity p its m o m e n tu m , ttn d /i (p ) d p ii th c n u m b e r t t/} ) T h c f p a r tic le s p e r u n it v o lu m e w ith m o m e n īa w ith in th c in te r v tlı(p , p he re

pro th e

u

f o f th is th e o

o

re m

is

as

fo llo w

s:

o n s id e r 11 s u r th e e

C

(t c a l o r im

g in a r y ) w ith in lh e m o m e n tu m

a

f p a r tic le s T h e p r e s s u r e o n th is s u Ľ la c e re s u lts lľ o b r 1ıe d b y im p a r te d b y p a r tic le s c o llid in g e la s tic a lly w ith it T h e m o m e n tu m Lr a n s ı \c c a n in c id e n t p a r tic le is tw ic e th e m o m e n tu m c o m p o n e n t n o r m a l to th e s u r lł s y s te m

o

A p

C an

b e th e

w

n u

d ir e c tio

beam

n s w

ith in

th e n u m b e r o an

g le

,

o

(3 5 )

o

a con e

f p a r tic le s

(0 0

+ d 0 ) S in

w

c e th e

p a r tic le d is tr ib u tio n is is o tro p ic ith in a n y s o lid a n g le tlm is p ıo p o r tio n a l to th e s o lid ,

,

o r

n

{? p ) d e 山)

be r

d co

,

n

T he

co s

f p a r tic le s im p in g in g o n th e s u ľ la c e a t a v e lo c ity u m a k in g a n ith th e n o r m a l to th e s u l-fa c e (a s s h o w n in F ig u r e 3 1) L e t /ı(O , p ) 4 0 d p m b e r d e n s ity o f p a r tic le s w ith m o m e n ta in th e r a n e ( g p , p + dp)and

o n s id e r a

g le 0

2p

=

=

(p )d p

4 7r

2 Tt s in o cle =

4 7r

ģ in s

=

0 00

(3 6 )

f p a r tic le s fr o m th is b e a m s tr ik in th e s u r Fa c i e n a tim e in te r v a l g ô t is g iv e n b y th e n u m b e r d e n s ity m u lti lie d b th e v o lu m e u ò t d s c o s O w h e re p y , d s is th e a r e a o f in c id e n c e o f th e b e a m o n th e s u l fa c e H e n c e th e m tu m n u m

o

o m en

tr a n s fe r r e d to th e s u r fa c e b y th e s e a r tic le s p

Bp e

=

n

(?

,

p)d 0 d p

u

is g iv e n b y ôt d S

co s

o h p

(3 1 )

Scanned by CamScanner



卫ı Th * h 附

t h e w w w iln ııi{ ın u n it tim e *

pcr

湖南 ó q ıı《 in

dp

į

=

s in

u

rı n9¢ em%łp « f ıh ırq e p m c ı * ı n ın n « n ¢u m ı ı h ¢p m * u m r ı Io ı n ii w r fıc t a r e a ls ıh e ır g iv e n b y pĄ w łltm (3 7 ) C O m b o

-

.

(3 5 ) a n d (3 6 ) ın e r d lv ı d in g b y B rd S

m

.

o do

n

( p )d p

d th e tm aı m u r e is ım o (O £ Q 5 ar /2 ) a n d a ı

u co s

an

#

o m

Q 2p co s a

u

.

p n (p ) d p

b t a in e d b y in ı e g r a tin g e n ta S in c e

/2

co s

o v ¢r a

'

lıa n g le q

ı

co s

2

Q s in o d Q

cos

_

2

Qd

co s

ů # ln tņ d Q

o

o

f in c id e n c e

4

.

(3 8 )

(3 9 )

p ro o f \s c o m p le te d O b v io u s ly th e p r e s s u re o f a m ix ıu re o f fr e e n n n ın te r ıc tm l e l o f d ifr e r e n t s p c c Ie s w iı ıb e g iv e n b y ıh e s u M o f th e p m l u re s e M a d p a r tıc ı h ic h il th e b y e a c h s p e c ie s s e p a r a te ly T h is w iı ıin c ı u d e th e ra d ia tio n p r e » s u re w o f th re e p re s s u re e x e r te d b y p h o ıo n s C o n s e q u e n tly in s ta rs P w ilıb e th e s u m fo r th e p h o to n * Th e fo r th e e le c tr o n s a n d P d i t m n ıls : P fo r th e io n s lıe ı

,

,

.

,

Ą

ı

ir s ıtw ı

o c o n s titu tin

g

th e to ta l g a s

P

ï t is

c u s to m a r y to

d e fin e

P \+ P c + P m

-

a

p re s s u r e

p a ra m

e te r

d

,

th e

fr a c tio n

ßP

\ l \

þa s

0) (3 ı

P ra d

P g. +

=

o

f th e p r e m

u r e c o n tn

bu ı ed

b y th e g a s ; th tıs

P ea s

Pm

e

qm

io

n o

f s ta le fo

Pr w

h e re

n ıis

th e n u m b e r o

in g th e 【h e o r c m w

l io n « W

U = in g m m sł ı

r e la tio n *

in g

(2 A 7 )

ıth c o ver aı

,

io

a

=

(3 ı2

p re s s u

n ik T

w e

re

ll k n o w

M

um c r u n it v o ı

w e o

ax w

(3 13 1 T h is

b tıin e d b y a p p ı y ib n u m o d y n n m ic e q u iı

a tio n re ı

p ıırtic le g n s in th e r m o c i[y d lıtr ib u tio ia n v e ı c lı

b ta in th e to ta l n u m b e r

n * p c e ie »

/J ı=

a tio n n re ı

,

Io a fre e

ju ril p ro v e n

h ic h is c h a ra c ıe r i» e d b y

n

id e a ıio n g a s is th e

r an

(3 ıI

P )j

(1

=

T h e io

3 2

T he

d

=

u

f lo

ls

o

,

n

l vo ı um e n ıi In a u n ı

by

t n i

Scanned by CamScanner

3 2

T he

The ı o n p re ssu

37

re

c o n tr ib u

tio n o f th e s e a r tic le s to th e r e s s u r e th e m o m e n tu m transfemd \ r p p u n it tim e p e r u n it s u r fa c e a r e a is th e r e fo r e g iv e n b y E q u a tio n (3 7 ), c o m b in e d

ith E q u a tio

w

d p

ļ s \n

=

(3 5 ) a n d (3 6 ) a fte r d iv id in g b y B t U S

n s

,

? đo

n

(p ) d p

d th e to ta l p re s s u r e is (0 < 0 5 ır /2 ) a n d a ll m o an

n

u co s

o m

o łp

cos

o

p n (p ) d p

u

=

b ta in e d b y in te g r a tin g e n ta S in c e

/2

co s

over a

ll

ż

13 8 )

e s \n o d e

an

g le s

o

f in c id e n c e

1 co s

2

s in

0

0 do

Co c Os S

_

2'

0 d

CO S

e

(3 9 )

ģ

=

i th e p r o o f is c o m p le te d O b v io u s ly , th e p r e s s u re o f a m ix tu r e o f fr e e , n o n in te r a c t n g iv e n b y th e s u m o f th e p re s s u r e s e x e r te d e s o f d iffe r e n t s e c ie s w ill b e a r tic ı

p by

p

eac

h

s p e c ie s s e

p a r a te ı y T h is e x e r te d b y p h o to n s C o

pre ssu re d iffe r e n t te r m fir s t tw

a r y to

b y th e g a s ; th u

d e fin e

a

Pi+ P e + n p a rm

e e

q u a tio n

p

e te r

f s ta te fo r

o

T h e io

id e a l io

an

w

he re

n l

n u m

in g th e th e o r e m w

h ic h is

c

su m m

be r

o

fo

r th e

w

h ic h is th e

su m

o

p h o to

f th r e e ns

th e

n o

(3 10 )

d

f th e p re s s u

r e c o n tr ib u te

d

ju s t p r o v e n a

=

over a

(2 4 7 )

,

ll th e

w e o

io n

re

pre ssu

n

lt lk

T

w e

ll k n

o w n r e la tio n

(3 13 ) ,

b a l l e T h is r e la tio n is o b ta in e d y p p y p e r u n it v o u m ib ń u m i th e r m o d y n a m ic e q u iı to a fr e e p a r tic le g a s n ib tio n M a x w e llia n v e lo c ity d is tr u

f io n

h a r a c te r iz e d b y

r e la tio n s

in g

+ n

s

th e fra c tio

s

n i4 tr p

U s in g

Pg a

-

g a s is th e

n

Pk is th e

d

,

,

d

as

pre s s u r e ill b e th e

s

3 2

th

,

,

tin g th e to ta l g a s p r e s s u r e -

r a d ia tio n

q u e n tly in s ta r s P w fo r th e e le c tr o n s a n d n

n se

,

o c o n s titu

c u s to m

w

P ï fo r th e io n s p e

s:

P

It is

g ill in c lu d e th e

b ta in th e to ta l

s p e c ie s

dp

(3 14 )

nu m

=

be r

o

f io n s in

a u n

it

v o lu m e

by

i P

ï ıI

,

/? i

X

艺众



i

(3 15 )

Scanned by CamScanner

3

*m Eı

* n ta r y

p h y r la

o

fg

an

d

a t io n ra dı

38 s o o n tic m a s T hc n n e a n a ı

l s te lla r

i cd ıï is d c ın m a te r ia l ı

by

6) (3 ı

§0 th a t

(3 17 ) nl

an

d $- ! m

ay

,

lıï ï n \1

by

a te d

tx a p p ro x im

=

(A )

4

Al ı

le m e n ts o th e r th a n f th e /ie a vy e le ın e n ts (e < l th e S u n fo r e x a m p e fe r re d to a s ın e ta ls ) F o r h y d ro g e n a n d h e liu m s o m e tim e s re i 1 2 9 T h e ra tio k /m H 8 H 2 0 ; w h e n c e /Łı= X = 0 70 7 r = 0 2 7 4 a n d (A ) l a s c o n s ta n t u s u a ll kn o w n a s th e id e a g w

is th e

h e re

a v e r a g e a to m

ic

m a ss o

,

,

,

y

k

9) (3 ı

冠王 n zH

E u a tio n (3 13 ) S u b s titu tin g E q u a tio n s (3 17 ) a n d (3 19 ) in to q ,

pi

If th e e le c tr o n s

c o n s titu te a n

The

ly o b ta in fin a ı

(3 20 )

pT

-

P

3 3

w e

I

e le c t r o n

p re s s u r e

id e a l g a s th e e q u a tio n ,

o f s ta te

is

,

as

3) E q u a tio n (3 ı

a bo v e ,



n ekT



(3 2 1)

,

b e r o f (fr e e ) e le c tro n s p e r u n it v o lu m e H e re w e s h a ll m a k e s im p lify in g a s s u m p tio n b y ta kin g th e a to m s to b e c o m p le te ly io n iz e d T h is is c e r ta in ly c o rre c t fo r th e m a in s te lla r c o n s titu e n ts h y d ro g e n a n d h e liu m a t w

h e re

n

e

is th e

n um

,

te m p e r a tu re s

6 e x c e e din g 10 K T h e

a ssu m

,

p tio n is o b v io u s ly in c o rre c t fo r s te lla r

p h o to s p he re s b u t w e a re m a in ly c o n c e rn e d w ith th e in te r io r W ith this a s s u m p tio n th e to ta l n u m be r o f e le c tro n s p e r u n it v o lu m e is ,



W

e

define

ı

c

1



互 二・ 。 /



a s the a v e ra g e n u ı n be r o

忐三 叠 x.

F IT c c e le c tro n s pc l

士亞二 丑 一

・・



n u c le o n

(3 2 2 )

,

(3 2 3 )

Scanned by CamScanner

nlırCinRWMfı iT1ı m om l Į wles X iř [a a '



_





刀 。 。







召 一

人 月

)

人 。 エ



(





-



多 一



ミ 、

.



。 、









(

一一

圧島 侧 ロ

人 り二

ロ ー







多多



卜 刊 岡 )

コ ロ ㈹ ( 一



刊 們 )















ミ ぷ り

(



コ の ニ っ ニ し





瓮 の

)













)





ー ー



亡 团 コ 团 の (

口 り り ー 口 ) ロ







ロ ン 划















ロ コ



)









( )







そ 材兩







の ン











)





)

卜 口



そ り

事ミ

個 コ 丁

? 闃 口



召 の









.





-



刀 口







口 人 出与











っ 臼



쩝 ン ニ

日 。

















。 (

一 ・

一 一

-



\这 艺 り

1

+

口 っ

-过 一

m

\



一 一



っ 島

ミ っ





ミ っ



)











ン の

み っ 二 、

巴 の

ミ 一

口 っ ー





)



の し

コ 阴





团 团





エ ー





岛 口

っ ー

の 卫 一

口 囹



二 閱

三 む し

コ 阴

名 田 一

口 っ ー







ミ っ り (

刀 )

っ 口 囹









闐 口



ロ レ













的 ー







の ー

り ー



づ ロ ロ

ミ っ

圧 叩 一





の 日



日 )

口 個





ミ ー



め ー









































の り

9





ー 一













相 リ ニ



口 ー







口 の









臼 三

















三 器





















ニ 閱





腎 一 츠







(















-



り ニ





、 。



(



















0



-







ミ 、







三 ミ 口



























名 、



り ー

口 囹 ぷ り む

ミ ミ コ ー

口 囹 コ



리 一

口 む

日 の ー

の の

ミ コ ー

っ ン 日

日 ー

ぷ ー

ヲ っ







闐 口 一





っ ー







り り





っ 日 서





ら 囹





Scanned by CamScanner

'

em Eı

3

C o n s id e r th e

now

aveı ı gť

e n ta

an I

ve 1 (o r c n tu n

f cs o

i

ry

and

u is u n iq lo c ity)

e ly

r a d ia

L

tio n

d b T Im a gin e de te rm in e y

Ep

m o nl

l c ity, a ge v e o

or

e ffe c ts

noīnentum)

om th a t c

so

r ho w e v e ,

l E v e n tu a ly

,

pre s

d e c re a s e o

(

s io n

f A v ) do e s

A*

s ity th e d e n

m

e

M g h (A v l ow

is in v m

)

im p o rtaa « in M e iĺ « s itie s fo r a giw « É i

ł aı a n d m a y « aı yb

,

ic o f d e ha ræ te fis ı

,

,

n « ed

pto porū o r

ın e n t s f o r C W a re n e arı y 2000

m g a s te to th e °

is h a v e the

ı 5m

ha w

w e

m ay bec o

J

-

not

Practical1TE m e an s that tu re p e ra th e te m p e m ire I din g n k rre d fro m e sp o n a t in h ll c o rı T l u t n e m o ı T th e ı i o n s w e h a v e to take i t d n o c th e s e u n de r re s su re n i x c lu s io n p ń n c iple o p r t c l e e th e P a u l e tim a te th e c iple ń n s o r de r to e s i h an c p tu m m e c f a n o the r q u a n ac co u n t o le c tro n c an h av e tw o n c e an e s in Si e s a rn e p h t d n a tu m q u a n tu m

pr e s«u ıe o (

y

w

sin ce

?

e

eneĺEV

C

m en sam e m o

,

T h e p re ssu re tr o n s a t m o s t d b y tw o e le c an m s ta te s a s th e ir den tu m spa c e c r m o m e n tu an d m o m e n i n to high e d e c r f o e t ar l t de g e n e ra cy is d b e le c ? o n s th a ta te o f c o m p e e ge n e ra te y s u re A s s e r c a ı p 1e d de ge n e y is c a ı m a x im u m t s ity in c re a s e s o c c u p ie d u p o a m sta te s ar e l e m o m e n tu b l i a a v a h e t l l h n a 3 30)b e c o tn es o b ta in e d w e 3 is m in im a l a n d c o n ditio n ( e A V A p s a i c h s t I n e lu te m pe ra tu re m o m e n tu m v a l b e a c h ie v e d a t z e ro i t u a tio n c a n o n y l s d a i e n a h Su c a n e qu a lity e r a c y a n d ha s the t te s o f h igh de g e n x im a tio n to s a ro d a o o p a p bu t it c o n s ū tu te s g f io n o f th e pre ss1Jr e T he re o re f h t o rw a rd c a lc u la t i a t r s a l i g b n a g a dv a n ta ge o f e n te m o m en llia n to a c o m p le te ly de ge n e ra i i n fro m a M a x w e t o a ltho u gh th e tra n s i tio n s ll disc u s s o n ly th e e x tr e m e s tu a ra d u a lly w e sh a tu m dis tribu tio n o c c u rs g b e fo u n d in u a tio n o f s ta te m a y de ta ile d tre a tm e n t o f the de ge n e ra te e q

Ex e r&

o c c u p ie

be

e

3\

fa r a dc g n

In s e rtin g dae

w

m

1

h e re K

siŭ o n an d

l

n a

d e v o id c

be n c e th e

,

A

m o re

w

A p pe n d ix B an d

A pp ly in g the H e ise n b e rg

P au li prin c ip le s to

n

e

(p )dp

2

į

-

=

AV

13

2

4 trp d p

,

e n e rat

p

H the

y de g p lđe ı tro ľ th e n iu m b e r o f e le c

a com

iso tro pic e le c tro n ga s y ie lds the m o m e n tu m dis tribu ū o n d p )pe r u n it v o lu m w ith m o m e n ta in th e in te rv a l (p , p +

h e r e K r is e

ple te \) Ū su c h a t

co m

e

contute <

(3 31

po

II 田0 田 en 加

i ūc re la tiv s e« th e e x tı

T he

m a x im a l m o m e n tu m

a n d re v e rs in g the re la tio n

po

c an

be tw

be o bta in e d by in te r a tin g g

een n e an d

o ,

n

e

=

n,

{P)d

pre s su

w

e m a y n o w u se

he re

M

e

T heo re m

it the e le c tro n

i

po

3:

w

re

fo r the ĺ in ri the ı

/lmt e' qu a tio n (3 3 ı ) ta kin g u = F rleť l in ti a n d c a rr in y g th e in te gr a l u p to p o to o b ta

(3 4) su bstitu tin g E

t

,

m a ss ,

,

:

Scanned by CamScanner

3 3

d e ge n

e ra c y

h e re

p re s s u re

o

fa n

Tı «e d

e le c tr o n

em

no n

p re ss u



re

ga s

ha v e

u s e d re la tio n (3 2 4 ) fo r H c W e n o te th a t th e d e g e n e r a c y p r e s s u r e is in v e r s e ı y p r o p o r tio n a l [o th e p a r tic le (e ı e c tr o n ) m a s s H e n c e A lth o u g h th e a r g u m e n ts p r e s e n te d fo r e le c tr o n s c o u ld b e e q u a lly a p p lie d to p ro to n s a n d n e u tro n s A s th e y a r e n e a r ı 2 0 00 i t m e s m o r e m a s s iv e th a n e le c tr o n s y q u a n tu m e F « c ts B e c o m e im p o r ta n t in th e ir c a s e u n d e r m u c h m o r e e x tr e m e c o n d itio n s (m u c h h i h e r d e n g s itie s

an c

d

w e

fo

g iv e rf te m p e ra tu re A n d a y u s u a lly b e i n o r e d W e g

m

r a

h a r a c te r is tic

o

f d e g e n e ra te

s in c e th e p a r tic le e n e rg y

fo

e n e rgy o

a ls o

m a tte r

f th e

o

p e r a tu r e s fo r a g iv e n d e n s ity ) n o te th a L in s p ite o f th e M g h d e n s itie s Th e p a r tic ļ e s m a y b e s ń 1ıc o n s id e r e d Jee

m u Ëņ lo w e r te m

rd e r o f p

ś/2 m

is s till h ig h e r th a n th e C o u lo m b

e

C

e n e r a te e le c tr o n

r a

tn s e r tin g th e

g a s to b e

n u m e r ic a l v a lu e s o

1 00

10 7

4

kg

c o n s id e re

d p e r fe c L

f c o n s ta n ts in E q u a tio n (3 3 3 )

,

2 /3

2

[1 0 0

×

10 ı3 c m

4

2 3

g

w

h e re K

an

l iv e n b y d h e n c e th e d e g e n e r a c y p r e s s u r e (3 3 3 ) is s im p y g

=

×

m

Ą w

he r e K

ta n t , is a c o n s

T his

S

deg

5 3 K ıp /

=

re la tio n w

w e o

s

2

b ta in

] Fo r a

com

po

(3 3 5 )

,

ill b e o fte n

ıfu tu r e u s e d iı

d is c u ss io n s

i a l m o m e n tu m in a d e n s ity is in c r e a s e d ħm h e r th e m a x m l e r E v e n tu a lly a d e n s ity is r e a c h e d e le c m »n g a s g ro w s a rg c o m p le te ly ? g e n e r a te li h t T h e e le c tr o n s n o w ro a c h e s th e s p e e d o f g a m i w h th a t th e v e lo c ty p o / e p p a ū o n b e tw e e n h i h th e s im p le re ı 加加is lic d e g e n e ra te g a s fo r w c 抱抱 a r e ı c o n s姓 d h a s to b e r e p la c e d b y th e = m u n o lo n g e r h o ld s a n ı it m o m e n tu m a n d v e o c y p in fo r s im p lic ity w e s h a ll o n ly c o n s id e r i s re la tio n H e r e a g a c t a m i k e n ū i c i l v s t re a R la c in g u b y c in th e h th e v e lo c ity is v e ry c lo se to c e p th e e x tf e m e c a s e in w h ic

If th e

e le c tro n

,

,

,

,

,

n te g ra l (3 4 ) pres su re ¡ .

w e o b ta in

by e

sam e

p ro c e du te

as

be fo re

in t re \a ū v istic e le c u o n ga s c o m p le te ly de g e n e ra e fo r th e p ress u re e x e rte d b y a 36 is a sm oo M h e tw ee n re la tio n s (3 3 3) a n d (3 ) i i n n f s a n ï t T h e e lim it u 4 c

Scanned by CamScanner

E ıe

3 42

/

or fu n c ń o n o f u c

w

c p /n ıc

f ic a th e n u m e

In s e r tin g

h e re K

=

fo r a fix e d

l 24

v a lu e o

,

ln o t a d

ha l 1v e s

hic h

w

l v a lu e s

o

fc o

o

h

b ta in e d

d ix

h

4 /3

[i 2 4

!

l/3 s

kg



Xsīİ =X o n th e a s s u m

bu t se e A pp d re s s h e re (

ts in n s ta n

K 2P

=

ř. r

"

d ia tio n

(3 3? )

3 lo × 10 m

fP e

\d r a aı

æ

of

te m

f v a n is h in g p tio n o it

Cm

3

g

1/3

'

S

] a n d fin all ı

4 /3

(3 30

,

3 3 8 ) fo r th e p re s s u re w e re (3 3 5 ) a n d (

" a t M a ti.

f n c tio n o f de n s y p re ss u r e is o n ly a u o m p le te th a t e v e n in th e c a s e o f in c

5

1 10

×

p e ra ttıre

g iv e n

(fo r a

co m

d he n c e

an

n a tu ra ll

y the i I t i i s t t n o ru ) e ho w ev po s e ,

,

,

r,

d e g e n e r a c y Th e te m pe ra tu re n e r a te ) g a s T h d e e n o n l d a e ( i g u s as fan l th a n in th e c a s e o p la y s a fa r s m a lle r ro e i d d e n s re i o b a c s e n se n siti ve d e n e ra c y p re s s u re m a y a c ru ? a pp ro x im a tio n Th e e g l i f T k n o a s r a c tio n o f th y i o o d p r o v id e d e to te m p e ra tu re T h e a pp ro x im a tio n s g A n t m m u o ) n e ( re m o a t m c h o s c e M p . u h rat i le w ith t e

kin e tic

e n e rg y o

tneatment o

f a pa rt c

f d e g e n e r a c y p re s s u re

34

m

Th e

T ia o r pa ı

t

.

g a y b e fo u n d in A pp e n d ix B

ra

d ia tio n p r e s s u

R a dia tio n p re ss u r e is d u e to h o to n s th a t tra n s fe r p w h e n e v e r th e a r e a b so r be d o r sc a tt y e re d I h n

to n

dis tr ib u tio n is is o tro ic p

ra n g e

(u

,

v

a n d th e n u m

n

T h e p r e s s u re is th e n

(リ)d v

i

re a d il o bta y n ed -

Pra d w

he re

a

is th e





g a s pa rtic les ic e q u ilib r iu m the pho

m o m e n tu m

b e r o f p h o to n s

8tr v 2 一

re

t e rm o d y n a m

+ d u ) is g iv e n b y th e P la n c k b l ( a c kb o d

e

w

to

ith fr e q u e n c ie s in the

y d is tr ib u tio n ) fu n c tio n

dv



e

(3 39)

1

fr o m E u a tio q n (3 4 )

々( ) C

n

U

du

=

į

a

T4

(3 40)

,

ra dia tio n c o n s ta n t

a

8Jr Ĵ k 4

4 cr

(3 4 1)

a

p h o to n T he d ir e c tio

n o f th e em

itte d

p h o to n is

ra n

do m

in

,

th e in itia l dire c r

闭目■

Scanned by CamScanner

3

t%

q ieb w

w qūł

.

w

.

łf

lm

pı lt lııla p

« «

w

=

d

w

l ı1 m

ļ tūl ł

\

ıi

)*

P

P

0 4 31

a

s ?d iı i

w w

n

N

a W

e *a l

* '

ııM a m p e a 国w

c

h ıy b

y l a « * b r1

¢y * i ıe d * i ı* tıd ib ıa łfı

yb W W W

国四凶 シj* 目i加b o e n ı1 e = ¢防国 国ı

溆 晖 la 口

《 硝 月八 烈 削

c e hlır o f d e b ılbd ? b«« * ¢N 1 ł4 1 ( w ıi la c iı» ıı * a 闻 》 咱 は朝 如 目 曲 国 回 n ıı ı娴 岫够 沁 ıı M e h t o ı印 }2A 日 回 画 声 叫 即 出 ダ o 日tł 峙 ıc ı 娴 嗜d 力 r * f 口 啊 圈 妇謝 嚕 畔 ¢出 m a tb o 電前 目 国 聞 密 ie ı e 曾 旧 照 夢 出 l¢妞 砂对 以 ı -

P !材

34

庐 層

=

P 3

si

ŝ

nw T ła k p ıa łs ・ r n iı

.

2

ニヱ _

o n

e*n

k iiw

c

w

yg ï e n

c p s ehT e c ıfı

h t y tis n e d y g a

ie ih ¢g n ım

r n fr e p

n c c

l

( m

a re

F )=

ır e p

»m

)w M u ı



c i ıs i v ı k y łi y g r e n e e h t



p ,d )p {k p ltıı

0 4 31 yb

ın ig y ı ı

» e* eb

* d »

d

e n e g qi

h c ih w

k

:b

c i t r * p ı« d iin d » a r r e p ・ fo »

W

«

=

n

pa



跡 滿

Fa

*= t e g *



04

ı

m

i



m

bt

@

ı



*

« i»

2 /'p



* 凇 嘶劇 铷 翩

W

*m

» H «

in

«

e ı* e ı d e no

c

**

c Ĥ e m k



M

Ħ

1

eh

T

s )

Eı 奄齢 妇 佬 阔 抑 eh tn *

C

卢 回聞 曲 朝 《

W



l tn t h ï 隗目

而心 平 舗

e q r 1 [ ı« w ? l d * ı ł 卢 en T 帽 啼 莺隴 翻 姗

R ı * n*

帛個辆 陶 ㈹

曾四

翩 * ew

w

w



» ı¢ e ı*

g d k

¢ n

=

.

-

= H H ı« \ m

曲臨削 阳 朝 缉

ıd «

ap ı

沏 阑 懒 d t ıra m

w k ¢ d»

t Ą

滢四 魚 湖

赚 歯



i« a n i n in k

e



C



ħm

Ĥ M p «



*

h l o ıi d ııe ııd ıı

d n a s p d ı * ı¢r * m ım

嚇 翔栩

bW

Ĥ

ıe d ıı ıc w ı

Fn « ,

fo m i ıw t * ıfo m y g *t * e ł

eı ū

*

i

ı ¢i

« ag

ieqe

į o ıï

h t r o f n ia ıb ò

p ń m iı

«

p

軌 自 輸國邮曲昭 曾 ぎ小 ド叫岫 ポ门

l rM

ıe h

* *

w m » n m ıp « ıı» ¢* ı« ıı* h ł

w

d* R

w

ł*

»

ū ft

\ )

p ı

Scanned by CamScanner

X

v

ı '"

. ,

)

t

g

U

i ii

2

in p lir t

m le u sł

ho

mttintainingt

cdntmcts o ï r th c lĮ ta r Į y \c n c ı l x ) tc n tia v im lrtm n ĺ ,

p

+

c

g r«

lc u im

e r u ,d ia l

lcnscd is

n ifo

d

tw

r th e

lim its

/}

ï ı rı

ay nn

,

h ic h fm

w

d

ß

h ic h fm

w

I c

a nd

tio n o f

c tio n

is

turncd n m h e ilt?

The

3 6

a

c a b a tı dı

ex

n e n

po

t

h ic h w ill b e o f in te r e s t in la ter i l k in d w f a s pe c a o s e s s e c T h c r m ıx ly n a m ic p r o ith o u t e x c h ıin g e o f h e a t w ith s tc ilì w i n g in a s y rr u c c o e s h o h e fir s t la w o f th e rm o a s c u w iio n s a r e t i b tłtic F r o m t a lle d tıtl tt s se s m e c e c o r h s c u t p e m ir o n m e n th a t a d ia b a tic p r o c e s s e s s a tis fy 2 2 it fo llo w s i n S e c tio n d e i n o t n e m i c s m ( dy n a

)

th e

co n

d itio n

du + p d In th e p r e v io u s pe c

ific

en e

r8 y

s s e c tio n u

is

ha v e

w e

a lw a y s

w

h ic h b y d iffe r e n tia tin g

A

c c o r d in

an

d

g ly , th e d e p e n d e n c e

su

o

na

=

l to P

/p

) is

ca

W

f th e p r e s s u r e

o n

th a t the p le s y s te m s a y th e r e fo r e w r ite

r s im

e m

b s titu tin g in to E q u a tio

la w

T h e p o w e r (d In P /d In p P o r tio n a lity fa c to r (to b

(3 48)

0

le a s t fo

at

se e n

p r o p o r tio

{1 \p j

n

(3 4 8 ) le a d s ,

to

d e n s ity is d e s c r ib e d b y

a

po w

er

lle d th e

d itıb t7 ric e r o tı tı e n t d e n o te d y a ; th e pru p d e n o te d K i ) s d .. he e te i m in e d b s y s te m (it is a d ir e y th e p r o p e r tie s o r t c t fu n c tio n o f th e e ı m ņ p y ) In c o n c lu s io n ł a r e c h a r a c te r iz e d b d ia b a tic pmcesL s ı y th e la w ,

e

,

P in th e an

K up

=

f a n o n r c l{ i ł t v is lic id e tll a s d 4 /3 in th e c g a se o l a r e la tiv i s tic

yn

(3



c a so o

«lc

o ıa c o tï tp le te

s e n e i n te

ly d e g e n

c le c tıo n

gas

e r a te e le c tro n

o r o

f p u ïĘ

È

it

ra d iıt

■ 阿 国 酽

Scanned by CamScanner

ı&

ï nlť rtrnclintc m Ų W X ï W \\W

S n th ľ

lhll

cusd

la !+ t

lı l \\b lï ï in ı o r

w

s TIL l\ i\N a m o

ı n

ix tu r e s

su c

,

n en

h

45

t

as

gas

an

d

u c ru lc ı y re la liv is tic d e g e n e ra te

ra

d ia tio

e le c tr o n

n

,

an

d fo

r

gas

c t in s id c tt d

g tls e s o l a fixed n u m b e r o l p a r tic le s : e ith e f in lh c u c c p s lc lı i ı a r in te t io r , o r (a ı m o s l) fu ı y r e c o m b in e d , a s n \l l n t u o ıs lc llm n o s p h e re w h e n io n iz a tio n ta k e s p la c e a n d u tı

,

n u n \h c ľ u

,

h ttl t

w c

i\ìn il c tł ł\

rh t o u lc ľ

tlw

v a lu t

Th ı a d ı ıb ・t ı c e x po

ts

r p ı\r tiĽ le s

th e r p h y s ic a l p r o p e r tie s , th e a d ia b a tic S in c e th is w iı l p r o v e to b e o f p a r tic u ı a r im p o r ta n c e to th e c

ha n ge s

ith th e

w

o

p \m c n ıL h n n g e s lu o s tn h ilil o l s lu r s il Łle s c r v e s

t \

s o M e d is c u s s io n W e s h a ı l o n ly c o n s id e r th e v e r y i s n g ly io n ir e d p u r e g a s (r a th e r th a n a m ix tu f e o f g a s e s ) s a y w c h a v e to d e u ıw ith th r e e d iffe r e n t t y p e s o f p a r tic le s : n e u tr a l

,

s in tp lc

? u o

Ľ

lw \ l\\ rg t

r

n

,

tł cnce

n

hu

h e r d e n s ity

,

d e n o te b y n o , io n s o f n u m b e r d e n s ity n + a n d l\ţ c t lc c lm n s t) ľ n u m b e r 山 n s ily II (o b v io u s l n = /ı ) T h e p re s s u r e e x e r te d y . + . h y lh c g a s is p m p o r titm a ıIo / 1o + II + ll w h iı h a s s d e n s ity is p r o p o r tio n a l t m e e ľ c «l o n \

w

.

sc n u m

w e

,

,

,

t\ì lło 十 ıł1

T ht

W h e i g is c re a te a n io

a c o n s ta n t a n

io n iz a tio n

.

d

by

n w e

°

R

re m o v

d Saha

'

s e

llim

[io lıis

d X is th e io n iz a tio n p o te n tia l (th e e n e r g y r e q u ir e d to in g a n e le c tr o n fr o m a n a to m ) In te r m s o f th e d e g r e e o f

q u a tio

n

(1 +

=

be c o

x

)(n

1

X

/ı +

ene

c a se o

/p

=

X

o

+

n +

)k T

x

2

F

rBy o f io n iz a tio

n

+

x

/ı+

)m

n

]

=

e

p

.

)7Z p T

(3 5 5 )

,

x

x

/m

H

,

w

ific

x

lk T

(3 5 6 )

rg y h a s a n a d d itio n a l te rm , h ic h is d u e to th e a v a ila b le p o te n tia l

spe c

,

/[(n o

(1 +

(kTÝ/ł g (ZTmcìlł -

f a p a r tia lly io n iz e d g a s th e n +

=

m es

X

In th e

d e fin e d b y

ha v e P

an

ų f io

lt } o

ene

T hu s

E q u a tio n (3 4 9 ) U s in g E q u a tio n s (3 5 5 ) a n d (3 5 6 ) to e x p r e s s th e d e g re e o f io n iz a tio n a s a fu n c tio n o f p r e s s u f e a n d d e n s ity x = x (P p ) d iffe r e n tia tin g E q u a tio n (3 5 7 ) a n d s u b s titu tin g in to E q u a tio n (3 4 8 ) y ie ı ds r e p la c e s

,

,

,

(3 5 8 )

Scanned by CamScanner

籤 難 E le rn

3

ı e n ta y

cs sı

ıy

a n

g

f

o

d

ra

d ia t io

n

46

H

苺 g ワ



F ig u

M

re

3 2 R a d ia tio

/p

ltip ly in g b y p

u

n

h n u x p a s s in g th r o u g

an

d

a s la

b lin g te r m

a sse m

b

w e

s

ha v e

-

(3 5 9) fr o

m

w

h ic h

,

a

fte r



y a (x

0

In th e lim it x

-

is

r x

o

b ta in e d fo

o r x -

)

-

o n s id e r a s la

b

o

ip u la tio

n

,

y a (x

)m

a

y be

c a lc u la te d

(3 60)

1

,

b ta in y a 1 6 3 fo r x

w e o

0 5 ; it is

f th ic k n

an

m

=

3 7 C

b le

n o t in c o n s id e r a

-

5 /3

/k T

=

R a d ia t iv e t r a

,

as

b e fo

1 fo ,

r

th e m in im

re

ex a m

p le

,

an

u m

v a lu e

d 1 2 1 fo r

n s fe r

dr

a n d d e n s it y p b e tw e e n p a r a lle l s u r fa c e s A a n d in F ig u r e 3 2 A r a d ia tio n H u x H (e n e r g y p e r u n it a f e a p e r u n it tim e ) in c id e n t o n A e m e rg e s a t B a fte r lo s in ic h h a s b e e n a b s o r b e d b th g an am o u n t d H , w h y e s la b (in r e a lit y th e s la b m a a ls o e m it d ia tio n w h ic h w o u ld h a v e to b e ta k ra y , e n in to a c c o u n t) o b i v o u s l th d ia tio n e y a m a , s h o u ld b e d o f u f b t n b e o a so r p r o p o r tio n a l to th e in i c d e n t fl u x an d t is , to th e d e n s it o f o th e a m o u n t o f m a te ń a l th a t a b s o r b in y g (s c a tte r in ) th g p a r tic le s a n d to h tr a v e lle d b th e t e le n g th o f th e p a y p h o to n s a n d h e n ce t

B

o

f u n it

a re a

,

e ss

a s sho w n

,

,

,

o

dH

.

th e ir

«

p ro d u c t H p d

ï lp d ,

r

W

e

m a

e e fo r y th e f

(3 6 1

四国国■圈■回国同

Scanned by CamScanner

Scanned by CamScanner

en

E le m

3

ta r

48

) and

ra

intuı e n lpe ı

X

]

a c la s s ic

n com m o

j

r ee a

re m o v a l o

o u tt

o

f a bo u n d

In th e d e e p

s te

h ig h e r

e le c tr o n to a

,

w

e x c ite

h e re b y

,

s c a tte r in

d

,

th e p h o t ' on

ex c

ita tio n

o

f

e n e r g y s ta te

n

is

em

r

b in a tio

a n a to m

s

n

a

g

w

ith

a

iz a tio

n the b s o r p tio n o f

n

du

to th e tr a n s itio n

e

b s o r p tio n o f a p h o to n s ly o r b y c o llis io n w ith

b y th e

eo u e ith e r s p o n ta n

r a c tin

p h o to io s e d b y th e

fo

(o r io n ) c a u

eco m r a d ia tiv e r

p h o to

a

b y b r ie fly in te

a

itte d

,

w

,

p le te ly io n iz e d F u r th e r m P la n c k d is tr ih u tio n is o f th e o r d e r o f k e v

in th e

g

h e r e te m p e r a tu r e s a r e v e r y h ig h , th e fir s t tw o in a n t s im p ly b e c a u s e th e r e a r e v e r y fe w b o u n d e le c tro n s

lla r in te r io r s

p ro c e s s e s a r e d o m th e m a te r ia l b e in g s

is

p a r tic le

th

(a fte r J J T h ' " n )

g

n

nam e a n o th e r

a n a to m

ff o m

e le c tr o n

is th e n d e

a to m

a n o th e r

p to

s ta te e n e rgy

h ic h is

w

b s o rp tio n

fan

B

T he

p h o to n

h ig h e r

a

ss T h e in v e r s e p ro c e p h o to n th e d b o u n d ü b s o rp tio n

a

4

o m

rtru

'

to tr a n s itio n

M a ke s a

o u lzd

C

as

kn o w n

se is tic c a , re la tiv

,

2

B

,

r in s c a tte

n h o rï rs o

(r a th e r th a n th e

. .

h a n ge s

e n e rg y c

3

l

.

in g irıv o lv

T

ri a s

kn o w

f ga s

"

se

th o

a fe d ia tio n

c ase

y pw

a lm

o st c o m

o re ,

w

,

th e e n e r g y o f m o st

h e re

a s th e s e p a r a tio n

e n e r8 y o f a to m ic le v e ls is o n ly a fe w te n s e v H e n c e m o s t h o to n s in te r a c tin g w ith p b o u n d e le c tr o n s w o u ld s e t th e m fr e e T h u s b o u n d b o u d n (a n d e v e n b o u n d fre e ) tr a n s itio n s h a v e e x tr e m e l lo w y tl p r o b a b ilitie s in t

e ra c

,

b e tw

p h o to n s a n d 加 e e le c tr o n O p a c ity c o e ffic ie n ts m a b e een

y

in te r io r s

c a lc u la te d ta k in ,

tio n s o c c u ï T in

g p re d o

m

in a n y

s

m e a su re d o r

g in to

fo

r co n

d itio n

s ty p ic a

la r l o f s te ı

a c c o u n t a ll th e p o s s ib le in te r a c tio n s b e tw e e n f d iffe r e n t fre q u e n c ie s T h is is a te d io u s ta sk th a t r e q u ir e s a n e n o rm o u s a m ount of c l a c u la tio n W ħe n it h a s b e e n p e r fo r n re d th e r e s u lts a r e u s u a lly a p p r o x im a te d b r e l y a tiv e l s i y m p le fo r m u la e in th e fo r n i o f p o w e r la w s in d e n s it a n d te m p e r a tu y re fo r a g iv e n c o m p o s itio n

d ifre r e n t e le m

e n ts a n

d p h o to n

s o

K

P e n d e n t (a

=

b

.

o ); it is

g iv e n b y IC

es

=

« op

a

T

b

(3 H



1

abo u t

0 0

th e n

is tı

,

(th e tim is o tť o p y

Scanned by CamScanner

e

3 7

R a d ia t ı v e tr a

L o g T (K

Fig u

re

tio n

o

3 3 0 p a c ity f te

lo g p (8

c m

he re

w

m

flic ie n

co e

fo

ts

d iffe

(in

u n its o

t d e n s ity

p

e r a tu r e

3

) (d a ta fr o m C A Ig le s ia s

ı ce s o

0 04

-

m

r

2

re n

'

kg

(0 4

c m

v

a lu

'

g

b s o r p tio n fir s t d e ń v e d b y H e n d ń k A K la w o f th e fo r m (3 6 3 ) w ith a - 1 a n d b

a

,

o

h e re

c o m

p le te io

h a s th e

v a lu e

f a bo

t 20 %

o

u

e le c tr o n s

7 5

iz a tio

n

10

×

E le c tr o

; b o th

co e

"

is

n

5

m

a s su m e

kg

n s c a tte

ffic ie n ts ,

2

ram

es

an

d ×

d

K ff ņ

e rs ,

(

p o s itio

b e r s b e s id e

(19 9 6 )

A

,

s tr o

e ac

fu

n

a s a

h

curv e

n c

a re

p hys J 464 )

p a c ity r e s u 1ū n g fr o m fre e fr e e is w e ll a p p r o x im a te d b y a p o w e r

)

10 2 2

a re

c o m

o

d fr e e fr e e

an

n u m

o w n

,

an

la r

a so

7 /2 k n

K 7 /2 (7 5

ńng K

d

) fo r

g e rs

) T he

,

w

'

g

e s ; th e

& F J R

2

cm

)

2

f

49

n s fe r

o

E

=

cm

5

,

a s

X

g

p a c itie s

,

2

th e K r a m e r s o p a c ily

g

K

T he

7 /2

a re

c o n s ta n t r « '

) w ith

b o th d u

th u s p r o p o r tio n a l to

a n a c c u ra c

e to th e

th e

y

fr e e

e le c tr o n

' b e r d e n s ity a n d h e n c e to H . (s e e E q u a tio n (3 2 4 )) O p a c ity c o e ffic ie n ts fo r s o la r c o m p o s itio n m a te ń a l a r e g iv e n a s a n e x a m p le in F ig u r e 3 3 ; n o te th a t a b o v e a fe w 1 0 ¢K th e y m a y in d e e d b e q u ite a c c u r a te ly r e p r e s e n te d b y p o w e r la w s

n u m

o

f0 1

m

a v e ra

ge

2

'

kg

o

(1

p a c ity

o

2

'

cm

g

f s te lla r

)

,

an

d

m

仃 乙 ¢

,

,

T he

舀 巨

a te

ń a l (o f

s in c e th e a v e r a

so

la r

p o s itio n ) is o f th e o r d e r s ity is o f th e o r d e r o f 10 0 0

co m

ge de n



m ヒ

(1 c m ) T h e te m p e r a tu r e d r o p o v e r s u c h a r a d ia l d is ta n c e w ith in a s ta r is d ia tio n in s te lı a r in te ń o r s is a b o u t 0 0 0 1 K (e s tim a te d a s Ť / R ) T h is is w h y th e r a

0 01m

so

c lo s e

th e n

,

to th a t o f

is th e

m

(th e fu n c tio n is o tr o p y is

su

a

b la c k b o d y B

u

s o is o tr o p ic ; w h a t, t b la c k b o d y r a d ia tio n is a ı

in g o f a r a d ia tio n flu x fr o m th e in te ń o r o f F in E q u a tio n (2 6 ))? It t u r n s o u t th a t th e m ffic ie n t fo r th e tr a n s fe r o f e n e r8 y th a t r e s u lts in e an

th e s ta r to th e s u r fa c e

in u te d e v ia tio

n

s te lla r lu

in

th e

m

fr o

m

o s ity

r .

, . . .

Scanned by CamScanner

S0

3

Eı em

en

p h y s ic s

ta r y

f ga s

o

an

d

ra

d ia t io

n

=ż H

K

d p ta d

P

dr

C

an

d

s in c e th e ra

d ia tio n

be

m ay

a ssu m e d

to b e b la c k b o d y

ra

d ia tio

(3 66

)

n

,

th e

p re sstr

ni

3

Ąa c T

dT

3« p

A ń g o ro u

s

a v e ra e o g

p a c ity ,

dr

d e ń v a tio n

o f th is e u a ń o n le a d i q n g to th e c o r re c t e v a l u a tio is g iv e n in A n i d e p p n x A T o o b ta in th e to ta l f lu x F

(3 67)

,

o f th

e

c ro s s i n

,

ga

:

F

4 Jr r 2

=

Ąa

c

T

3

dT

3« p

3

ir ı)

u ðr u

g

m

a s th e

in d e p e n d e n t

dT

e

ha v e

n ow

g a th e r e d

su

(3 68)

F

p

/

sp ac e v a ri a

b le

3

4a W

«

=

dr

F c

ffic ie n t in f o

T

3

(4 ï r r 2 )2

r m a tio n o n

(3 70)

th e p h s ic s f y o s te lla r in te ń o rs

Scanned by CamScanner

4

N u cı ea

p ro

r

p la c e in

th

e ev o

ra

d ia tio

lu

m

sm

in

lu tio n o

ń g in a tin g fr o

h a n g e o f s ta r s is d u e to th e ir s u s ta in e d e m is s io n o f a n internal s o u r c e T h e e n e r g y s o u r c e th a t s u p p lie s th e

m

o s ity o

f s ta rs d u ń n g a ll fr a c tio n o f th e r e s t m

ig h te e n th

T he

c

s ta r s

c o n tin u o u s c

n

b e g in n in g o f th e tw o f c o n v e r s io n o f m e

t h a t ta k e

ce sse s

cen

m o st o

f th e ir life tim

in to

a ss

e ner

es

is

n u c le a r

y A lth o u g h th is

u la

a tte r

n

h a n g in g

o

f b o d ie s in to lig h t

N

a

h ic h

w

m

An

a

lis m

=

h ic h tu rn s

a

n ly re a liz e d a t th e 2 th e c o n c e p t n tc

a t th e

d lig h t in to b o d ie s is

d e lig h te d

s

w

ith ı ran

sm u

Is a a c N

rm

E

w

b e g in n in g

f th e

o

tu r y

th e c o u r s e o f

T h e fo

w as o

e n tie th

c e n tu r y w ith E in s te in s fo r m in to ı ig h t d a te s b a c k to N e w to

fu s io n

by

w

h ic h

e a r r e a c tio n s a r e n u cı

in

v e r y c o n fo r m a

b le to

ta tio n s e w to n :

c o r p o ra te

O p tic k s 17 0 4

d in to th e

s te

lla r

evo

g iv e n in S e c tio n 2 6 T h e p u r p o s e o f th e p n e s e n t c h a p te r is to e x a m in e in m o re d e ta il th e n u c le a r p r o c e s s e s th a t a r e b o u n d to ta k e p la c e in s t? s a n d th e e n e rg y e a c h o f th e m c a n s u p p ı y lu tio n th e o r y

w as

4 ı T h e b in d in g T he

e n e r g y r e le a s e

d

o r a

f th e

e n e rg y o

b s o r b e d in

a

t o m ic

a n u c le a r r e a c tio n

n u cı eu s

b e in g

a

fr a c tio n

o

f th e

n o t sı r ic tly c o n s e r v e d th e f th e p a r tic le s in v o lv e d m a s s to ta l m a s s o f th e p r o d u c ts d ifĺ e r s s lig h tly fr o m th e to ta l m a s s o f th e r e a c ta n ts th e d ifr e r e n c e d e p e n d in g o n th e b in d in g e n e r g ie s o f th e in te r a c tin g n u c le i A s w e

re s t m a s s e n e rg y

o

is

,

,

ha v e

sæ n

in S æ tio

n

2 6 th e g e n e r a l d e s c ń p tio n ,

o

f

a n u c le a r r e a c

ūo

n

is

o

f th e

fo r m (2 4 8 )

,



Scanned by CamScanner

N u c le a

4

p

f

52 o o unt th e a m w e e I o f ty p c le u s u n a f m a ss o

n

th e e g le c tin g

Q ijk

[(M

-

h e r e th e

w

A

se c o n

en e

(1 M

e

A

k

o n

de pe n d o

fm

10 6

o n

e m

by

e

v

a

is

su c

n in

h

ic

y

ber

o

f

r e a c tio n s

İ

f e n e r8 y

r e le a s e

J

-

pe r

n u c le a r r e a c tio n s r a te o

it

un

,

it

o

is h e

s id e v a n

em

vo

e

s,

A

i

IN

un

H

s m a ss e xce s

f

J) W

13

it m

H

(M

)

u

l+

th a t a p p e a r s o n th e r i h t g

by

A

,

c o n se rv a

lın H

)lcı

n u

e

Q

bu t

ij k

,

th a t m a s s

a ss u n

g iv

u r p er u n

į

p o in t

,

m e a s ur

e

M ev

s

a i dividit)ý p

in g

A

i

o v er

to o b ta in the

A j

s id e o

e

tim e s

u su a

For

o

p e r n u c le o t】

I q u a tio n (2 6) n le s s If n e u u in o s u e

f th e

e n e rg y e

tio n s

e x tr e m e

n

e n e rg y

pe i

in dec ı

be

e

d e u te r iu m

e le c tr o ' n s m

lly

a

p h o to n s th in m a n y

p r o to n

n u c le a r r eac

fie ld (P h o to n s i ), n w h ic h a c h a n g e in th e th e e m e r in g g p h o to n is s o m

f

th e b i

isotopes a i

hav e

ij

th e o

a s e le c tr o n

e n e r g y r e le a se d m m

en e

is o to p e s o f T h is im p ı ie a ls o u n s ta Ł

d iffe re n c e

p o in t in star ļ ļ v o lg m e u n i t Su

ffic ie

een

ev en

en

,

b

M g h te r e u tr in o s

e n e rgy

it

a se a t a

re

han d

ly p r o d u c d e in

A ll th

b e tw

e x c e s s v al u es

o lv e s

h ic h in v

w

,

oton

c ase

w ave

T he

ıL J ' " _ i d D ie e n e rg y (to b e turned in to h e a t) m a b y e p r o d u c e d b y th e n u c le a r r e a c tio n s o b ( r y o th e r p r o c e s s e s ) th e ir e n e r is lo st to gy , th e s ta r , w h ic h is tr a n s p a r e n t to n e u tr in o s T h e ' s e p a r tic le s ' le a v e th e s ta r w itho u t u n d e rg o in g c o l s io n s a n d s h a r in th e ir g n e t r a te o f e n e rg y r e le a s e is ą nuc q . . w h e re ą 4 an d n u c is g iv e n b ą u is th e n e u tr in o e n e y E q u a tio n (4 ) r8 y lo s t p e r u n it m a ss p e r u n it tim e N e u tr in o s a r e n ıu Æ

in th is

(4 3)

n o te

1

v e ry

yo n

of

r

e le c tr o m a n ĺ g

tio n o f b ar

2

p la c e d b y n ) th e n it tim e is n i tt j R ij k Q ij k

ld b e

a ss, w e

ijk

a y a ls o b e d e c a y in to a m

d e s p ite its b e in g a c le a r d a ta in u n its

,

(a r b itr a r y ) m

th a t c a n o c c u r a t th a t

d pe r

)c

f e n e r8 y r e le (2 4 8 ) th a t

per

i

c a u se e

p lo y e d ,

f ty p e

lu m

y b e in v o lv e d u s

to n

10

×

km

a

f tw

p r o b a b ility , is d e c e ı e r a te «

a

(4 2)

lle d

n i lıj s h o u

H

fo r th e te rm

A

k

to ta l r a te o

f r e a c tio n s

,

,

is in d e p e n d e n t o f th e c a lc u la te th e

n ow

j R ijk

m a ss u n

N

2

han d

ca

1 6 0 2 17 7 2

-

th e a to m

s in c e th e n u m

tim e

OU

)

n zH

(I ) = (M

i n e g a tiv e ) s

o r

a ss e x c e sse s,

W

A j

r ig h t

th e

d b y

An

c r e a tio n o

te d in ta b le s o M a s s e x c e s s e s a r e lis

r8 y v -

r e a c tio n

2

d iffe r e n c e (2 4 9 ) T h e

n

(w h e th e r p o s itiv e f

d in th is

e

hav

A ı)1? t H c

A M

o

e n e rg y

) + (J U j

j

d te r m

b e r E q u a tio

n u m

iıııH

(A + A

+

se r e le a

s ta rs

in

ce

ic le s th a t m Iig h t p a r t s s ib le o f se s o p 4 1) a s a ll m a s a tio n ( i te E q u r w w e m ay

sm

i

f

k e p la

ta

th a t

se s ro c e s

in v o lv in g

o m e n tu m

ly

g p h o to

n

se

ld o

T he

m

an n

re

a

X

. n

bre ak u p c o n te x t \

To th e

A

=

b in

5

an

d s art

e le c tf o n

o c c u rs

r e le a s e

S im pl)

p la c e

" 1

Ĺ

ih ila tio n

!a

In s e c tie

iur

Scanned by CamScanner

53

4 1

p l\\\tn h N ity li t n lų lu l 1o n ı

t m a tin \\ n

\ ł

pn ?

l tw

u

p n \d u e Ģ

\\ t\y ı

,

ľ ,

o n r e n c tı

N u «ı en r

llre

t\ n o u lt In

un m n r lľ n h ı

rn te ı

n n t in c u tr In o

o

Ĥ p h t t io

nn

,

d p a ir in s te a

itte d

o m

w

w

ith

a n e le c tr o n

he n

lf \y t\ p h o to n m a y its e lr lıin n ı p ln ? ų \l h y ł\ n c u lr in \t n n tln c u tr \n o p n d is a ffe c te d b y th e in o u \t ln \ \ lì n lr w h e n th c ľ n d in tio n {ie l w In \\ \ *\ \tü u tľ in o a n ı \ lt\ ? ł l ed c e lT o n is r e p a c l th c o ı l \ m ı\\łw n ų tlç t\l u u ıth c M ų IIH Ľ p ln Ñm tt T h e I o o o c k l tiz c d p a s m a e w łe n tit\lly tl q u a n ì u ť tlc lų c n llc \ l p lN s N IT)I? w lľ tuul ı in th is ť l\w b y ł i o r at cithe llt v e l y h ig h d e n s it e s I\ ll \ h c e w w p m L e s M l h c c u N o ln \p o ľ tu n t l m a te r ia ı a r e n c y o r s te l a r T ı w n c lu e to th c 11 lln s p w r y h ig h te n \ p e ın \u re s (t \r h u th ) 9 m ay i o s is a b o u t 10 R o l) th e y we m (th c m e a n ı n e u \r lw lì n th (1 l s te lla r n t»u tr n l 11n 8 c a u se < 1li? i? ttt lu c n Ľ u o ce i a m e a s u r e o f th e d iffe r e n T h c e n e m y \ų le łï s c u in a n u c lc ıtľ w u c tio n Q lj k s i d i n b l n g d th c p t o d u c ts T h e to ta b c ï ų w n th t h in t lin g c n c ľ g i? s o r ih c r e t\c ta n ts łtn b u t s n l o e " ; c f u n o b r e m u n c tio n o ıth e n u ť c o u ls e a ı e n e w ł u l a n u c le u s is u n g e le m e n t o r a m o o t t n e l m e e r m II( le o n d iHb t s ıo c w n th c b in L Iin g e n e r gy p ť r IŁ d iffe r e n t A ) l i w ith th c s a m e Z b u t is o ĺ u p c s o ıth c ł \m ţ c h e in ic u l c le m e n t (n u c e h r e s T h e re a re s ta b Je th a n o t e n ı s tıu c tu r o s a r c m o r e 7 h is im p lit s th t\t s o m e n u c ı h ittin g lig h t p a f tic le s s u c M ť n u c le i th a t s p o n tłm e o u s ly d e c iry b y e m s ttł tls o w ı ı d io a c tiv e + d th e s e a ıe c a lle d r a e c ay) o s itr o n s ( o a s c le c tn } rts (/i d e c a y ) r p h t e m it e n e r g e tic l i in a h ig h e n e r g y s ta te t a ix o m p ť s a n Łl th e r e a t ( ť ( irť d n u c e il T h e n u c le a r s h e 1ım o d e l, s im a r m o l s tr o n g ly b o u n d p h o to 11s Th e tĘ b y lecoming i th e s e p r o p e r tie s h ll m o d e l o f th e a to m e x p la n s in \tru n y \ţ s p c e ts to th c c le c tm n s e i o f b in d in g e n e r g y t re s u lt is th e v a r ia t o n F o ľ o u r p u t p o s e s th c im p o r ta n i F ig u r e 4 1 r e la t iv e to th e fr e e ith b n ť y o n n u m b e r A s h o w n n p e r n u c le o n w f th e b in d in g T h e g c n e ıa l tıe n d is a n in c r e a s e o th c h y d m g e n n u c le u s n t o m p l w m o n o to n ic to iro n (A = 5 6 ) a n d a s o w ith itto m ic m a s s u p l e n ıJ w ' p e r n ï ıc e o n h o u gh e r g y fr o m h y d r o g e n t r r is e o f th e b in d in g e n d e c lin e b e y o n d im n T h c s te e p s h o u ld e n in to h e liu m d Ą ' H e im p lie s th a t firs io n o f h y r o g d e u tc r iu m a n d H e Ta id e r a b ly la r g e r c le o n (u n it m a s s ) c o n s n t o f e n e rg y p e r n u s c a la tg c a m o u ı t? le ı a in e d b f h e liu m in to c a r b o n E n e r g y m a y e g i n s a y fu s io n o d e s l ı r c Ę t r h t a h n t a le s s e r e x te n t b y i n e s u p to ir o n a n d , to a f li h t n u c le i in to h e a v e r o w \\1ł

* l« \ \w

m

ı

,

,

,

,

,

,

,

,

b y /řł3 iu

g

o

u

b re a k u p

or

Jis s ia ıï o f h e a v y

e s d o w n to n u c le i in to lig h te r o n

ir o n

In

a

d iffe r e n t

h is m o f th e H b o m b fi t r o c e s s a s th e b a s ic m e c a n g n iz e th e ıs p f t re la te d f th e A b o m b A n o th e r im p o r ta n t a c h e m e c h a n is m o t s d A n o c e h s e d t n iı f n o s ta b le c o n fig u r a tio n s o r f a to m ic n u c le i is th a t th e i e iu e to ih c b in d in g e n e ig y o i n e d ia te n e ig h b o u r s ł i m o r e tig h tly b o u n d th a n its lLu 5 a n d fo r A = 8 : H e s = c o n te x t

,

Ęco w e ı

'

A

4 2 ) j¡

"

In S e c tio th e

a l\ o ī

pm

n

2 6

du c t

o

w e

f th e

h ł1v e

se e n

ea r Nu cı

o n re a c tı

ra

te s

l [e ra te o f a n u c e iu th a t tþ

a c r o s s s e c tio n a l a ıe

o

f

a

(ta r g e t)

r e a c tio n

n u c le u s

an

is

e s s e n tia lly

d th e

r e la

tiv e

ı

Scanned by CamScanner

四 国团团团■

e

o tt

!r

r

N u c le a

4

tM

a c pı

e ı ¢ t ta

in

e



sta rs

54

fhËr

-

e

a ' "

f °







斗 勇 黒 ご 币

6Li

名 目



드 っ

드 国

严 t

Fig u

re

v e lo c

M

4 I V

ax w

A to

a n a tio n o

f th e b in ?

n

g

en e

ic

m

rg y p e r

ig h t

Fig u

n u c le o n

w

ith b a r y o

o

v e lo c

S in c e

,

ity

o

f

a

p a r tic le

o

f

m a ss m

S e c tio n 2 6 ) a n d

as u

re d u c e d m a s s

is th e

[m

j /( g m

b a rr ie r a t a th e e le c tr ic

a re

p o s itiv e ly

s e p a r a tio n

a

c

d is ta n

ce co m

h a r g e d to d o ,

d is ta n c e d ,

p o te n tia l e n e r8 y

w

ith in

w

p o te n tia l 1 a

e an s

an

ber

n u m

s im

y

p ly

th a t th e

in te r v a l d

th e w

p r o b a b ilin u

d

aro u n

a

2

/2 k T ) d e c r e a s in g w ith in c r e a s in g g o t a t r e s t (a s a s s u m e d fo r s i m p lic ity In m

u

ldĺ eı

a ssu m e a

,

f

o

m a

gn 】

is illu s tr a e n e rg y o

C

l

o u ı o n ıŁ

,

W

e C

as

th

,

P ro d u c t P r e s e n ts a m o re d iffic u lt p r o b le m n u c le i h a v e to c o m e w i th in

m

n

4 2

re

e iıc o m ıÆ

ity o f th e in te r a c tin g p a r tic le s I a n d J m i + m g j )] T h e c r o s s s e c ti o n a l te r m ç in the

r e la tiv e v e lo c

g im g

b e in g

g

ld b e p r o p o r tio n a l to e x l p in r e a lity , th e ta r g e t n u c le i a r e n

S in c e th e y

w e m

,

v e lo c ity u w o u

is th e ir

w e

f th e in te r a c tin g g a s p a r tic le s F o r th e la tte r e Jlia n v e lo c ity d is tr ib u tio n (E q u a tio n (3 14 )): th is

ity

o f th e

H

in

o rd e r

p a r a b le so

to

in d u

to th e r a n

c e a n u c le a r r e a c tio n

ge

o

f th e

th e y m u s t o v e r c o m e th e

h e r e th e k i n e tic

e n e rg y o

,

g fo rc e C o u lo in b

s tr o n

f th e p a r tic le s e q u a ls

it w

a p p e a re «

q m m fic e it to p ro b a b i to c a iT y

in

co n n

e n e rg y s o o n a ft

O

a re s u c H th a t th e

c

o u lo m

b b a r r ie r is

(4 5)

śï n g u 2

T he C TO S S se

c o n c lu s

se t a t a

d is ta n c

e w

h ic h is

a lm o s t th r e e

ordrs

Scanned by CamScanner







ııı N u ıı * n o * r n * ¢ıı

r*

SS

ııı

.

( ( ・

置 百

I

(

鬼 O la \a n e e

Ile

I

N U g j l ・nneılra ıw e ll

ı

n a ln g (o ı

g y)

e

4

Fı gu

4 2 Shcntutic

re

e n c o u n lc r c

po

te n tin

th e w e

ıw

d by e

rc

cuN nucı

ı n n nı p re N e n ı ı n

tìu tlt)n ı

u e to th e ll th a t l* t ı

ll d e p e n d

n

ı lntlvo

e nr nucı

c ttľ c h a rg e \u c ı \e ı 1 tı o ı

th o rţ p u ls iv e

l th e C n u lu m h b u \T le ! to n m ì th c \

ı ol e

(a to m ic

'

an

d th c

rı w h e ig h t o ıth e b m nu m

sh o rt ra n r ie r im

ge

po

te n tia

ı

negNive

d th e d e p ť h

o

f

b e r)

c le a r ro m e ! T h is ittıd c ltı/w e r th u n th e ly p lc n l Ia n g o u l th c s tľ o n g n u h w m x ls Th e k in e tic (th e m r a l) is illutrilted « c h c m a lic u lly In F ig u re \ 2 In o ī e r l I te r lo l}i ls o ıilie u ĺ d o r o ık o v w h ile th ı) h e ig h t o f th e ı e n e r g y o l th e g u s in s te u r n l l o ľde r o l M eV C o u lo m b b tu T ie r a t n u c le a r d is lu n c e +i ls o i ie 11 \ľ te r o f th e tw e n tie th c e n tu r y W e c a n n o w u n t le i s ta n d w h y , tlu r in g lh e 1 s l q l\ł i Io tu k e p la c e in s ta ls s im p ly s ta ts jt w a s th o u g h t im p o łiFilb lc lb r H u c H In te r w tio n ł l l h o l T h e >in lu tio n īo th is p u z z le w n s p ın v id e d b y a p p e a re d n o t to h ċ # u lĺ lc o n l y S\ı n n rttio n ls h c y o n d th Ľ s c o p e o f th is te x t : A r ig o ro u N e x p ı q u a n tu m m e c h Į tn le s hi u m m e c h t\n le s th c lţ is t\ lìn ite (n o n v a n is n g ) fic e jt Io s a y th trl a c e o rd ln g Io q u tin ı i l 1o p c n c lr t\[o ih e C o u h ì m h h a ľ ľ ie ľ z\s if i\ tu n n c r e x is te d p r o b a bility lb ľ a p a r l c c m o w in 19 2 8 ı tì o 11c e l, tllscovettl b y G e o rg e G ı to c a r ry il th ro u g h T h l» q tıu n tļ rı lo u c llv l[ lti In tlo c Łl c n \lc u tu n n e llin g It Lv w w p tie d to o

f

n agn ı

,

.

'

,

,

,

In

c o n n e c tio n w

ith

Iļ m

y, h y lĮ o h o r l A lk in s tm

'



tm tl \ t itz l u u t e m i a n s in 19 2 9 g e n e r a tio n in H l111H c o v e ry s o o n a lLe J its U itł d i h i th u le a r t h e p o n e lr tılio n p ro h ttb llity , tl# c u lc u ltitc tl h y g n m o w u n w t t e n c a n b ll u ), th u s inctasing w ith u ı c ro s s s e c tio n , JFi p r o p o ľ llo m \l Io e x p l 1r B l ¢ / o a / o x p ( 1148 u z /2 k T ) W h e th e tìls t c o n c lu s io n , th e p r o d u c l ¢x p ( 1r Z /Z j a /« o łu )

e n e r8 y

,

,

.

Scanned by CamScanner

N

4 56

in c ıe a s e s e x po n e n t

co th e s e

and

c 】e a s nd de

It

c re a s e s w

na p o r tio

te r a c tin

"

n

.

Va :

th a t th e

l to th e m a x im

"

um

f th

o

e

F th e p ı 1y p r itıc lp le ı

o

" 3

6)

an

,

tr e n d

o to n ic

o ccu r w

,

le v e l o f th e

d to a n e n e rg y th e in te r a c tin g p a r tic le s c o r r e s p o n s i? (İ + J i w liic h is fo r m e d tb r a v e r y b r ie f p e r

o

f

,

p r o d u c ts K Shaþp e a k ãt th e r e s o n th e r e a c tio n

c ro ss se c

ha s

,

sho w n

be

can

"

i d d e c r e a s e s w ith in c r e a s n g c h a r g e s o fthe d h e a v ie r n u c le i w o u ld th e r e fo r e re q u irt o f h e a v ie r a n i l ty p e c a lle d r e s o lı R e a c tio n s o f a s p e c a

tu r e ith in c r e a s in g te m p e r a

io n g p a r tic le s F u s m t e h p e r a tu r e s h ig h e r a n d h ig e r hi m o n r e a c tio n s in te r fe r e w ith t s in

s ta rs

kfleohm (nzizjeł

-

U

in

i ith in c r e a s n g

es w

ues it v a ı v e lo c y r a ll e v o t is p r o ro d u c ra te , in te g r a le th e p a c tio n e r e h t i h t l a n d w it th e in te g m s fo r r u c w h ic h o c p ro d u c t

in

a ce pı

¢e ı h a t ta es t c e ss o r f p u c le a

an

In M īs

d L

,

n

co m

b e fo

re

th e e n e rg

po u n d m d e c a y in

th e r e a c tio n c r o s s s e c tlm

c a se

a n t e n e r8 y , s e v e r a

W

aı u

he

l o rd e r s

o

f

m

a

m

y of s

g in to

à

v e ry

g n itu d e h ig h e r th a n the

tio n s a t n e ig h b o u r in g e n e r g ie s

T h e ty p ic a l tim e s c a le o f a n u c le a r r e a c tio n is in v e r s e ly p r o p o r tio n a l to the r e a c tio n r a te F o r e x a m p le th e c h a r a c te r is tic tim e o f d e s tr u c tio n o f ty p e / n u c le i b y c o llis io n s w ith ty p e J n u c le i le a d in to r e a c ti o n s o f th e fo r m , g (2 4 8 ), w o u ld b e g iv e n b y ,

ri

T he

e x tr e m e

to th e c o n c e t o p

has o

fm

ly h ig h '

a ty p ic a l n a r r o w a g n itu

s e n s itiv

f ig n itio n

d e , fr o m

'

o

f

ĺn j R

-

ity

o

ijk

)

f n u c le a r

a n u c le m

fu e l:

\

r e a c tio n r a te s eac

te m p e r a tu r e ra n g e o v e r w

h

en ce

,

b y E u a ti q o n (4 4 ),

w e sho u

q

m o tio n

th e r e a c ti o n s be tw e e n S e c tio n 2 6 th e m T h e s im l p e c h a in

ld

qo p T

y be

(o r

n es

w e

c h a r a c te i r s tic a

A

re

le a ds

p r o c e ss) b y o rd e rs

n u c le a r

in c r e a s e s

r a te

ific a n t o

m a

d e fin e d H

r e a c tio n

h ic h its

n e g li ib le v a lu e s to g v e ry s i n th e te m g e r t a u r p e de e n de p n c e o f th e r e a c tio n r a te

to te m p e r a tu

ro u n

d th is

ll a p p r o x im

lly h a v e q

ra n ge

by a

a te d

o(

村 pT

n

or

(4 7)

,

o

th e p a r ti c u la r s t r u c tli

re

(e n e r8

f

\

a re c a l le d th e rm o n u l c e a r a s m e n tio n t , um ent s p r e s e n te d h e te a t re m a y be m

y s ta te s )

ill

b

o

f th e i n te r a c i tng

acc n u c le

i A d e ta ile d a c e

it it

Scanned by CamScanner

4 3

H y d r o g e n b ıım iıı Ł d ¢

,

ı*

57

p d=

p

f th c i» h y s ic s o f n u c le a r r e a c tio n s m a b e fo u n d in D o n a ld C ı ıS e l a s s i e a y to ı y lu r E v o lu tio n a n d N u c le o s n ıh e s i F s t P r irrc ip le s o ï S te ı is h e d h ı 0 6 8 n s y p u b iı o

3 T he F u s io an

o st a

m

H yd

bu n da n t

ro

ge

e le m e n t

burning

n

in

ly b o

n ew

f h y d r o g e n in to th e n e x t e le m u n te r o f th r e e o r fo u r p r o to n s

en co

is

s ta r s

m

h e liu m

e n t,

o

n

p d

ı th e p

hy?

o

w

h

y

i出 Z

c le m 】

ge n

ıa in

2

=

i

w

iıh Z

w

w o u

ith in

r e q u ir e

d ı

d is ła n

a

ı

=

f

ce o

ı f fe r m is T h e p r o b a b ility o f s u c h a m u lt ip le e n c o t M e r is v a n is h in g y iıım d o e s i to h e ı ıT h u s th e p r o c e s s b y w h ic h h y d r o g e n is e v e n tu a lly m m e d n aı f r e æ tio n s E æ h im n lv in g th e i t h a p p e n a t o n c e b u t g r a d u a lly th r o u g h a c h a n o d O b v io u s ly T lie ū r s t lin k o f th is c h a in s h o ırı l e e n c o u n te r o f o n ly tw o p a r tic e s

th e o r d e r o sm

no

,

,

,

c lo s

b e fu s io

n o

f tw

e in g p a r tic ı b a c k in to tw

o

w o

u c le a r

p r o to n s (b y th e n ho w e v e r u ld b e

u n s ta

,

,

fo

th e s r m n g in te f æ tio n

rc e

b le

d it

an

w o u

ld im

e

m

se

a r a te

re su

d ia te ly di si ne \ fo r d b y H «

t o f th is im p a s s e p r o to n s T h e w a y o u p Th e lo s e e n c o u n te r o f tw o p r o to n s B e th e in 1 9 3 9 : d u ń n g th e c h e a v ie ī tr o n th u s fo n ï u n g a e p r o to n in to a n e u m a y c o n v e rt o n h y d r o g e n d e u te ń u m o

) T he

16 e a

lt

an s

k in te r a c tio

n

.

s t a b le

is o to p e

o

f

,

,

p + p

W

e

n u m

th a t a ll th r e e

n o te

be r

is o to p e

3 ,

d

an

H

c

h a rg e

T he

n

u te

h e re y

n o w

ra m

o th e f ,

ca

m

e

+

o

a re

s

p tu

+

re s a

v

be ye d

p ro

to rıto

n u m b e le p to

b a ry o

n

fo

rm

th e

w

h ic h

H

e

tig h t

r

n

h e liıım

e 2

w

ńu

D +

la w

c o n s e r v a tio n

de

2

>

in d ic a te

ifie s

o n e

s

th e

em

D + p

is s io

f

o

n

3

>

H

+ y

e

e n e r g e tic

an

e w in g th e b r a n c b fo u o 3 e w ith f a H e is o to p

,

pho

f tw

n c o u n te r o 4

a

H

e o n e

e

+ 2P

to n

o

3

ill

w

is o to p e s

soo n

,

be

a iıd th e

te r o th e e n c o u n

3

H

+

e

3

H

4

>

e

o r

3

H

e

+

4

H

e

>

H

7

B

.

e

ca

lle d th e p

p l

c

h a in

th a t

Scanned by CamScanner



券 每 ■

四 四 国团团



-



ce

pe

a f

e Nu cı

4

H y d ro g

58

a c pı

ta k e th a t sse s

in

î

s

ta r s

u rn in g en b

r

參 Fig u

re

4 3 T he

is s io

em

n o

fa

n u c le a r r e a c

n eu

tio

n s o

d th e

su

b s e q u e n t c a p tu r e

o

B

p III c h a in

r e su

+

e

im

m e

tiv e

b o r o n is o to e p

d ia te ly b r e a k s i n to tw

o

4

B 8

H

e

u

P o n th e

co n

im p o r ta n ce d itio n s f o

o

+ p

8

}

e n u c le



f th e s e

hy d ro

4

2

v

ge n

B

8

B

H

s

,

e

+

e n u c le

H

i

" .

7

B

e

o

f

a

p r o to

n

in s te a d o f an

,

B + y 8

B

e

,

i e

4

tw o

e

by

B de c a s i y n to

8

r e la tiv e

L i+

th e c a p tu r e



T he

7

e

L i+ p

lts fr o m

7 r a d itta c

h a in

,

e le c tr o n

T he

c

f a n o th e r p r o to n to fo r m 7

T he p

d IU

an

tr in o 7

an

p I U

f th e p

e

+

2 4H



w

h ic h is M g h ly

and u n s ta b le



e

t c h a in

s,

th a t is th e b r a , te m p e r a tu r e

burning

,

n c

h iï ıg

ra

.

tio s

,

i uı

d

d

Scanned by CamScanner

o

f th e

e

le

p lï

p a bo

ve

3

a tu l e s

m

e n

ts in

v o

lv e d F o

r ex a m

g r a d u a lly b e tw 10 7 K th c p p Ill

l» le

een

c h a in

d iffe r e

n

r

x

th e Lr lln s itio n

Y

-

te m p e r a lu r c s o l l

O C C U RS ×

a

fo

,

c lo

m

3

×

\0

ľ ıo

K

an

w e v e r, a l s u c

Ho

in a te s

7

t h y d r o g e n b u ın in g p ľ o c e s s m a y ra v o

u ra

bı y

m

p

d 2

×

h h ig h

p e te

c o m

P \ to 10 7 K

pc ı ith ili e

to m w

p c h a in s a s w e s h a ll s e c b h o r tly ' T h e e n e ıg y r e le a s e d in th e Fo r m a tio n o F a n a p a r tic le b y fu s io n o F 1o u r P ıo to ly g iv e n b y th e diFlıe n c e o F th c m a s s e x c e s s e s o r fo u r p r o to n s a n d o is e s s e n tia ı

p

a

p a r tic le

n s n c

,

Q

p

4

-

p

ı

6

4 ( H e)

A M

(H )

26 73 M

=

e

v

is h e s ı tio n c h a in th a t a c c o m p itte d m e u tıin o s a l e th is ta s k m u s t a ls o tu r n tw o p r o to n s in to n e u tl o n s , tw o n e F t it is th e s e n c u tıin o s th a t w h ic h c a r r y e n e r g y a w a y fr o m th e r e a c tio n s ite (In a c , in th e in te r io r s o f b e a r d ir e c t te s tim o n y to th e o c c u r r e n c e o f n u c le a r r e a c tio n s in t in b le W e s h a ll r e tu r n to th is p o s ta r s , w h ic h w o u ld b e o th e r w is e u n o b s e r v a a c c o r d in

g to th e

a to m

S e c tio

9 3,

n

n

b y th e

n e u

w

he

ic

an

y

】e a c

) T he

s s s o la r n e u tr in o s

d is c u

w e

S in c e

b le

a s s ta

m

tr in o s v a r y fo r th e d iffe r e

n

t r e a c tio

n

c

a m o u n ts o

h a in

s:

fıo

m

e n e ıg y c a r r ie

f

0 2 6 M e v fo

J

d

r th e

p 111 c h a in h in g r a tio ), 2 6 M e v h m a ll p r o b a b ility (b r a n c w h ic h in c lu d e s th e b o r o n d e c a y , a s a s b le d w h ic h , tıa n s la te d f a c h h e liu m n u c le u s a s s e m a r e lib e r a te d o n th e a v e r a g e o r e ' " ' 4 ı 1 kg (6 × 10 e r g g ) in to e n e r g y p e r u n it m a s s y ie ld s 6 × 10 i d b y th e s lo w e s t r e a c tio n in th e F in a lly , th e r a te o f e n e r g y r e le a s e is d e te r m n e 10 " y r It m a y b e fir s t o n e w ith a ty p ic a l tim e s c a le o f a lm o s t c h a in , w h ic h is th e in fro m le s s l w in te m p e l a tu r e w ith a n e x p o n e n t r a n g g r o x im a te d b y a p o w e r a a c r e a tio n o

f d e u te r iu

m

to 7 2 M e v

,

fo

r th e

bo

ro n

d e c a y S in

c e th e

p

,

C

9

,

,

,

pp th a n 4

an

d

u

6 R

p to

o u

g h ly

,

w e m a

qp

N

p

p c h a in ly d o e s th e p l e x h ib its th e r o c e s s e s , b u t it a s o o t o n

an

4 4

d

w

p

a ssu m e

o(

pT

(4 8 )

4

r a tu r e q u ire th e lo w e s t te m p e i i ity e a k e s t te m p e r a tu r e s e n s t v

H y d ro ge n b u

r n in

am o n

g fu s io

n

ı t h e C N O b i c y c le g ı

ii n of n ta g e o f th e in itia l c o m p o s t o in C h a p te r 1 th a t a s m a ll p e r c e C N O ) n u c le i T h e s e n 1 e i m a y f c a r b o n n itr o g e n a n d o x y g e n ( a n y s ta r c o n s is ts o in w h ic h th e y h t tr a n s fo r m h y d r o g e n in to h e liu m in d u c e a c h a in o f r e a c tio n s t a i : th e y a re d e s tr o y e d l to c a ta ly s ts in c h e m ic a l r e a c t o n s th e m s e lv e s a c t s im ila r y d T h e p r o c e s s , w h ic h is a c c o r d in g ly n a m e c y c lic p r o c e s s a n d r e fo r m e d in a d in d e p e n d e n tly b y C ? l F r ie d r ic h e s te d b y B e th e a n th e C N O c y c le , w a s s u g g l d a r e s h o w n s c h e m a tic a lly in in 1 9 3 8 T h e r e a c tio n s in v o v e v o n W e iz s äc k e r p c h a in , th e p r o c e s s to o a s in th e c a s e o f th e p F ig u r e 4 4 W e n o te th a t h e r e h e s fo r m in g a b i c y c le E a c h o f th e th e tw o d iffe r e n t b r a n c M a y r a m ify , w ith

W Įn

re

y

e

ha v e

se e n

,

,

,

,

,

ay

,

Scanned by CamScanner

(

岣吻 昭 胡 加 利 叫

F ig u

re

4 4 T he

n u c le a r r e a c ti o n s o

t w o c lo s e d c h a in s th a t o

f

fo

on e

th e

n n 4

H

f th e C N O b i c y c le

e

By

C N O b i c c le i y n v o lv e s s i x r e a c tio n n u c le u s : fo u r p r o to n c a p tu r e s a n d tw o

s r e s u ltin

p

p a r a lle l

ı 4 15

15 16

I5

N +

ı

H

>

12

C +

4

H

e

P a r t in th e r o c e s s is c p o n s ta n t i n tim de pe n d u p o n th e c o n d iti o n s o f b

u r n in

17

e

g

; th e ,

N +

'

0

ı 5

>

H

N +

'

0 +

ı

0 +

'

H

>

N + 〉

-

H

}

H

>

15

e

+

g

d e c a ys

0 + y

+

+

V

ı 6

0 十ア

ı 7

F + y

I4

N +

4

H

e

r e la

m a in

tiv e a b u n d a n c e s o f th e s e c ie s p ly th e r e p v a ilin g te m e r a tu r e T h e p

Scanned by CamScanner

in th e

h a in

In th is

it is im p o r ta n t to n o te th ł\t w h ile tll d e c a y s a in d e p e n d e n t o f external c o n d itio n s c a tu r e re a c tio n s m » e x tr e m e ly s e n s itiv e to p te m p e r a tu r e H e n c e a v e r y w id e r a n g e o f burning ra te s is to b c e x p c c lc \l B u t o lıï y s o lo n g a s c a p tu r e r e a c tio n s p ro c e e d m o r e s lo w l th ı cł l) s A t th c e x tre m e l) ı n p dı y c

c o n te x t,

,

,

h ig h te m p e r a tu r e s fo r w h ic h th e s itu ıttio n is æ v e is e d p d e c ıry s w o u ld a c t a s a b o ttle n e c k to th e n u c le a r r e a c tio n s e q u e n c e Re a n lle s s o l te m p e n ıtu ıĘ T h is m a ) g o c c u r in e x p lo s iv e h y d r o g e n burning (s e e S e c tio n 1 1 6 ) T h e e n e r g y r e le a s e d in th e fo r m a tio n o f a 4 H e n u c le u s b y th e C N O c y c le is 2 5 M e y a fte r s u b tr a c tin g th e e n e r g y c a r r ie d a w a b y th e n e u tr in o s T h e tc m \ y -

d e pe n d e n c e

a tu r e

by

a s te e

p po

o

f th e

g e n e r a tio

e n e rg y

w

in b o th

ro le

P h y s ic s fo

M

h is

r

in th e

s

co

re a c

Butw w

in

tio n

a

ha v e

e

ith A

8

=

8

b u t th e

B

e

Heı iu

bu

m

f hy? o ge n h e liu m g a s s h o

se e n

in S e c tio

te m p e r a tu r e

(r e g a r d le s s

life tim

8

B

e

a

th a t a n

a

(4 9 )

e

is

o

o n

ce

p a r tic le

w

o

f

m a in

s o u rc e

ill

u

ld b e fu s io

iu he ı

16

10

s

m

m ean

f 10

8

in 10 w

K

co

e st a n d m pı f tw o h e liu m

n u c le

!T he

llis io

n

im

n

b v io

o st o

in

s ta n

u s

n u c le a r

b e fu

ay

s

B

n u c le

e

se

even

d in to

a

b e r y lliu

n ew

p r o b le m

w as

life tim

e m a

y

It is

a t th e

e

o

f

se e m

se e m

p a r tic le s a t in g ly n e g ı ig i

(¥

9

p a r tic le s th e re is a n o n v a n is h in g p ro b a b ilit) ith a s B e n u c le u s b e fo re it d e c a y s To p r o d u c e

o

,

o

f

p tu r e ha d a n

a n ct c a

n u c le u s

s f h i i B e and 4H e rg y le v e l c lo s e to th e c o m b in e d e n e r g e s o t e re a c t n g T h e re a c tio n w o u ld th e n b e a r e la tiv e ly fa s t ıe s o n a ï zï r e a c tio n R e m a r k a b ly en e

re s o n a n t e n e rg y

in th e K

e

le v e l o f

llo g g R a d ia tio

n

12

c

m

to th is

(s c a tte ń n g ) tim

T h e re fo m

lla r

i (c t p ł? tic le s ) e n u c le zw c o n fig u m tio n s ta b ı

s o lu tio n

a s th e

s te

t io n

o r re a c

e x is ts / ıo

S h o rt

b

m de

co

×

o

o

n

f

d b e th e p la y e d a c r u c ia l a rd e d th e N o b e l Ħi z e ť o r

s im

Th e

o

an

e

in g t h e t r ip le

burning

ly 2 6

o ne

rn

) TW



o rd e r o

f th e

bu n d a n

th e

e r e a liz e d s h o r tly a fte r w a r d s th a t th e s m a lıp r o b a b ility yı b e ry lliu m n u c le u s w o u ld b e g re a tly e n h a n c e d if th e c ? b o n

F re d H by

a

s o

«ed x im ı

"

p T

4 1 th a t th e r e

n

p ro v id e d b y E d w in S a lp e te r n e v e r th e le s s lo n g e r th a n th e

b le

oc

,

o

c a se

y a p p ro ghł

ro u

he w a s a w y y e a r s la te r in W i b t i n r u t o n to th e u n d e rs ta n d in g o f e n e r g y p r o d u c tio

an

4 5 A

be

lìr a y

b o th p r o c e s s e s o f h y d r o g e n burning e r e b r o u g h t to lig h t a t a b o u t th e s a m e tim

s,

e n e rg y

q

la w

w e r

qc N o

T hu

n r a te

,

n u c le

i

h

a

su c

(a t

L a bo

r a to r y a t

th e California ĺ n s titu te o f T e c h n o lo g y T h e

Scanned by CamScanner

M

4

¢l r p r Q ¢¢ lł u £¢

ı« * ı n ¢ta r ı pł

J

'

h r e e c r p lm ic ïe * w ith M 8 h k In ll l ¢ b a bił iı d t i n J ı l m e ą r u e i i o [ m ttın g w ł h # tttłn n p # ll# lh le p n rl» łb lllly lļ d e c ay * ı g a ıı rï tï łï tł( y tlö & try ) pł la e rc a c liu n th a t k a d s l0 th rttıt* h a llıJtft In iln ln # p rn c e « l» In iï ¢w o » g e Iz C tren¢ a m e o f lh jli re a c tio n ¢r f l h n e t e p e a ( n ï ł iı rıh łłrllłm m Jg l¢l ï ¢}ııï or lc u ïM 1 « û n o rgy ı» lo a * « d In + u c h a re iw ıln n l# c a » ily c a

l u ņ * ĺ rlïłų ï 1/ ( m k le u \ tle « « y ¢ ı

p

,

,

'

Q \,

=

4 3u

W he n

a »u

JZ A M ( C ) = 7 275 M

4 3 A M ( 51¢)

ĺ w c ic n l n u m b e r

o

Z P T

b y tb e lw

v

,

40

(4 lo

n u c le i h a v e a c c u m u la te d

f c a rb o n

ł w ¢m ji r e a » o n a b lc th a t u c a p tu re #

0(

e

by 3a

n a c tio n

d p o s s ib ly b y th e ir lo d ua p p a f tic ï e s In re a lity it M Bm

n u c le i, a n

n s

ld le a d to th e R tr m a tio n o f h e s v ie r a n d h e a v ie r ou b ili f b t h h o o a t r « e ķ ? c # r i a t b n b r e r e u r y r r l a C p e s v ef i th a t th e in c re d it in g o u o m p i l h h l i l t t n e t u e e a i s t u a o m t b n 3 c a a e h f f t ć m d a ix z t h e i h lo w e o n ]p a r e d w t t a t o ,

co u

,

he c o

m e# »m a

ll ï ï e n e e th e

¢ m

ly » ig n ific a n t a 12

rh c 1b a

e r8 y re le a iw e īı

n u m m a r iæ

b u n d a n e e Įi

w

d b y th is

4

C +

r e iw tio n

H

c a p tu r e r e a c tio n th a t ta k e s

16

e

ili 7 ]6 2 M

e

0

v , am

0 ı3 J k g ï g to 4 3 × ı a n d o x y g e n in re la tine

o u n tin

p ro d u c t# o f h e liu m burning a r e c a r b o n h ic h d e p e n d o n ie m p e r a ttıre T h e p r o c e s s is

,

p la c e is

th e

,

sho w n

s c b c m a ï ic a ll\

in Į ig u re 4 5 7

l a d in Jc d ï J o y le ta th e p re d ic tio n o f th e re m n a n t e n e rg y le w l in th e c a r b o n n u c le u s A « ! l h e liım ) 19 44l w ith re m a rk a ble ïb rc a ig h t, H o y le h a d p o ßtu la M th a t a tt n u c le i (n o t o n y o f s tm b u ild u p fM Jn lig b te r n u c le i b y ih tíio n re a a io n s th a t (a k e p Ja c e in th e in te ń o r t In o n ic k p u r# u in g th i# id e a , h e e o n # id e re d th e » y n tb a ij# o f e le m e n ts fr o m c a f b o n t ,

ed

ith th e s a lp e te r p ro c e # » a ¢i « ta rtin g p o in t H e th e n s h o w e d th a t th e o b s fo r lb r i? # u e : c o c o u jd b e m a d e to fit th e y ie ld s c a lc u la te d a ı ce ı )u n i« a b u n d a fł c¢ e la ił 4 to a le v above re a c ti? n s . I lh e ße + 11e J\e iıc tio n h a d a r e £o lla n c e c o r r e s p o n d in g 19 5 3 19 5 4 ,

m

w

.

/ v

7 7 M e v in th e

ı zc

n u c le u »

o the rw is e , th e in fe rr e d

F a g e r [o te # t th i» p r e d ic tio n H o y le d e te c t » u c h a [# v e ] c x p e rim e n ta lly

b ¢ t? o lo w

,

,

e ven eo

c o sm

ic

c a rb o n a b u n

dd da n ce w o

fir s t attemp lı a b o r a ï e d in th e

to

Scanned by CamScanner

4 I

C ır b o n

ıııdın

H *

O

O

Fig u

re

4 5 T h e tr ip le

Ex

e r c is e

4 ı C

p ro d u c e s

e

ot

10 8 K

p

10 5

a rb o n

5

×

burning

10 8 K

an

ly n u c le i n e e d

o c c u rs o n

in te r m w

a

e

a

d

o u n ts

(m

fu s io yge n

n ot

be

a ss

n

o

f tw

>

n

(8 B e ) : n (4 H e )

1 : 1 09

3

cm

fia c tio l1s ) o f c a r b o n

n

a n

d

c a rb o n

o

o x

and

yge n b u

n u c le

i

ox

rn

b b a r ie l

,

,

,

fo r a t th e in te r m

if h e liu

m

burning

yge n

in g

q u ire s te m p e r a tu re s a b o v e s till h ig h e r C o u lo m b b a r r ie r

re

h a v in g to o v e r c o m e a in e x c e s s o f 10 9 K ı n te r a c tio n s

burning

c o n s id e r e d

o u lo m

g

=

Ca rbo

t te m p e r a tu r e s

d ia te C

ith th e m

o x

;

th e e n e r g y g e n e ra te d p e r u n it m a s s

4 6 C

o

z

p ro c e s s

a lc u la te

qu a l a m

b u tn M g

-

T

b ıım ł n s

.

o f c a rbo

n an

d

o x y ge n

e d ia te te m

e i a re c a rb o n n u c ı

p e r a tu r e r e q u ire d b y th e q u ic k ly e x h a u s te d b y in te in c tin g

s e lv e s

' T h e p ro c e s s e s o f c a r b o n a n d o l o x y g e n burning a rc v e ıy s im ila r in b o th c a s e s e v e l a n d it s u b s e q u e n tly c o m p o u n d n u c le u s is p ro d u c e d a t a n e x c ite d e n e rg y ı

de c a y s s e v e ra l d e c a y

,

o p tio n & a r e o p e n , w

,

ith d iffe re n t

,

temperatureependent

Scanned by CamScanner

=

国 团团

p ıo

- ・"



m O ņ )g e n b u

i p r o b a b ilitie s (b r a n c h n g 12

C +

"

C

}



O a bo u t

n

r e a c tio n c

th e a v e r a e g

]l6 M

P a r tic le s ,

ev

fo r

su c h a s

,

)

M g + y

23

M g +

23

N

a

+ p

N

e

+

16

"

0 +

O

n

»

ce

0 + 2 ce

h a n n e ls

13 M

ns

+

m

theheaynucleipret ,

3Z

s + y

3r

s +

3'

p + p

28

s i+

n

a r e a c tio n

2 4 A n + 2a

a re s h o w n s c h e m a tic a ll

ev

e a c h 16 0

? g@



24

16



ť

g

r a tio s

2o

T h e p o s s ib le

=

*@

-

are 16

0

r e a c tio n

he ?

be c åu

r e le a s e

m

nu

se o

f th e

,

d fo

r

e ac

h

tin

g

am o u n

?

i

w iç h

r e a tiv e

y

a re o w

c

m e

d ia te ly

o u lo m

b b a©

im

zs

N

US

Scanned by CamScanner

4 7

s ilk

T ıb l* 4 ı M

rı ıin

j

a or nuc ı ear

n u 《ı * a r ıt a



u c le a r

fu e l

P ro

H

H

10 0

C

C + C

600

0

0 + 0 N uc eq

10 0 0

Si

Æ d iffe r e n t i s o E a

c

H

e

6 25

O

0 61

N Ą M g M g S S i C o Fe N i

0 54

C

0

30 0 0

N

e

ily p ro d u c e d b y fu s io n o f c a r b o n o f o x y g e n T h e m th o u g h o th e r e le m e n ts burning S s ilic o n (2 8 S i) a ı ,

4 7

S iı ic o

n

bu

rn

in g

n u cı e a r s ta

3 «

r e a c tio n s ,

££e a tie d b y s e c o n d a r y

m

6 55

H

15

3a

e

n u c le o n

p r o d t«c ts

4

p p C N 0

H

E n e rg y p e r (M e v )

d » \&

( \Q fł K )

c e ss

65

m ı ib r ı ıı u ı 则能 k a ı《 ı

burning p ro c e s s e s fd »

N

m

bu

e n

0 18

b e s id e s th o

a r e a ls o

fo

d by

p r im

ar

yge n t s ig n ilic a n tly a b u n ? n

a o r n u c le u s

j

se

rm e

o x

ib r iu m t is t ic a l e q u iı

l i u ld fu s e g y th a t tw o s ilic o n n u c e c o i th e e n d p r o d u c t o f th e n u c le a r fu s o n m o s t s ta b le e le m e n t , i i l la r g e A t n r e a lity , h o w e v e r th e C o u lo m b b a rr ie r h a s b e c o m e p r o h ib t v e y c h a in ı h e th a t w o u ld b e l te m p e r a tu r e s a b o v e th e o x y g e n burning r a n g e b u t w a y b e o w t o s l f r o c e s s ta k e s p la c e It in v o lv e s re q u ir e d fo r s ilic o n fu s io n , a n o th e r ty p e o n u c e a r p h t n s w h ic h a r e c a p a b le i th e in te r a c tio n o f m a s s iv e p a r tic le s w ith e n e f g e t c p o o tic p h o to n s a f e c a p a b le o f b r e a k in g o f d is in te g r a tin g n u c le i, m u c h a s le s s e n e rg e T h e p r o c e s s c a lle d p ìio to d is in te g r a tio n is u p a to m s b y te a f in g e le c tr o n s a w a y ıo f a to m s , e x c e p t th a t th e b in d in g fo r c e o to io n iz a tio ı s im ila r in m a n y r e s p e c ts to p lı l i in s te a d o f li h is n u c ]e a f , in s te a d o f e le c tń c a n d th e e m itte d p a r tic le s a r e g t n u c e i ti r e a c tio n s c a n p r o c e e d b o th w a y s a n d e q u i e le c tr o n s A s in th e c a s e o f io n z a o n , di th e p r e v a ilin g lib r iu m m a y b e a c h ie v e d w ith r e la tiv e a b u n d a n c e s d e p e n n g o n o 2 16 N e + y , fo r e x a m p le p r o d u c e s 0 + ce a c tio n p h y s ic a l c o ĺ ıd itio n s T h e r e 9 b v e 1 5 × 10 9 K T h e i i s a ro u n d ļ 0 K b u t fe v e rse s d re c t o n a o

In p ń n c ip le w e m to c re a te ir o n th e ,

ay n o w

by

a ss u m e

a n a lo

,

,

,

,

,

,

,

,

,

p e r a tu r e e n e r gy a b s o r b e d in th e in v e r s e r a d ia tio n fie ld n e o n a t te m

S ilic o

n

d is in te g f a tio

a r e r e c a p tu r e d

by

n

,

re a c

tio n

o c c u rs a ro u n

(p h o to d is in te g r a tio n ) is d 3

×

10 9 K

i b u ild in g

o th e r s ilic o n n u c le

,

u

p

su

p p lie d b y th e

p a r tic le s e m itte d e tw o r k o f n u c le a r

th e lig h t an

e n tir e n

lig h t p a r tic le s e x c h a n g e d b e tw e e n h e a v y n u c le i A lth o u g h th e w h e r e d if e c t a n d in v e r s e r e a c tio n s o c c u r a t n u c le a f f e a c tio n s te n d to e q u ilib ń u m (a lm o s t) th e s a m e r a te th e r e s u ltin g s ta te o f n u c le a r s ta tis E c a l æiu ilib r iu m is n o t d th e s ta b le iro ń g r o u p n u c le i (F e C o N ir w ï iic h \ r fe c t a Je a k a g e o c c u r s to w a r h 7 × 10 9 K r e s is t p h o to d is in te g r a tio n u n til th e te m p e r a tu r e r e a c e s T h e m a jo r n u c le a F b u r n in & p r o c e s s e s th a t w e h a v e e n c o u n te r e d a n d th e ir i â m a in c h a r a c te r is tic s a r e s u m m a r iz e d in T äb le 4 1 T h e r c o m m o n fe tu r e is th e

re a c

tio n s , w ith

,

,

,

,

-

Scanned by CamScanner

4

66

l e n u gy f c n c tg y J c Jc a s u

r e le a s e o o

N

t h a t ta ¢l e 1 p ro c e

J c le a r ı

o n su m upo n c

v a ry ,

p tio r】

o

n o rm ho w e v e r c

k e p lm

e

ip

ï

ta r s

o u n t# a n d th e r ą lç # fu e l 丁h e a m f r】u c le a r o r r a l e p c e tĺ « e s th a t ab#ïrr,b uc n t u B o u a ly

o r c is e

u e 4 2 E s lin la te 1 f e ls n t n u c le a r u

th e d illb re

T ıin tts s u ı

by no

a u n t iı

E iï ł e r ı

ly , o e c ia ı an d esp r b s o rb e d e n e g y in g w u n lo ra ll o o b ïn f a h c l h e t d e p e n d in g o n s s e d in e s d is c u e p ro c e s s h t e r a h c S u u b s o J p tio n

Ex

4

in im

m

a

Ja r m ls te ı

a c c o r d in

r o file s it 吕 (a ) a d e n y p

g

as

to th e

ir e d iH s r e q u

fo r t h e

th r e s h o Jd tE

m

]2

in E x e r c is

n

th e r a te o f e n e r

s e c tio n s

c e n tf a

p e r a tu r e 8 o

(b}¢ olar

co m

l ig n itio

n o

n

w a

c r e a te d

gy

f

n

o

f he a v y

em eı

en

ts

w e

ha v e

th e s

a n

d

r

p ro

ce sse s

o

F th e

s a m e e le m e n t

]$

d e c iıy s

in d e p e n d t m

erM

y c h a n ge i t e n s m ay

æ e a r din

T he

g

M

c o n s id e i e d c h a r g e

pe s



r

h

m a

r e tsu ltin

g

ieii

ra a r

c lıa im i o

c a lle d th e

W

f

re a

£a n

w m

a n d G e o f ĺ fe B tn b y f 1 9 5 7 ) T h is is illu s l

a rg a r -

p\

th u s c r e a tin g h e a v ie r a n d h e a v ie r is o to

/

e £c a

ui % ta ï ı

(c )

h i r a te s b e in g c o n d p a r tic le in te r a c tio n s t e r tio n s o f n u c le i w ith a c t e r i d n o m b b a r r ie r a n h Couı tro lle d b y th e h e ig h t o f t e t m p e r a tu r e s A n o th e r ty p e o f in te r a c e e ffic ie n t a t h ig h e p h o to n s w h ic h b e c o m h ic h a r e p r o d u c e d d u r in g e o F fr e e n e u tr o n s , w tio n b e c o m e s p o s s ib le in th e p r e s e n c b y h e a v y n u c le i b u r n in g N e u tr o n c a p m ï e y r e la tiv e ı c a r b o n o x y g e n a n d s ilic o n f r o c e e d a t r e la tiv e ly lo w is n o t lim ite d b y th e C o u lo m b b a rr ie r a n d e a n th e r e o r e p f t n c a p tu r e r e a c tio n s is th e o u r n e h o a w y te m p e l a tu r e s T h e o n ı y o b s ta c le in t e s c a r c jty o f Ĥ e e n e u tr o n s A c h a in o f a b le S u p p o s e a s u M c ie n t n u m b e r d e n s ity o f n e u tr o n s is a v a iı i d h l i m o r e n e u tr o n s r e a c tio n s w o u ld th e n b e tr ig g e r e d w it n u c e c a p tu r n g m o r e a n S o Ib r

A

e

c a se

c r e a t io



T he tim

n d c g c n e ra c y

4 8

)

In th e l» # )c e $ s ju l t J9 d e e a y $ a n d M ro ty e » f p t) n u c le i m iw o f w w I , tin d e r tr a c k s a æ o p e n a n d th

fTb ] e 4 1

p o s itio

M a b łe Ħıa

r o

p r o d u c ts

a ī e la b e lle d s ū b e p r o d u c e d b y b o ih a ï e In th e c o u r s e o f ū )e se c o n

d a ry

re a a

b u n da n

ces o

f e le m

as a

W

io n s em s

w s

m

an

he

a lr e a d y s e e n in lig h ť a ll th e m a io r fr a c tio n (le s s th a n ı% ) ? e

have

in to

m

ass

D

u

is a ı e s o p o s s ib ı ń n g th e in te m c ti

p o s itr o n p a r tic ļ e p a ir p r 2 p a r tic le s h u > 2 m e c 1 o u s c o n s e rv a

S o lo n g

IN is s ta b le , th e

c h a in o f n e u tr o n c a tu r e s m a y c o n tin u e b u t e v e n tu a lly p , tiv e is o to p e s h o u ld b e fo r m e d S u c h a n is o to ld e w o u s u b s e q u e n tly p d e c a y b y e m ittin a n e le c t r o n (a n d a n a n tin g e u tr in o ) th u s c r e a tin a n e w e le m e n t , a

as

ra d io a c

g

If th e w

n ew

is e it m ,

e le m e n t is s ta b l e ay u n

d e rg o

,

it

a s e r ie s o

w

ill r e s u m

fp

io n

o

fm

o

c o n d itio n fo r p a ir p to d u 10 y ie ld in g T H 1 2 ×

f p h o to n s a a lr e a d y s u ffic ie n tly e n e

n u m

be r

th e

in v e r s e

o

re a c tio n

te n d s to d e s tr o y th e n e th e c h a in o

de c a ys

f

n e u tr o n c a

p tu r e s O th e r

re a c h e s e q u

ilib t iu m

e

F

th e io n iz a tio n p r o c e s s

b e r o f p a r tic le s a t th e T hu s o p p o s ite e ffe c t ,

Scanned by CamScanner

bı e n

u n til a s ta

E ith e r w c re a te d

u c le u s o

y

m a

d tw

an

f

o

,

ju s t d e s c r ib e d

c e ss

? ac ks a re o

T he

an

pe n tim e s c a le s

ty p e s

o

c o u rs e an

,

d th e

u n

o

fn

o n

i

s ta

ly

ic

b le

be r z + M

nu m

d th e ir

f

re a c

an

n e u tr o n

d e pe n d s

o u tc o m e

m

tw o ty p e s o

u c le

d e rg o

d a to

e n ts a n

,

p de c a y s i

A + N

ass

y in c r e a s in g ly h e a v ie ı e ı em

a

In th e p r o n u c le

fm

d

p ro d u c e d a f e th e r e b y

s a y , is

b le is o to p e s

s ta

tio n s

p tu r e s a n d lv e d S ta b le

n e u tro n c a

u n s ta b le

a re

p tu r e s ; fo es tim e s c a ı

ca

o n th e

,

in v o

r u n s ta o

b le

f th e tw

o

o nes

b o th

p ro c e s s e s

f þ d e c a y s (o r h a lf life tim e s o f ßu n s ta b ı e is o to p e s ) a r e c o n in d e p e n d e n t o f p re v a ilin g p h y s ic a l c o n d itio n s T h o s e o f n e u tro n c a p tu f e s

s ta n ts

m ay chan

o

g to te m p e r a tu r e m o r e Ñ o w fy o r m o r e

a c c o r d in

ge

đm ity H

e n c e n e u tr o n

c a p tu re r e a c

p e tin g P d e c a y s fo r m e r o f r e a c tio n s a n d p ro d u c ts w ill b e d iffe r e n t in th e T h e re s u c o in e d b y c a s e c a lle d th e s p r o c e s s a n d in th e la tte r c a lle d th e r p r o c e s s (te r m s M a r g a r e t a n d G e o ffr e y B u r b id g e W illia m F o w le r a n d F re d H o y le in th e ir s e m in a l 7 w h e r e th e s p r o c e s s p a p e r o f 19 5 7 ) T h is is illu s tr a te d s c h e m a tic a lly in F ig u r e 4 d th o s e w h ic h m a y l d p r o d u c ts a r e la b e lle d s th o s e o f th e r p r o c e s s a r e la b e l e r a n

p ro c e e d m ltin g c h a in s

tio n s m a y

,

ra

p id ly th a n th e

co m

,

,

,

,

,

b e p ro d u c e d b y b o th a r e la b e lle d s T In th e c o u r s e o f th e m a in burning p r o c e s s e s th e s a n d r p r o c e s s e s o p e r a te lts a lth o u g h th e a s s e c o n d a f y r e a c tio n s a n d a w e a lth o f n u c le a r s p e c ie s r e s u J

,

,

a

bu n d a n c e s

o

f e le m

e n ts

h e a v ie r th a n ir o

4 9

W

a lr e a

ha v e

e

dy

in th is

se e n

c

n a r e r e la tiv e

P a ir p r o d u c t io

h a p te r

m an

y

e x a ]n

ly

sm

a ll

n

p le s

o

f tr a n

sm u

ta tio n s o f m a s s

lig h ť : a ll th e m a jo r burning s ta \ s r e le a s e e n e rg y a t th e e x p e n fr a c tio n (le s s th a n 1 % ) o f th e m a s s B u t th e r e v e r s e ? a n s m u ta tio n in to

'

se o

o

f

a sm a

ll

f lig h t in to

p o s s ib le D u ń n g th e in te r a c tio n w ith a n u c le u s a p h o to n m a y tu m in to a n e le c tr o n id d its e n e r g y h u e x c e e d s th e r e s t m a s s e n e r g y o f th e p o s itro n p a r tic le p a ir p r o v e 2 e o f th e n u c le u s is r e q u ir e d fo r th e s im u lta n e p a r tic le s h u > 2 m . c T h e p r e s e n c T h e ty p ic a l te m p e r a tu r e a t w h ic h th e o u s c o n s e r v a tio n o f m o m e n tu m a n d e n e r g y m a ss

is

a ls o

,

,

,

2 i ń d m a y b e e s tim a te d b y k T H h u H 2 m e c p a ir p r o d u c tio n is s a t s e " 10 9 K a la r g e 1 2 × 10 K H o w e v e r e v e n a t te m p e r a tu r e s T y ie ld in g T a re a t th e ta il o f th e P la n c k d is tr ib u tio n fu n c tio n (3 3 9 ) n u m b e r o f p h o to n s it i A t th e s a m e tim e a lre a d y s u ffic ie n tly e n e r g e tic to p f o d u c e e le c tr o n p o s r o n p a r s th e in v e r s e r e a c tio n a n n ih ila tio n o f e le c tr o n p o s itr o n p a h s in to p h o to n p a ir s

con

d itio

n

fo

r

,

,

,

,

te n

d s to d e s tr o y th e

ly c r e a te d p o s itr o n s A s a r e s u lt th e n u m b e r o f p o s itr o n s P a ir p r o d u c tio n , a s p h o to d is in te g r a tio n b e a r s s im ila r ity to

n ew

,

q u ilib r iu m th e io n iz a tio n p r o c e s s : a n in c r e a s e in te m p e r a tu r e le a d s to a n in c re a s e in th e n u m b e r o f p a r tic le s a t th e e x p e n s e o f th e p h o to n e n e r g y ; a n in c r e a s e in d e n s ity h a s th e 9 o p p o s ite e ffe c t T h u s a t a fe w tim e s 1 0 K (d e p e n d in g o n th e e le c tr o n d e n s ity )

re a c h e s e

,

,

,

Scanned by CamScanner

u

ıo

a

N



马 Fig u

4 7 S c he m

re

ūo n o a tic r e p r e s e n ta

d th e r p r o c e s s s h o w in g re a c p ro c e s s a n le a d in g to th e fo r m a tio n o f a n d þ de c a ys

f th e

l e n e u tro n c a p tu r e s tio n c h a in s th a t in v o v

s

,

,

f r m e d b y o n e o f th e p r o c e s s e s (re spec i a rk e d s r o r s r a r e o p e s N u c le m S t lla r E v o lu tio n a ird C la y to n (19 8 3 ) P rin c ip le s o f e d a p te d fr o m D h a b t b o ( r l o i v e t y y) f C h ic a g o P r e s s ) h e s is U n iv e r s ity o t n N u c le o s y s ta

b le is o

to

,

,

,

,

,

ifi n t fr a c tio n o f th e n u m b e r o f e le c tro n s b e r o f p o s itr o n s b e c o m e s a s ig n c a 9 m u c h le s s tha n e r a tu r e o f a fe w 1 0 K ( t w e n o te th a t h a v in g a lo t o f p a ir s a t a e m p d en id e r a b le fr a c tio n o f, s a y io n iz e d h y ro g 9 1 2 × 10 K ) is s im ila r to h a v in g a c o n s 6 v 4 15 × 10 4 K , c o rT e s p o n d in g to X - 13 e ) l th a n a t a fe w 10 K (m u c h e s s th e

n u m

,

-

0 4 ı If

su

su rv

ı ro

n

p h o t o d is in t e g r a t io

n

ffic ie n tly h ig h te m p e ra tu re s a r e a c h ie v e d , e v e n th e s ta b le ir o n iv e p h o to d is in te g r a tio n T h e y b re a k in to a p a r tic le s a n d n e u tr o 56

Fe

13 4 H

e

+ 4n

do n o ( n u c le i n s,

,

Scanned by CamScanner

4 ı ı

dw

s r e v e r s in

g

h s o rb s

a

k in d

a

a

hn o

nt c n

n te ı ıł r ıt M p h o to d ł

ir c ly th c ı

b o u t 12 4 M

c

V

o

n u c k n y n ıı* pm c« ! #

l» h re a lio

r «ï r ı

f e n e rg y

o tı M n d m ıth a n lr lu m b e c o m e # m «)re ı o 9 K he ı A t te m p e r a tu r e s a b o v e 7 × ı i ha t th c m e rg o l l p l ln le g r ıle d b y f¡ s dı iu m lts e ı A t s till h ig h e r te m p e r a tu r e s h c ı tu r ı e m p e rł re q u in ¢ eı u s io n h o u n d n u c ı In to p m lo n s a n d n e u [r o n s ï n c o n c ı e b d ¢l¢o y 6 0 9 K ıo a a n a t to o w a fe w ı i K n o r d e r to b e c re a te d a n d b c ı 0 ] w k f » te lı a e r ll llc o c h ır a c ı f o temperature e n l h r i a t I e ı ı g T h is A s w e s h a s e e s p re c s e y ,

in te r io

rs

Scanned by CamScanner

ı 自 lb r iu E q u iı to n

Ħg u

s te

m

ı ı a r

p le

s im

r a t io n s

th e r m a ł q

m

u

ilib r iu m

d e ls

o

ı n te g r a titM th R o u

gho

in te r e s t

m

S ı The

r s tr u c

tu r e

e

q

t io n

u a

s

a

(o r

d ia tio

tu r e o

o f c h a p te r 2 w a s th a t th c e v o lu tio n o f a s ta 】 m a y b e p e r c e iv e d T ħe ia in c o o w ly a llo w in a q u a s ı s ta tic p ro c e s s in w h ic h th c c o ı n p o s itio n c h a n g e s s ı g th e ib r iu m a n d g e n e ra ı r Io m a ım a in h y d r o s ta tic c q u iı ly th e n n a l e q u ilib r iu m a s

s im

T h e c h a ın o F p r o c e s s e s th r o u g h w h ic h th e c o m p o s itio n r a d u a ll c h a g n ge s y b e e n d e s c r ib e d in th e p r e v io u s c h a te r O u r r e s e n t ta s k is to d p e s c r ib e th e p b riu m s tr u c tu r e o f a s ta r o F a iv e n c o m o s itio n th i h g ( s c a p te r ) a n d to fin d p h e ttłc r th e e q u ilib r iu m is s ta b le (n e x t c h a t p e r ) T h e (s ta tic ) s tr u c tu r e o f a s ta r is jn e d fro m th e s o lu tio n o f th e s e t o f d iff e r e n tia l e u a tio n s k n o w n a s th e s te lh ır q u æ e q u a tio n s Fo n n u la te d in te im s o f e ith e r o f th e r i e v l o u s p y e n c o u n te r e d ce v a n a b le s r o r m

(5 7 1

on n c lu s ı

m a

M

e

ra

n

tm

t io n s a r e

th e

fo

G

r

3

\R

r

«

p

F

dT

m

3 -

nuı ty

K

aı re a d y

m e

In t r o d u c tio

ly m n tio ıı

n 1o

irst p u b lis h

as

Ex

e r c is e

o

fa

r



4

In

F

s ta r

5 ı

by

钕 k P

p q

w

h a t fo

g a in e

d b o th b y s e e k in g s im p le

(4 1r r 2 )2

t/ F °

a lł i ł

a

4冗 r 2

1 4 Ī

dr

t

itu te

its s o l m i o

=

dT

n

w e re n o t o n

(5 1)

4 rr r 4

M

s e c o ııd ly cm

y

m

-

at

? te s b a c k to th t

w

d p

=

F

=

b ta in e d

,

s

at T

L

p le r b y fa r th a d iīs e lf to s im

,

c

sïa

y be de suppied T h c

be s t e lla

th e s t

o

u t th e

q

q u a llo n , th e th i d r i# thıĻc ı r uu d ia tiv e lľ i u I o n c o n {j m s tr e lu tc s th e ųnj q u ıttio n y IT lC ņ n s o l c rte l g y tl lln s lb r ) ł m

(p r o v id e «l r a d ia tiv e d th c lo

u l th

is th e

A fu n ?

m e n t&

ıin d in g

. la

a

pr

th e s u r fa c e to s ig h t th is

de n

70

Scanned by CamScanner

S 2 ta lq

d ıc m

u

iı ih r iu

m

qu

e

m

h

a tio n

P

a s lm

p p le m

su

pk

e n te

P T +

_

du o

n o

f th e s e d iffe r e n tia l e

u g h o u t th e

T

s tm

,

p

n z

q u a tio

(o r

r

ı ı ar m

d b y th e

Pe +

/T l

e g m tio ı nı

lte

ļ

a

T



d ıı ? dı

re ı a tio n s

4

(5 5 )

e s o F fo u r fu n c t to p ro v id e s th e p r o fiı ) a n d F fr o m w h ic h a n y o th e r fu n c tio n

n s

ns o

f

y b e d e r iv e d F o u r b o u n d a r c o n d iti o n s (in te g ra tio n c o n s ta n ts ) h a v e to y b e s u p p lie d T h e th r e e s tr a i h tfo r w a rd g o n e s a re a t ın = 0 r - 0 and F _ 0 at M (o r a t r - R ) P _ 0 A na m o re c o m l i p c a te d c o n d itio n r e la te s th e e m itte d F (R ) o r e u iv a le n tl n d ia tio n L _ h t q e e ffe c tiv e te m y to th e te m p e r p e r a tu re a m re o b ta in e d a t s o m e d e th b e lo w th e s u r fa c e A lth o u h th is s e t o f e u a tio n s is p g q s im p le r b y fa r th a n th e s e t o f e v o ı i u t o n e q u a tio n s d e r iv e d in C h a te r 2 It d o es n o t p ı e n d its e lf to s im p le a n a l tic s o lu ti o n s T h e r e a s o n is th r e e fo ld fir s t Th e e u a y q tio n s a r e h ig h ly n o n lin e a r p a r tic u la r ly in v ie w o f th e p o w e r la w r e la tio n s (5 5 ) to 5 7 ); s e c o n d ly th e y a r e c o u le d a n d h a v e to b p e s o lv e d s im u ı ta n e o u s ly ; th ir d ly th e y c o n s titu te a tw o p o in t b o u n d a r v a lu e l b r o h i em w y c h r e q u ir e s ite r a tio n s p fo r its s o lu tio n A n d y e t a g r e a t d e a l o f o u r u n d e r t d i s an n g o f s te lla r s tr u c tu r e d a te s b a c k to th e e a r ly d e c a d e s o f th e tw e n tie th c e t n u r y w h e n fa s t c o m p u te r s w e r e n o t o n ly u n a v a ila b le b u t in c o n c e iv b l a e E d d in g to n s b o o k w h ic h w e h a v e a lr e a d y m e n tio n e d s a w ı ig h t in 19 2 6 ; S u b r a m a n y a n C h a n d r a s e k h a r b s o o k A n In ın g d u c lio n to lite S tu d y O f S te lla r S tr u c tu r e a c o r n e r s t o n e in th e s tu d y o f s ta r s Jva s fir s t p u b lis h e d in 1 9 3 9

ia ıe ıe s t

m a

,

,

,

,

,

,

,

,

,

'

,

,

'

,

,

Ex

e r c is e

o

fa

r

=

In

s ta r

5 I D

b y T a y lo r

O pc Pc

w

e riv e th e

an

h a t fo llo w

ex

b e h a v io u

p a n s io n fo

r

r o

f ın (r ) P (r ), F (r ) a n d T (r ) n ,

g iv e n

co m

p o s itio

n an

e ar

th e c e n tr e

d p h y s ic a l p r o p e r tie s

at

d Tc

s w e

sha

lıs e e th a t in s ig h t in to th e

g a in e d b o th b y a n a ly s in g th e e q u a tio n s s e e k in g tiim p le s o lu tio n s b a s e d o n a d d itio ,

5 2

W ha t ı s a

s lm

w

ith o u t

a c tu a

s tru c tu r e o

ı ı y

n a l s im p lify in g

la r e s te ı pı

m o

s o lv in

assu m

ť

y be A n d b)

s tł u s m a

g th e m p tio n s

de ı ?

Scanned by CamScanner

u n brı ı ı ıq u ı

S

su c

h

ils s u m

\n ı

(ł \\1 h c

tie s p n )P C r

n

W

p ıio

n

ı pı

n o ı

d*ı ı

h t\n c lo v e n ! ı

b ıll ) u n t ıth e prcNurc y i ıilic u n tı y ıh u n g c s g ı ft»u n t l th t\t d o n o l

tling tt ) s in \p (ł\ctı

mlı ı iniLIt ł (w ı

m ıı

t

lc

n rc

c s tin t lıte s

Iu s tilic t l ıt w

tlu

0 r a s tu r w ı

ı t ıb c

h ic h is th o

ith

w

rn

b e in d e p e

d ia ı

so

g h ly

ro u

M

ix e d

m

A

s u r Ĥ lc e

t ı c th ł p ľ in c ip ı

ena

repnscntł ttion o r u

s m n i is th e

s u r fa c e

(th e

is

o

tco

h s u r fiıc e a r e p o in ts o n t e

ı y tic in v e

b le s

nn ana

s ta r

b y ils tw

u ıs e

s t ig a tio n

id e n tic a l b y

th e

p o in ts

o e x tre m e

tr ic t h p o in t in t e s th e s p h e r ic a l s y m

n o ta

l th e b e h a v io

o

se n se o

c e n tr e a n

f th e

w o rd

m e tr y a s s u m

p tio n

u r o

an

th e

d

d ic ta te th e

s in c e n u c le a r

evo

se e

g lo b a l q u a n titie s

in C h a p te r 7 , Fo r

un

now

,

rm

w

an

d

re la tio n s

) T he

W

lu tio

se t o

f s tr u c tu r e

ith o u t s o lv in g th e

w e sha

ll c o n s id e r

se v e ra

l s im p ı e m

ith

w

e e n th e m

ay

m

c o n s id e r e c

e n o w

b e tw e e n th e s e tw o

n a ry

pace

th e

ce n

w

,

o

be

h e re K

d Y ar d e f m e tı

an

to m a r y to

ith

w

an

e x tr e m e

tr e

q u a tio in d e x o f

s th e e

T hu

qu

r e la tiv

e

a tio n

o n

o

q u a tio o d e ls b a s e d

m o

s ta

d iffe r e n tia l e q u

e

on

b ta in e d ,

a s w e s h a ll

n s o n

th e p r in c ip le o f a

T he

s o lu tio n

d iū o

n s

an

T he st

à d p lď r

d p

ld r

titie s

P o ly t r o p ic

f

S u b s titu tin

th r e e

5 3

o

=

O

p a ra n w a s fu n

It is T h e firs t p a ir o f t l s e la r s tr u c tu r e e q u a tio n s (5 1 ) (5 2 ), is lin k e d to th e s e c o n d , P a ir (5 3 ) (5 4 ) b y th e d e p e n d e n c e o f p r e s s u r e o n te m e r a tu r e If th e p r e s s u r e p w e r e o n l a fu n c tio n o f d e n i y s ty (a n d c o m i i t o s o f n o p

co

by

,

c o u rse



a c c e le r a tio n

de ı s

,

i

ly ' p o in ť w h o s e b s e r v a tio n s In s o m e

it is th e

b e tw

a tio

b u t a ll

ifo rm p r o p e ıt y

,

a

ltip ly in g E u a l q

u

f

m o s t e v o lv e

is im p o r ta n t fr o m a n e n tir e ly d iffe r e n t p o in t o f v ie w m o d e l d e r iv e d p r o p e r tie s c a n b e d ir e c tly c o m p a r e d c a se s

co \

ld b e

d th e

p ro c e s s e s ld b e a b le to te a m a g r e a t d e a l d a r p t o f th e s ta r W e s h o u w o u ld b e id e r in g its c e n tr a l p o in t a lo n e T h is w ill b e a b o u t th e e v o lu tio n o f a s ta r b y c o n s ń ti th e s u b je c t o f C h a p te r 7 T h e s u r fa c e o f th e s ta r (th e g lo b a l s te lla r c h a r a c te s c s ) fa s te s t

f th is fo

d

S u b s titu tin g E q u

ı ı e m o n o to n ic a y i h a t p ro p e r tie s c h a n g h id d e n im p lic a tio n s t io n (5 I) a n d a ls o fo ľ t a E u q f th e p r e s s u r e fr o m i i c e r ta in ly c o r r e c t o r p o in ts T h s s 0 T h e la tte r fr o m E q u a tio n (5 4 ), F B y E q u a tio n (5 3 ) s in c e th e te m p e r a tu r e is s io n , w h ic h i th e c a s e o l s tr o n g n e u tr in o e m e s s a r ily c o r re c t n m n d itio n is n o ( n e c r e in v e r s io n t u r a e d m a y e v e n tu a lly le a d to a te m p th e n e t q n e g a tiv e a n n i a y tu m ic a tio n s l d is lle g a r d s u c h c o m p ı B u t w e sha ı l o n e o f th e e x tr e m e a y r e p r e s e n t a s ta r b y o n y m e w i n t o ific a A s a fu r th e r s im p ı d T d e c r e a s e o u tw a r d fo r e x a m p le A s s u m in g th a t b o th P a n p o in ts : th e c e n tr e bı e s itu a tio n in w h ic h t o u ld e n c o u n te r th e u n s a (a n d s o m u s t p , o th e r w is e w e w t r n o v e r ), th e c e n tr e ie s o n to p o f lig h t m a te ń a l, re s u ltin g in a u h e a v y m a te r ia l ı i f t d d e n s e s t p la c e T h e r e , th e r e o r e , h e n u c le a r r e a c t o n s o f a s ta r is th e h o tte s t a n a re

n s o

an

w o u

n ts

cn w fc ı

n o th e r

de n t

hav e

r e s s u re i# d o m in a te d lm c n w h e re (h c g a s p h e ıw ic r th a n h y t g ll ı h is v e r y n e a r y 2 rc g a r t e « s o ľ th c m a in ly d s o n /t ı w h ic h e n c ıJ d e p e n l t n t ł r s 1 r \ y o u n g s ta r s s o ty p ic a ıo b y e lta m i n is a ı s c o n \p ° s it o h o m o ge n e o u A s e c n d a n d e ta ile d a b u o

lu t io

n

r a tio n

fr g u

c o n

) th e ū r s t p a ir ,

w ou

ld

Scanned by CamScanner

召 回

S 3

b e in d e p e n d e r a tio n c o n fig u

i n s o s o lu t o

M

u

t an d

n

w o u

f th is fo

c o u

ld b e rm

ld b e

s o lv e d in d e p e n d e n t

a re n o w

ltip ly in g E q u

Po ı ytro p ı c

a tio n

deı s

m o

p a r a te ly , f th e flo w

se

o

/p

r

an

d d ift e r e

hav e

S u b s titu tin g E q u

a tio n

(5 2 ) o n th e

ń ght ha n d

s id e

六壬( ) c o n s

e n o w

id e

r e

qu

a tio n s o

f s ta te

o

f th e fo

P

w

d y a re fin e th e d e t a ry o

h e re K

to m

c o n s ta n ts

an

,

c o rre s p o n

kn

o w n

d in g p

K p

-

ld n tiu t in

g

w

ith

r e s p e c t to

(5 9 )

° °

ıu ı

(5 10 )

v

la te p o ly tro p ic e q u a tio n s o f s ly tr o p ic in d e x d e n o te d b y n a s as

o

r w e

b ta in

w e o

4 ?r G p

-

W

o

m o r e th a n a c e n tu r y o

(5 1 ) b y

in g th a t th c h y t h OStNic f h e a t th r o u g h it A n a ly tic

m ean

It is

0

cu s

D -

l tr o p ic le te ly d e g e n e r a te e le c tr o n g a s is p o y f m q u a tio n o f s ta te o a c o p 4 /3 ) in th e n d 3 (y f 1 5 (y = 5 /3 ) in th e n o n r e la tiv is tic c a s e a w ith a n in d e x o b y a po ı y tr o p ic to o m a y b e d e s c ń b e d i i c lim it A n id e a l g a s t i s l t v a e r e m t re x e h c a s e s la te r i i s w e s h a ll e n c o u n te r s u c t u n d e r c e r ta in c o n d t o n ; e q u a tio n o f s ta e b t in a s e c o n d o r d e r 10 ) (5 1 1 ) in to (5 9 ) w e o a S u b s titu tin g E q u a tio n s (5 on

T hu

,

s th e e

U C 7

,

,

,

d iffe r e n tia l e q u a tio

T he

so

d itio n an

lu tio

n

d d p /d r

d p /d r

p (r ) fo

T he se

s

It is

=

a re

O

p

o

r

<

fu

c o n v e n ie n

n d a ry c o n r e q u ir e s tw o b o u p o ly tr o p e P (R ) = O R ) w h ic h fo llo w s fr o m s u r fa c e (r im p lie s h d r o s ta t ic e q u ilib ń u m (r = O ) s in c e y ń e d by l tr o p e is u n iq u e ly d e n 2 3) H e n c e a po y ,

c a lle

d

a

,

,

O

=

a t th e

n c tio n s o

R

<

r

a t th e cen ? e

tio o th e r e (s e e s e c

=

titie s a s

n

f

ra

t to

d iu

s,

d e fin

n

,

,

p re s su r e

th e su c h a s

e a

d im

,

r a v it a t io n a l th e m a s s o r th e g

l s v a r ia b e e n s io n le s

P

-

P

0 in th e

ran

ge O

<

e

<

1

(5 13 )

" ,



国 區

Scanned by CamScanner

F ig u

re

5 ıN

o rm a

f r liz e d p o ly tr o p e s o

i n to o b ta in E q u a t o

(5 12 ) in

h ic h

can

be

u se

d in

o rd e r

rm

an

d

r

th e le ft

o n

f le n g th

e n s io n o

by

to r e p la c e r

コ ー

3

=

n

,

b r a c k e ts

squ are

o b v io u s ly th e h in th e d im (5 14 ) is a c o n s ta n t a v g

w

1 5

-

p le r fo

a s im

i c o e fric ie n t n

ıt

a

d im

s id e o

ha n d

f E q u a tio

d

s q u a re

i e n s io n le s s v a r a

b le

Ę

,

(5 1 6 )

Ę

c¢

=

E u a tio S u b s titu tin g E q u a tio n (5 16 ) in to q L a n e E m d e n e q u a tio n o f in d e x n

n

n

(5 14 )

,

o

w e n ow

b ta in th e

w e

ll k n

ow n

,

su

b je c t to th e b o u n d a r y

(5 17 )c a n b e in te g ra te d d e c re a s e

m o n o to n ic a

lly

co n

d itio

s ta r tin an

n s:

g a tş

d hav e

=

0

1

=

an

O ; fo r 11

a z e ro a t a

d d 0 /d Ę = <

fin ite

O

at

5 th e

s o lu tio n s

v a lu e

Ę

,

=

0 E q u a tio n o (Ę) a re fo u n d to

Ę

=

ş ı w h ic h ,

c o r re s p o n

ds

to th e s te lla r r a d iu s

R

-

a

şl

(5 18 )

p le s o f s o lu tio n s (p /p c a s a fu n c ū o n o f r / R ), fo r n - 1 5 a n d n - 3 , a re g iv e n in F ig u r e 5 1 A s s h o w n th e s tr u c tu r e o f a p o ly tro p e d e p e n d s o n ly o n n A p o ly tro p e o f in d e x 3 d e s c r ib e s a s ta r in w h ic h th e m a s s is s tr o n g ly c o n c e n tr a te d E

x am

,

Scanned by CamScanner

S 3

Poł ptn

k

ı p

m

o

d*ı ı

7S

=

仁 ü く

at

e th e c e n t r

w

d is tf ib u tio n T h e to ta l m

he

ass

re a s

M

o

p o ly tr o p e

a

o

f a p o ly tr o p ic

f in d e x

I 5 d e sc ń be

is g iv

s ta r

F ro m E q u a ū o

(5

n

4 7c

=

17 ) w

hav

e

r

4 är a

=

\

(b ) n

-

1

an

d fin d

In la te r d is c u

e

.

81

th e an

r

Şl

4 Jr c r3 p .

=

( )

pc

S o lv

2

Exercise

3

p d

'

.

n E m d e n d M (R

) in

s s io n s w e s h a ll o

ş

2

(5 19 )

e ・d

eac

fte n

e

h

4 rr a

-

3

:

p.Ę

()

(5 2 0 )

..

q u a tio n

a n a ly tic a lly

fo

r

(a ) n

0

-

r e s o r t to

ge n

e ra

l re ı a tio n

s

b e tw

O

h ic h is g e n e r a lly E q u a tio n (5 17 ) a n d d e p e n d s w

ly th e c o n s ta n t D l ofn o n th e v a u e

.

n

d e r iv

es

fr o

m

e en

e as

d

s te

u

ar

ily fr o m b ta in a

w e o

,

lid

an

c a se

T h e s e fo llo w ltin g fr o m a p o ly tr o p ic q u a tio n o f s ta te p r o p e r tie s r e s u b e tw e e n E q u a tio n s (5 1 8 ) a n d (5 2 0 ) i E q u a tio ï ı(5 2 0 ) E lim in a t n g a d e n s ity p tr a l d e n s ity a n d th e a v e r a g e lin e a r r e la tio n b e tw e e n th e c e n

v a

m ass

e

°

M

2

ev en

m o re

by

en

R

M

a

s

,

th e

so

lu tio n

o

f

ci r

bu t n o w e n th e U s in g E q u a tio n (5 2 0 ) a g a in r e la tio n b e tw e w e o b ta in a i o n (5 1 8 ) t a u E q s ta n ts M tı (5 15 ) a n d s u b s titu tin g (e fr o m s o f tw o c o n e d in te r m b e e x p re s s a m h i y s te lla r m a s s a n d f a d iu s w h c C t l ııı

,

,

A

,

te d

,

J

\

Scanned by CamScanner

S 4 ¢ O łl»r N łıls n b ln ł\ï y

r e is e

l

(x

h ic h

w

e n \:

b le s ılw c n łı



8 \

s k r \ ï lh ť \tw\\\\ıln

d e \e r n \ln m lu n ĵ tt

n

ï \h o

1H tJ9 ,

ı h ı

w

\tÌ W H \ \ı ł

nn tlı ı ıı \ı \\ ı \n n * * ł

lı l

lıiı hı

Įi ı h p ltr lu lıı lı

tl

rt ltl ıił ln # lh l\ĺ ıı ł ı c n n tw d c s c r i l b y ł \ pulytn1pĐ t\ r In \ı n ıl ĺ ı ı o ł lı \ı * H iı ı ın l ı \ \ 3 ïh u l ı \t) \te n ı v n s ity C lm k w ł c e n m l «ı \c tı w \ \h o m n lrn ı n px « \ı ı r* llı n o tı y (a IH ) » #ł ı \\ln llo » ı co m

ĺu m

10

Ķ

k#

n n tl N

" Q 55 × ı n ,

ı \\

\nw

m

'

,

p

S 4

T h e C h a n d ra s e k h a r

.

S ta rs th a t

f in d e x

n se

hc

n s t0

n

15

=

w

ith K

=

A

o u ı tıh c

m a ıı

t IR? ( ıi ilı lLj p ıt\ H H ı ıg t\ ı 1t\ l ł ıl t H I lh t' \ l h y lıp [t ly lrt p r tilt Iy t ı t\c e \ı

t io n \ in ł ï tc t ıh y

(d is c u s s e d in C h u p ltT 3 ) w

e le c tro n s o

de

a re 50

,

d lt

ł

L t'

'



t E ļq u n lit m ( 1 3 5 ) W

, o

kn o

ť

w

Ir u

\ın ı

hnd

lo n n lv n ı

\i l ¢ lıı( lııłp ı , il m )I lıH ıL II In rH ? I lllłıiłlh cl e to [h c S u n s N m ır ı \t ı w h ic h h a v e m a s s e s c o m p ıw n b ı ' ' 0 11 k 8 m ( IO A L l11 ) n h n \ıl E a r th s T h e ir a v e n ıg e d e n s ity is th u s h ig h e r th u n ı lı W t! IIılH lıl fiv e o r d e r s o f m a g n itu d e h ig h e r th a n th e łw c r u g t d e n s ity u ľ ilic llı l te a m s o m e m o r e a b o u t th e s e s ta r s b y in v e s tig a tin g ıh c p rt )p c r [IL H n l ıh lH p tlr ılu ıırır lu N h e u t )IN c H tı rł ı p o ly tr o p e F r o m E q u a tio n (5 2 3 ) th e r e la titm h e tw c e n ı11t\pi łın d

th a t s u c h c o m

p a c t s ta rs

e x is t

/

th e y n tų ı h e \ľ /liw

' ı H lll

A

'

n \t!n lln n t\ d

'

.

'

,

R

T h e d e n s ity th e r e fo ,

re

,

in c r e a s e s

c(

Ar ・

(5 2 9 )

ı /3

,

a s th e s q u a re o

o(

3

M R

o(

M

t th e

Is s , IL1 Ł

(5 10 )

2

.

* he i h d e g e n e m te g ıts e o u s s p h e re s w ith h lg h o l a n d h ı ıIn c rc ııN c in h r ie s a n d th e d e n # ity w lı m a s s e s T h e r a d ii w ill d e c r e a s e a lo n g t e s c 2 E v e n tu a lly th e d e n s ity w ill b e c o ın e s o h ig h th a i th e d e g c n c n ıle p r o p o r tio n to M " I 5 p o ly n p lo II to b e re la tiv is tic d e p a r tin g 1ľ o m th e s iı e le c tro n g a s w ill tu m tio n ı T oo l equ ł th e c o ı th e d e n s ity in c r e a s e s (th e ra d iu s te n d in g [o z e ro ) 3 3 8 ) s till a p o ı y tr o p c b u t o f in t lc x ıl = 3 , w ith o f s ta te w ill a p p r o a c h th e fo r m ( th e re is o n ı y o n c p o » s lh le K = K 2 W e h a v e s e e n h o w e v e r th a t i4ĉ s u c h a c a s e Im

a g in e n o w

a s e r ie s o

f

su c

,

,

tropes

,

,

,

,

in 19 3 1

an

,

sh m e

d

e v o lu tio n

ce

th e u p p e r lim it b e a r s

h is

e, Tı naı

w

ith F o w

)

s u b s titu tin g K

z

M

ch

A b o u t h a ll

ı l c e n tu ry

b ľ P h y s ic s w h ic h d C h a n d r a s e k h a r th e 19 8 3 N o b e l P T Iz c ı ı ar le r (fo r th e ir c o n tr ib u tio n s to th c u n d e rs ta n d in g o l s tc ı

w o rk e a rn e

la te r th is he

d hen

l

,

l

in E q u m io n 5 2 4 ),

w e

lın v e

Scanned by CamScanner

O ,健 S r r

'

X

仪體 卜

)

W D

0015

0 01

0 00 5



0



0 5

M LM

R g ıır e S 2 T h e In

s x tin

m a ss r a

g th e v u e s

o

d im

f c o n s ta n

ts

M w

h ic h y ıe ld s fo r ¢t¢ = M lle d w a r fs is s h o w

2

fo

neı a tio n

a

lim itin g

.

(/ı¢

2)

-

b ta in 2

5 83p

=

a r fs

h ite d w

r w

w e o

ch

1 5

1

m a ss o

,

M

o

f 1 46M

(5 3 2 )

,

T he

o

Th e lim itin g m

Ex

]e s Ħ u Ľ

=

S X an

s e

d

C a lc u la te c e n tr a

ad

w e

r

,

q u iv a le n t to

h a v e d e a lt

.

,

c r itic a

w

th e c

83

3 /2

v

a lu

sho w

m

f 1 46M

a ss o

In d e e d

o

,

n o

w

h ite d w

a rf

is

e

m a s s u s in

g

r e la tio n

th a t th e n u m e

(5 2 8 ) b e tw

ńcal

co e

in

it y

ffic ie n

t

een

c e n tr a l

in E q u a tio n

/3 2 ĵ ・

T h e E d d in g t o

ith th e fir s t tw

d th e th ird th tıs ta k in g in to ,

lm

ń tic a l

l d e n s ity

5 5 S o fa r

fo

,

th a m a s s e x c e e d in g th is

e r c is e

s r e la tio n

in F ig u r e 5 2 fo r /ıe = 2 (H e C O ) F o r H e = 2 15 a s s is 1 2 6 M o In c o n c lu s io n , h y d r o g e n p o o r c o m p a c t s ta r s is s u p p lie d p r e d o m in a n tly b y th e d e g e n e r a te e le c tr o n a s c a n g

h e » e th e p r e s s u r e 【 ıa i e m a s s e s o n l) u p to th e n w

d iu

n

,

Fe

m a s s ra

o

o

n

f th e

a c c o u n t th e te m

S u b s titu tin g th e ra d ia tio n p r e s s u r e P m d = E q u a tio n (5 3 ) b y E q u a tio n (5 ı) w e o b ta in

į

lu

m

o s

q u a tio n s W e s h a ll n o w a n d th e r a d ia tio n p r e s s u r e

s tr u c tu r e e

p e r a tu r e 4 in E q u a tio a T

(5 3 ) a n d d iv id in g

n

,

d Pm t [P

T he s te

r e s u lt o

lla r lu

m

f th is

in o

K

d

F

4 rr c G

ip u la tio n w ill b e th e d e r iv a tio n s ity S in c e P = P . + P m d a n d b o th P . g g m an

,

(5 3 3 )

n ı

o An

F

p p e r lim it fo r th e d P n ,đd e c r e a s e o u tw a r d an

u

Scanned by CamScanner

Rw lıe

Fig u

In

5 2 T he

re

s e r tin

g th e

m a s s r a d iu s r e la tio n

v a lu e s o

f co

n s ta n

h ic h y ie ld s fo r H e h ite d w a r fs is s h o w

2

ĥ

c

=

lim itin g

a

r w

h ite d w

ļM

w o

)

2

a

a r fs

(/L e

2)

-

ts , w e o b ta in

M w

fo

o

2

5 8 3 /Ł e

m a ss o

M

o

(5 3 2 )

,

f 1 46M

T he

o

m a s s ra

d iu

s r e la tio n

fo r

(F e ) th e lim itin g m w h e r e th e p r e s s u r e

in F ig u r e 5 2 fo r p e - 2 (H e C O ) F o r H e = 2 15 In c o n c lu s io n h y d r o g e n p o o r c o m p a c t s ta r s a s s is 1 2 6 M o is s u p p lie d p r e d o m in a n tly b y th e d e g e n e r a te e le c tr o n g a s c a n

hav

p to th e c ń tic a l m a s s o

w

,

kn

e m

a s se s o n

ow n w

Ex

ith

ly

n

,

d in g th is

c

f 1 46M

re

an

d

ń tic a l

m

a s s u s in

S o fa r

w e

hav

a d d th e th ir d

,

e

d e a lt

th u

w

T h e E d d in g t o

ith th e fir s t

g in to a c c o u n t th e r a d ia tio n p r e s s u r e P d ra n

(5 1)

,

w e o

T he

r e s u lt o

f th is

s te lla r lu m in o

,

n o

w

h ite d w

a rf

is

g

ľ e la tio n

lu

m

in

l

(5 2 8 ) b e tw co e

c e n tr a l

ffic ie n t in E q u a tio

n

o s it y

s tr u c tu r e e

q u a tio n s W e s h a ll n o w d th e r a d ia tio n p r e s s u r e

į

p e r a tu r e a n 4 in E q u a tio a T

K

F

te m

een

(5 3 ) a n d d iv id in g

n

b ta in

d P ra d

dp

n

f th e

tw o o

s ta k in

S u b s titu tin g th e E q u a tio n (5 3 ) b y E q u a tio

o

n u m e r ic a

cen

5 5

In d e e d

v a lu e

tr a l d e n s ity ; s h o w th a t th e 3 2 (5 3 1 ) is e q u iv a le n t to B 3 / /3 2 7r

p re s su

,

,

u

C a lc u la te th e

5 5

,

,

a m a ss e x c e e

e r c is e

,

(5 3 3 )

-

4 7r c G

m

ip u la tio n w ill b e th e d e r iv a tio n s ity S in c e P _ Pg a s + . d a n d b o th P g a , m an

,

f

p p e r lim it fo r th e a n d P r a d d e c l e a s e o u tw a rd o

an

u

Scanned by CamScanner

5 S

1

ı o w (p ro v id e d q Z O ) it fo ı

d p ra d /d p

<



T h e E td d ı n g to

s th a t s

g n [d p ra d j=

sgn

F

m

! im p ly in g K

T h is in e q u a lity f m a y r e s u lt r o m t e re d n u o as e n c

m

y be

a

in

v

te n s e

a t th e

io la te d

e ith e r

n u c le a r

io

4 rr c G

<

n iz a tio n

in th e

burning te m

79

ı u m ı n o ıı ty

n

ld p n i . ıa n d

fa

in th e

o r

b v io

u * ly



have



(5 3 4 )

c ase o

p e r a tu r e s o

w e o

v e ry

case o

la rg e h e a t n u

f

w

,

h ic h

h ig h o p a c ity In s u c h h e liu m f i w e r e q u ir e and

v e ry

a

f h y d ro g e n

x

o r

E q u a tio n s (5 1 ) a n d (5 3 ) c a n n o t s im u ı ta n e o u s ly h o ld ń c e q u ilib r iu m th e n h e a t tr a n s o r t m u s t b e d e s c r ib e d b y a d iffe r e n t p th a t is it m u s t o c c u r b e q u a t io n y a m e a n s o th e r th a n r a d ia tiv e d iffu s io n w h ic h i f i f i e n e t m c e W o n b e c k e n fr o m e v e r y d a y e x p e r ie n c e th a t n e a r a s tr o n g o w bas h h e a t s o u r c e s u c a s a s to v e c o n v e c tiv e m o tio n s d e v e lo p in th e s u r r o u n d in g a ir If th e s to v e w h ic h c a r r y th e h e a t e ffic ie n tly a n d d is tr ib u te it th r o u g h o u t th e r o o m h i h d is n o t v e r y o Ļ t s p r e a s h e a t b y th e r m a l r a d ia tio n a lo n e T h e s a m e p e n o m e n o n d ia tio n o n a p p r o p ń a te ly la r g e r s c a ı e s S ta r s tr a n s fe r e n e r g y b y r a o c c u r s in s ta r s id to b e in r a d ia tiv e a lo n e u n d e r m o d e r a t e c o n d itio n s in w h ic h c a s e th e y a r e s a i 4 i fi d o r b y c o n v e c tio n u n d e ]' " o r e s e v e r e e q u ilib r iıu ? t a n d in e q u a l ty (5 3 ) is s a t s e f h e a t g e n e r a tio n b e c o m e s to o r a p id fo r r a d ia tio n t o h c o n d itio n s w h e n t e r a te o It m a y f t m u c h w ith th e r a d ia tiv e tr a n s e r f T y o r w h e n io n iz a tio n in te r e r e s o o c a】 h s a re i n s o f a s ta r a r e in r a d ia tiv e e q u ilib r iu m a n d o t e r a ls o h a p p e n th a t s o m e r e g o ııv e c tiv e 1e d ra d ia tiv e r e g io n s o r z o n e s , a n d th e la tte r c o ı n o t th e fo r m e r a r e c a ,

h y d ro

s ta



,

학 エ

,

,

,

,

,





ones

Ex e

e r c is e

F in d th e

5 6

q u ilib ń u m

an

d its

ex

p r e s s io

r e la tio n to

n

fo

r th e

d ie n t g a s p re s s u r e g ra

a ssu m

in g



r a d ia t iv e

in e q u a lity (5 3 4 )





O O y ie ld F /m qc a s m 4 n d F (0 ) = f a s ta r E q u a tio n (5 ) a li it o n 3 4 ) im p o s e s a u n iv e r s a l u p p e r m h e n c e in e q u a lity (5 w he re q c = q (m = O ); d a te d b y r a d ia tiv e e n e r g y n be a cc o m m o i n r a te th a t c a o t a r e n e th e c e n tr a l e n e r g y g ,

N

e a r th e c e n tr e o

,

tr a n s fe r

4 7r c G

T he s m

=

M

u ,

w e

la y e r

o

f

a

s ta r

is





a lw a

ys

r a d ia tiv e

(5 3 5 ) ;

a ppı y in

g in e q u a lity

(5 3 4 ) fo r

ha v e 4 rr c G M

L

(5 3 6 )

<

K



ilib r iu m m a s s i n o f h y d r o s ta tic e q u im p lie s v io la t o v io la tio n o f th is c o b E d d in g to n th e r ig h t A s p o in te d o u t y d i n w r l l a to a s te th a t c a n n o t b e L m o tio n s a f is e le a d in g i ic a l lu m in o s ity c r it n ts a c f t e s e r e f 6 h a n d s id e o f in e q u a lity (5 3 ) p n d itio

n th e n

,

Scanned by CamScanner

-

r ib r iu ı Eq u ı

5

* im

m

80 s u rp a s s e

fo r e , d it is ł th e r e

e pı

d e ls

m o

lu m in

n

E d d irıg to

th e o w n as a lfio k n

o s ity

L

Edd

(5 0 ) e n s c a tt

e le c tro tiv e t o th e s e d r e la i ty is e x p r e ji c a o iz e b e t e p i w « a T o su m m a r tio n (3 6 4 )) see Equ a ( l a n t ıs a L 4 しe dd

w ı lic h p a c ity K e s ire s re u m ń u b i l q i equ

ńng

iv e r a d ia t

o

,

b m im a tio n L E d d e c o e s e a p p ro x bı re ? o n a a b e t o e o f i K es h a t fo r a c e r ta n W p If w e a s s u m e K a tio n ıı a p te r 1 t ı n n e e s e v h u m in o s ity a n d by M W e a he ı iq u e ly i n e d is ts b e tw e e n t u ı ı \a tio Ð e x d r a d ia tiv e e q u ilih h y d r o s ta tic a n r s a r e in t a s h c u f s l e rs o b m a s s If th e o u tie f a y

;q

l

d

u

e

p

se

th e ın a lis o p e r lim it o n

qu

en ce

to

have

an u

p pe r

ta r s s e q u e īre e s

a in

fm

W

an

e

d e lin e

a

,

T he

sta n

m

o

ld th e

n ex

a in n ı

p e c t th e

an

deı

? ń v e th e

p f o c e e d to d is th e r e fo f e

a ls o

kn

so

c a

lle d

s t a ltd a r

ı ddinglon s

o w n as

d

m o

m o

de ı

del

fu n c tio n 17 b y

,

w

F

L

m

M

s u r fa c e , 11

-

1

,

an

l c o r e , th u s

iııw

ar

&

d ıe

c e n tre o u tw a ld

g

d e c fe a s e s T h e

m es

4 tr c G M

d fo r

m a in ta in in

c em ïa

(5 3 8 )

h ic h b e c o

m

as m

d a rd

w e

33) d i n s e it in to E q u a tio n (5

A í tb e

e sh o u

d

en

6 ir is b ń e f d ig r » s s io n A fte r ı E d d in g to n w M c h is d rıe to

W

n u c le a r

bu m

s ta r s th a t

m o s t c o n s ta n t an aı

o

p a c ity

,

(5 3 9 )

K ri

flu x

o n th e o th e r

,

o s tly

o u ts id e th e c o r e

ha n d

,

in ,

a

n in

(s m

a

ll)

c re a s e s

lly in c r e a s e s fr o m in K is a p p r o x im a te ly

u su a

in c r e a s e

c e n tr e o u tw a r d , th e

If ff o m th e

fu e ım

t w e m a y ta k e th e ir p r o d u c t to b e c o n s ta n i p e n s a te d b y th e d e c r e a s e n )7 i n o t T h is iis d te u n ifo m ııp f o p e r ty o f th e E d d in g to n m o d e l (a c o n tr o v e r s ia l a s s u m p suþ w ł ric h h a s je c t 1o s e v e re c f itic is m o v e r th e y e a r s ) W ith com

,

K 】 t

W l ıe r c is th e s u e

o

p a c ity

,

c o n s ta n

=

w e

P ra d

t

=

K

$

«

=



(5 3 9 )

R p

L

ß

T T Y Ą tT c G M T



(5 4 0 )

,

h a v e b y in te g f a tin g E q u a tio n

,

,

(5 4 1 )

.



Scanned by CamScanner

5 6

The

s ta n

d a rd

m o



de ı

ıp r e s s u r e a n d th e r a d ia tio n p r e s s u r e te n d to z e r o a t th e s u r fa c e T h u s f n c t a o i s K } n o ı y ? m p ie s a c o n s ta n t ra i th e c t o o f ra d ia tio n p r e s s u re to to ta l p re s s u r e u t th e s ta r in o th e r w o rd s a c o th r o u g h o n s ta n t p (s e e E q u a tio n (3 12 )) w e a ls o o b ta in th e to ta

s in c e

,

4 7r c G M

L

(1



K

声)



L

E d d (l

S

(5 4 2 )

ß)



u m in o s it a g th a t th e ı y p p r o a c h e s th e lim itin v a lu e a s th e ra d ia tio n r e s s u n e g p O ) A s s u m in th e b e c o m e s d o m in a n t (þ+ a s g g p r e s s u r e to b e g iv e n b y th e id e a l i E t a u 3 o n 2 8 w l a ( w s ) q h e , ave ga

m e a n in

,

ı/

a

4

T

3 (1 C o m b in in g th e

Pm =

n

T

an

f s ta te

e q u a tio n o

d th e

P

S in c e K is

a c o n s ta n

h ic h im p lie s a th e p r e v io u s s e c tio 3

,

w

u n

n

m a

w e

iq u e R eam

P

=

aì r

_

e x tr e m e r i h t e x g

[ ]

_

y be

w

ń tte n

K pq

=

t,

ı

le ft a n d

e x tr e m e

d

K

ha v e

R

p r e s s io

(5 4 3 )

T

p

-

ge t

n s, w e

" 3

p

1/3

(5 4 4 )

as

Ľ ]

=

b ta in e d

1/3

(5 4 5 )

p o ly tn o p ic e q u a tio n o f s ta te o f in d e x r e la tio n b e tw e e n K a n d M E q u a tio n (5 2 4 ) d e r iv e d in n g in g te r m s a n d in s e r tin g th e v a lu e s o f c o n s ta n ts w e o

a

,

,

o b ta in

4

p

4

(5 4 6 )

,

2 q u a tio n fo r ß(/L M ), k n o w n a s th e E d d in g to n q u a r tic e q tta tio n w h o s e s o lu tio n is g iv e n in F i\ re 5 3 T h e q u a r tic e q u a tio n is v a lid fo r a h y p o th e t ic a lly w id e r a n g e o f m a s s e s W e n o te h o w e v e Ļ th a t o n ly fo r a r a th e r r e s tr ic te d f r a īı g e d o e s p d iffe r s ig n iń c a n tly fr o m u n ity (p u r e g a s p re s s u r e ) o r r o m z e ro (p u r e r a d ia tio n p re s s u r e ) a n d th is r a n g e m o r e o r le s s c o in c id e s w ith th e r a n g e o f s te lla r m a s s e s a s d e r iv e d fr o m o b s e r v a tio n s In E d d in g to n s o w n w o r d s a

fo u r th

o rd e r e

,

,

'

,

W

e can

im

o

f th e

o

f g lo b e s

th e n

a

g in

p h y s ic is t

s ta r s c a lc u la tin

o

f ga s

10 0 g m

R e g a rde d

as

he re

w e m

a

o

f

g th e

a

o n

r a tio o

,

an

tu s s le b e tw

d

ex

pe c t

m

d bo

,

d p la n e t

w

ho ha s

h e a r d te ll

never

n

,

a tte r a n

h e lm in g ly

s o m e th in

un

p r e s s u r e to g a s p re s s u r e fo r a s e r ie s s ta r tin g s a y w ith a g lo b e o f m a s s 10 g m o b e c o n ta in s 1 s o th a t M s n th g ı gm [ ]

f r a d ia tio

so o n

een

c o n te s t is o v e r w

y

a c lo u

v a r io u s s iz e s ,

10 0 0 g m

,

p r e s s u r e ) th e w

a

e

d

,

a e th e r

o n e s id e

d

(g a s ex ce

p re s s u r e

p t b e tw

an

een

N

d

ra

o s

d ia tio

n

33 35

,

h n g in te r e s tin g to a p p e

Scanned by CamScanner

82

S

Eq u ı ı lb r ı u m

ı

ı

0

0 2

ıı m

-

5 3 S o lu tio

re

W h a t h rtp p c n s

is th c

W

th c v e

a s id e

d raw

e

w o r k in

g

g lo b e s

o

B e tw

sa y

l th c E d d in g to

n o

L

J

0 6

0 8

an

d le t h iın lo

f ga s een

n e a r ly a

ļ

o

k

o

]

e q u a tio n

s till s

u

ll o f

d 5 0 tim

an

q LIŁıItic

n

rb

L

0 4

L o g tı la M ï M

Fig u

m o d ü lı

p lo

il

o

p

a t th e s k y

l

m a ss

d o lı cı

b e tw

b c n c n th

w

T h e re h c

w

h is 3 3 r d

een

p h y s ic i$il lm ill íin d ll th o u w m d

h ic h

nd tı

e r c is e

is

a co m

c a lc u

W hat

F

n a ru ľ ı rl c o n s ta n ts

w ľ ittc 11

bc

(a ) F in d th c

(b ) E x p r e s s th e C h a n d ra s e k h a r

le a r n

can o ne



n o

n

th a t is to

3 5 th g lo b e s

e s (h c s u n s m o s s

n ay a t lic e q u a tjo n ı

T he qu

b in a tio

la te i(

】 Fo r

V

5 7

iı lio

m

'

S ir A ıth u r S E d d in g to n : 7T re litte ıT m / C tılt vtirII/ia

Ex

be e n

s

o u l

u tio n o a b o u t th e e v o ı

in

te l m s o

e x p re s s io n

in te r m

m a ss

s o

l {/ie s lu r y 19 2 6

lt o

fM

,

fa

m a ss

ľ

th is ı rı a ss a n d

.

th a t

.

o n th is s im

f s ta r s b a s e d

M

p le

m o

d e l?

f g iv e n c o m p o s itio n (fix e d p ), P d e c r e a s e s a s M in c r e a s e s in g th a t r a d ia tio n p r e s s u r e b e c o m e s p a r tic u la t ly im p o r ta n t in m a s s iv e

s ta r s o

m ean

,

s ta f s

2

In

s e r tin

(5 4 6 )

g E q u a tio n (5 4 2 ) in to o

_

L

K

o

s

L

w e o

b ta in

() 3

4 JT c G M

L

,

o oo3p

4

p

4

(M

,

0

H

)

(5 4 7 )

to a p o w e ı la w r e la tio n b e tw e e n th e lu m in o s ity a n d th e i m a s s , s im la r to th a t o b ta in e d l+ o m o b s e r v a tio n s o f m a in s e q u e n c e s ta r s In fa c t th e m a s s lu m in o s ity r e la tio n d e r iv e d b y E d d in g to n w a s a t th e

T h is is

c lo s e

,

tim

e a th e o r e tic a l

D iffe r e n o

ces

bse rv e d

in

co

p r e d ic tio m p o s itio n

s c a tte r o

n ,

,

to b e c o n ŕir m e d o n ly la te r b y o b s e r v a tio n s

an

d h e n c e in th e

f p o in ts in th e (M

,

L

v a lu e o

F /Ä

,

m a

y

ex

p la in th e

) re la tio n

Scanned by CamScanner

S 7

g

a

m

M

v e n

g fe a

te r

sho u

ld

a

p p ro

th is a

in P first M

th e lu

m

h a v e fo

W

e

a

s im p le

an

d

in

rm

e a s y to

de

u n

m e a ]ı m o

by

le c

in g

f

e c

d

c

co m

at

de

s ta r w a s

as

S e c tio

(s e e

m ass

o

f

lu

in

o

s im

p le

m o

ld

d e ls

so

n o t ,

w

fa

s ta r

bo o

an

)

? W

a w

dMhich

W

(o

lu

ass

pac

o

in

m

ity A

fo

a y c o n s id e r ld in te n s ify a s

e m

sho u

y d e r iv

r th e

b s e r v a tio

g th e h ig h ly io o

p a c ity

o s ity r e la tio n

co e

in g

ssu m

r te r r e s tń a

l

n a

n iz e

ffic ie n

o n e o

ıc o

a te r ia

m

d

w

(5 4 7 ) h ? f th e m

fr o

e

l),

tw o

su c

m

h

p o r ta n t

E d d irıg to

f s te ı ]a r in te r io

h ic h

e x c ee

de d by

rs

th e

e

s ta r te

n

a v a lu e

ie d h ic h im p ı

w

e te r s

p a ra m

a y d e r iv

o n e m

u n te r p a r t

s ta te o

t

ffic ie n t th a t h a d b e e n

d by o

f 1ı

T h is le d to

fa c to

ab o u t a

1o w in g th e K a te d fo ı c a lc u ı

r

r a m e rs

th a t in c lu d in g a c o n s id e r a b le p r o p o r tio n o f h y d r o \ n in

an

d to

fo

had

ld

r e so

lv e th e d is c r e p a n c y Th is

o th e r s , a n r a tim e

an

I 3 ) T h e po n

ra d u a

a

c a u se

H

d th e

d th e

th e p r e v a le n c e o a

th a t 山行u s io

f h y d ro g e n in

dv o

c a te

d by B

n

in

gt

e

d

is h e d bı

o u n ts to

am

ab o u t

s u r fa c e o

s Ta T s s h o u

s te lla r in te r io r s

e n

se e m

e e s ta

am

f h y d r o g e n n o a tin g to th e

a lr e a d y s h o w n

n

a c o r r e c tio n to

f s e e k in g

d 19 3 0 it b e c

in g e n e r a l H y d r o g e n

s ta r s

s s ib ility o

d in d e p e n d e n tly

a lte r n a tiv e o

o w e v e r a ro u n

lu tio

so

S tr ö m g re n

ld p r o w as

o n

f th e cee

d

fin a lly

th e b a s is

o s ity r e la tio n

d e ls p r e s e n te d

c h a p te r w o u

n

p u rs u e d

,

m

d r o p p in g f s te lla r

E dd

s ta r s w o u

ly T h u s in 19 3 2 n

p fr o m

ith its

w

ic a l

T h e p o in t

5 7 M

lm o

f ir o

o

d is c a r d e d E d d in g to

r e c o g n iz e d b y E d d in g to

f th e

r e tic a

f th e S u n n

a c t io

th e c o m p le x s tr u c tu r e a n d e v o lu tio n o f s ta r s

d th e

w a s a w a re

p o s itio n

ffic ie n t w

n e g lig ib ly s lo w

o

a n

c o n s id e r in

h a t in th e a tm o s p h e f e s o ı m ass

n a ry c o u rse o

th e y a r e a c c e ta b le a n d th e p y p r o v id e im

s to

fir s t b o th to h im

o p a c iı y coe

h a lf th e

lu e

a s tr o n o m

an

lu tio

o

p

t

v e n

la te d

u

ig h t

m a

f2

gh h e

u

h e m ic a l

im p r o b a b le th e

w e

be

\

n u c le a r

s e c o n c lu s io n s v e r y c a u tio u s l y

rm

T h e th e o

te

g th e

c e

e x

he s L

ac

th e o re tic a l o p a c ity c o e

A lth o

tiï e o r y

p p ro

g th e r e la tio n

e x c e ss o

th e e s tim a te o

M

a

r s ta n

la r

u

s ta r s to

s lig h tly in

f IO th e

o

p a r in

co m

ity

la te d th e

u

a s a lo n

g / Ł S in

th e e x is te n c e o

n t to

o s

ld

u

to p r e

so as

d e l S o fo

m o

Ħis to r ic a l N

o

e

r is e

th e

g in g ıt

n

c r e a s in

t s o u rc e m o d l e

l re n s g l p e c t r a d ia tio n p r e s s u r e to i n s a e i r c y n g p la y a n g e ts o ld e Ľ w ith it b E u a t io n 5 4 2 th e ı u m in o s ity ( y q ) a c h its lim it i n g v a lu e c o u ld o se ĺ h is m e a n th a t a s ta r s h o u ld ı o f its m a s s i i n ts la te s ta e s o f e v o lu tio n c o m e n s a tin g fo r g

c re a s e

(e je c t ) s o m

a ssu m

ha

c

ith in

w

in ıL w e s h o r o le A s a s ta r

in

?

d

an

re a s e s

T h e p o in

be

fa r h a v co m

h ic h ta k e

w

accou

m

o

de ı

q u a tio n s T h is h ith o u t m e n tio n in g a n o t e r g r o u p o f r e la tiv e ly n t o f th e fo u r th e q u a tio n E q u a tio n (5 4 ), a n d

e c o n s id e r e

p le te

so u rc e

d th e ń r s t th r e e

s tr u c tu r e e

,

i in th e fo r m (5 6 ) If th e n u c le a r e n e r g y s o u r c e a ssu m e a p o w e r la w fo r th e o p a c ty o f a s ta r is c o n fin e d to a v e r y s m a ll c e n tr a l r e g io n it m a y b e c o n s id e r e d a p o in t I th is c a s e th e e q u a tio n o f th e r m a l e q u ilib r iu m s o u r c e s o th a t q = 0 fo r T > 0 n ,

,

,

Scanned by CamScanner

łį ĝĝĝğġ ĝĝ ĝĝ ĝ ğ I 巴

8





















0 =











づ っ 二 凶









7 り









在 ー

ミ コ

ヱ カ コ ヲ 비 비

コ り

己 人 闃





の り

쩝 口





呂っ





っ 已

。 侧

ロ ニ

島 っ















凹 。 。 り





コ 哟





人 力











っ り 囹



っ む 国



卷 =毛











に っ

田 田

。 每

H





\



闐 に





)

团 的

。 っ



。 り

往 コ っ 。



n っ





個 っ

り 囹







X

臼 の







划 コ ヲ の





っ の















ミ コ 。



书 钿

っ 。 っ















日月 晒



旧 闐 っ



っ 。









日 の の



二 っ





写 昌



。 っ









刀 0





召 回



り 侧

쩝 ト



回 节

島 っ





:

U

兆 铲







) U

-

q

=

쩝 日





U





/



=

:

の コ 口 っ m W 们



っ 侧 コ

の ン 侧

ぶ 人 個





.

(

-

一 )





.



鸟 闐 口

ヒ 闲



: .







Ų







.



吕 口

'





켭 口 く

)





巴 라 西



コ 了 口









コ 回

口 0







ミ ー の

っ 島



口 っ







后む の 召





日 っ





N



人 团











口 っ











。 囹





6

二 っ

口 の ン

























呂旧







v











闐 口





人 口



囹 的





/





6





コ ニ



ぶ 闐

の 闐

















8

目 コ

U



口 っ









り に

。 四





.







0

口 っ





















っ 口 囹

の り 口 の

回 っ







の 二



人 囹

日ミ

W

ロ の

j



毛ミ



龟 寸









6

m .





l







W





ģ:





U e



门 口

U 口 侧

W









フ 的







0



侧 コ

































人 力





. .

口 囹 の 细

心 口 侧

Scanned by CamScanner

5 7 nn

d c n t [ic ı u ılt io

The

(5 5 3 ) in th c I' o

n

n t po ı

so u rce

m

o

deı

8s

rm

)

T h u s th e o r ig in a l s c t o F ı b u r e u a ti q o n s ha s bee n r e d u c e d to a p a ir o f d iffe r e n tia l c q u tıtio n s (5 5 6 ) a n d (5 5 8 ) i n th r e e v a r i a b le s : p r d p a n a s th e in d e p e n d e n t ( n s g m d o n c ) W ith th c in tr o d u c tio n o f a p p r o r ia te d i p m e i n s l o n i b le s e s v s a x fo r p n,d y ar Ib r P a lls a n d z lb r r 1 th c e q u a tio n s to b e s o lv e d b eco m e d 2y

2 T hc

lu tio

d

4

=

z

'

y

=

d x

x

ı/4

(5 5 9 )

(x ) a n d

z (x ) m a y b e in v e r t d e to o b ta in p n s (r ) a n d p m d (r ) a n d g p e r a tu r e a n d d e n s ity v a r ia tio n th r o u h o u t th e s ta r E v e n th e g s o lu tio n o r th is p a ir o f e q u a tio n s is fa r f ro m b e in g s tr a ig h tfo r w a 】d (a d e ta ile d a n llı y s is m a y b e fo u n d in C h a n d r a s e k h a r s b o o k A n in tr o d u c tio n to th e s tu d y Of s te ttu r s tr u c tu r e 1 9 3 9 ) It is in te r e s tin g to n o te th a t th e o in t s o u r c e m o d e l p L u m in o s ity r e la tio n w h o s e y ie ld s a m a s s ı s lo p e o n lo g a r ith m ic s c a le s is m u c h a ig e m a s s e s th a n fo r s m a ll o n e s w h i h i in le s s s te e p b r ı c s q u a lita tiv e a g r e e m e n t w ith o b s e r v a tio n s (F ig u r e 1 6 ) A te n d e n c y to w a r d a s te e e r s lo p e fo r lo w m a s s w

so

ith th e

n s

y

th e

m

te m

ー 戛

,





,

,



p

is

ex

(5 4 7 ))

as

s ta r s

s lo

c

pe

h ib ite d b y th e w e ll (T h e d o

ha n ge

g a in is n s id e r e d a s

s a

e q u a tio n s c o n

,

,

ltin g fro m th e s ta n d a r d m o d e l (E q u a tio n a in o f v e r y lo w m a s s s ta r s o f F ig u r e 1 6 w h e r e th e t r e le v a n t h e r e , fo r th e s e s ta r s c a n n o t b e tr e a te d b y th e

r e la tio n m

o

w e sha

re s u



ll s e e la te r )

-



尸 ・

N

W

o te

IL p la y e d

at

in o s ity

r e la tio n

m

w

ith o u t c e r ta in Ie a c



ba se d

ha s be e n

s s io n

]u

be

r e la tio n

1T

r

a ssu m

p tio

h e d S o f? it is th e

fo r

it h a s b e e n p o s s ib le to

e s ta

e n e rg y

hen

w

ge n

r e la tio n

th e

o n

th e o r y ,

se o

ly

g a rd

ith

re

r e la

tio

n

b lis h W h e n

to s o m e o

e r a tio n

g e n e r a lly

b e tw ou r

f th e m

e e n th e u n

k n o w le d g e

kn o

no

ca

lle d th e kn

d e fin ite

ow ns

f th e

f th e p r iın

in q u

e n e rg y

en

g t s tľ ö m g

en

o

n

h ' " " ^





n



, 一

a ss

m

an

ow n s

山 ゲ



d

r e s u lts c a n

e s tio n

h ic h

w

g e n e r a tio

b e e s ta b lis h e d , w e s h a ll p r o h t o n e m o r e r e la tio n c a n th e s ta r s a d v m c e s s o t a i n tio n s r a is e d b y th e d is c u s s o e r s to th e q u e s b e a b le to g iv e d e fin ite a n s w

B



a ry

g r e a t d e a l o f c o n fu s io s till p r e v a ile d

a

h e r e la tio n h o w e v e r c o n ta in s s e v e r a l u n

n s w

on

in p a r tic u la r b e c a u

e v o lu tio n

l n u c le iu . R e a c tio n s r e s p o n s ib e

d is c u

u r

in o s ity

m

th e e a r ly s ta g e o f th e s te lla r

regirding th e O

lu

n a ss e s tr e s s th e ı

n

in

b a b ly い

OTı .X l j ri

ř iir A s rn g p ìıy s ik 19 3 3

\ 啕

an

d

,

a

fe w y e a r s la te r

T he re su

in

re se a ľ c

lte d in

s te

he s

,

t tw o f th e la s

c o n s id e r a

b le

lla r in te r io r s T h e

o

d e c a d e s in to

a dv a n c e

in th e

c e ss o c h ie f s u c

u n

th e c o n s titu tio n o

d e r s ta n d in g

f th e

o

f th e

in v e s ū g a tio n

s

f th e

s ta r s

have

p h y s ic a l p r o c e s s e s

is th e

e s ta

b lis h in g

o

f

Scanned by CamScanner

\ 、

回国 ■ ■



ib r iu E q u iı

5

s im

m

m o

p le

d e ls

86

th e th a t a r e a c tio n s l n u c le a r f e th c a c tu a c t Jb r e th a t e x a s th e r e

It fo llo w

kn o w

le d g e

an e o i c tio n o L1 th e r g s tı e s o m e re c l a p a

g iv

n en

g n u c le a r e n e ı

w ith th e s te

lla r

a

o

f th e

r

s te

r a te o

lla r

m e re e n e rg y ,

F ge n

o e r a tio n

it c o r r [lu m in o s y ]

de g n itu

ass

en m

p

w

fm

o

rc e 5 o t】

a

m o

dv en

d e ls

y g

om as

G

fir s t tim

c

fin a lly b e c a m

e

av a

a

tio n

ila b le

,

e

u n

so

p ìıic a

d e r s to

p le te a s lik e

co m

it

w

o

ic

d in g

to

l s o c ie ty

d

d a ta fo su

m

f s u b a to

e spo n

C

o w

m

,

19 3 9

lin g

w ro

i r c o n s tr u c t n

f y in g th e o ppı

te in

g

u r th

T ııe o r y o f S te į į a r e n t o f th e \in g T h e D e v e lo p m le ty 6 6 l A s t r o n o m ic a l S o c J o u r n a l o ï th e R o y a

ow

Q u cır te r į y

in

s ta r s

b lt d g e p ìıito

a m

l in fo r m p h y s ic a

n ew

fo r th e

w e re

tc tu r e

d in g s

in e n e r a tio n

t o f th is

Th s tn

lu c e e

c o f tlte

ly fro

d e v e lo p e d m o r e th a n ila b le S in c e th e a d v e n t o f c o m u te r s b e c a m e a v a 7 0 y e a r s a g o lo n g b e fo r e c o m p t tio n in v o lv e d fo r th e r e la tiv e ly s im p le c o m p u a e r a th e r o b s o le te p u te r s th e y b e c a m ib d h e r e m a in ly fo r o n e p u r d n ta g e T h e y h a v e b e e n d e s c r e c e a s e d to b e a r e a l a v a l ti n o f th e a p p a r e n tly s im p le s e t te h o w c o m p lic a te d is th e s o u o p o s e to d e m o n s tr a lify in g a s s u m p tio n s th a t i u n d e r th e m o s t e x tr e m e s m p o f s tr u c tu r e e q u a tio n s e v e n ith p h y s ic a l r e a lity a r e s tilı(b a r e ly ) c o n s is te n t w M

o

d e ls

su c

h

as

th o s e

b r ie fı y

m e n tio n e

d h e re

w e re

,

,

,

Scanned by CamScanner

6

T he

s ta

b ilit y

o

f s ta

rs

d In th e p r e v io u s c h a p te r w e h a v e d e a lt w ith m o d e ls o f th e s te lla r s tr u c tu f e u n e r f h l B u t in o r d e r to a c c o m p lis h o u r c o n d itio n s o t e r m a a n d h y d r o s ta tic e q u ilib r iu m th e in v e s tig a tio n firs t ta s k to w a r d u n d e r s ta n d in g th e p r o c e s s o f s te lla r e v o lu tio n fig u r a tio n s fo r is illu s tr a te d e e n s ta b le a n d u n s ta b le e q u ilib r iu m in F ig u r e 6 1 b y tw o b a lls : o n e o n to p o f a d o m e a n d th e o th e r a t th e b o tto m w h ile th e s ta te o f a b o w l O b v io u s ly th e fo r m e r is in a n u n s ta b le e q u ilib ń u m i la tte r is in a s ta b le o n e T h e w a y to p r o v e (o r te s t) th is s ta te m e n t is a ls o o b v o u s f th e e q u ilib ń u m i a n d it is g e n e r a lly a p p lic a b le ; it in v o lv e s a s m a ll p e r tu r b a t o n o its p o s itio n f e s u ltin g in a s ta te Im a g in e th e b a ll to b e s lig h tly p e r tu r b e d fr o m h ń r s t c a s e th is w o u ld c a u s e s lig h t im b a la n c e o f th e fo r c e s a c tin g o n it In t e In th e s e c o n d th e b a ll to s lid e d o w n r u n n in g a w a y fr o m its o ń g in a l p o s itio n ill le a d to s m a ll o s c illa tio n s a r o u n d c a s e o n th e o th e r h a n d th e p e r tu r b a tio n w th e b a ll th u s th e e q u ilib r iu m p o s itio n w h ic h fr ic tio n w ill e v e n tu a lly d a m p e n f i u i returning to its o r ig in a l p o in t T h e s m a ll im b a la n c e le d to th e r e s to r a t o n o e q ilib r iu m lib r iu m b y o p p o s in g th e te n d e n c y o f th e p e r tu r b a tio n T h u s a s ta b le e q u h ile a n u n s ta b le o n e m u s t e n d in a r u n a w a y m a y b e m a in ta in e d in d e ń n ite ly w h i l fo r r a n d o m s m a ll p e r tu r b a tio n s a r e a lw a y s to b e e x p e c te d in r e a lis tic p y s c a

f e q u ilib ń u m c o n fig u r a tio n s s ta b ility T h e d ifr e r e n c e b e tw

w e m u s t te s t

o

th e e q u ilib ń

co n

u m

,

,

,

,

,

,

,

,

,

,

,

i f v e r y lo n g p e r io d s o f tim e w e m a y g u e s s p r e s e r v e th e ir p r o p e r t e s o r ? W n a t is th e m e c h a n is m th a t th e ir s ta te o f e q u ilib ń u m is s ta b le B u t is it a lw a y s i ? If n o t w h a t a r e th e th a t r e n d e r s it s ta b le ? Is th is m e c h a n is m a lw a y s o p e r a t n g A

s s ta r s

,

,

W s r e q u ir e d fo r it to o p e r a te ?

co n

d itio n

fo r

each o

f th e tw

o

ty p e s o f

e

q u ilib ń u

ll p r e s e n tly a d d r e s s th e s e q u f s te lla r c o n ń g u r a tio n s : th e r m

e sha

m

o

e s tio n s a

l

an

d

h y d r o s ta tic

Scanned by CamScanner

自白

88

The

6

F ig u

6 1 illu s tr a tio

re

f s ta b le

n o

s ta

(le ft) a n d

b ilit y

u n s ta

6 ı Se c u ı a r the th

e to ta

internal

l

f

e n e rg y o

e n e rgy

U

a s ta r

d th e

an

C h a p te r 2 T h e s e

a r e r e la te

c a se o

f a n id e a l g a s

f s ta

rs

ib r iu b le (r ig h t) e q u iı

rm

a

d b y th e

ith

w

ir ia l th e o r e m

v

ť

dm

g lig ib le

n e

,

is g iv e n b y th e s u m a s w e ha v e e fg y Q ,

E q u a tio

(2

n

o

f th e in

se e n

23)



=

ra

s ta te s

m

l s t a b ilit y

in h y d r o s ta tic e q u ilib r iu m g r a v ita tio n a l p o te n tia l e n

3 In th e

o

d ia tio

p re s s u

n

re

,

w e

h a v e b y E q u a tio

n

(3 4 4 )

an

d

c o n se

qu

en

tly ,

E Fo

id e a l g a s

r an

an

d

g lig ib le d (3 4 7 )

,

+

-

A p p ly in g th e

P

P

v ir ia

l th e o r e m

ligas w

h e re

en e

ligas is

r8 y ,

w

hen

th e to ta l

internal

w e

+

h a v e fr o

ĝ

u

ra

m

E q u a tio

n s

d

b ta in

ĝ (Q

-

en e

rg y

ĝ (Q

+

o

+ U

d

f th e g a s

)

(6 3 )

,

an

d U

ra

d

is th e to ta l r a d ia tio n

ce

E

T he

,

ån g a s

-

3p

P

w e o

(6 2 )

tio n p r e s s u r e

+

-

P ,

U

_

r a d ia

a n o n n e

(3 2 8 ) (3 4 0 ) (3 4 4 ) a n ,

ģQ

-

ffe c t o f r a d ia tio

is to

_

d

)

=

ligas

6 4)

d u c e th e g r a v ita tio n a l a ttr a c tio n ; Q + U th u s ta d m a y b e r e g a r d e d a s a n e fr e c tiv e g r a v ita tio n a l o te n tia l e n e r p g y In b o th c a s e s th e s ta r h e a ts u p u p o n c o n tr a c tio n (In I in c r e a s e s a n d w ith it ligas a n d h e n c e th e a v e r a g e te m p e r a tu r e ) a n d c o o ls u p o n e x a n s io n p e

W

hav e

a ls o

n

re

th a t th e r a te o f c h a n g e o f th e e n e r g y is g iv e n b y th e d iffe r e n c e b e tw e e n th e r a te o f n u c le a r e n e r d i r g y p o u c t o n a n d th e r a te o f e m is s io n e

se e n

Scanned by CamScanner

b



6 2

i tio o f ra d a

ca w

L

s ta te o f th e r m a l e q u ilib r iu m c m ı

=

L

a

ıı m ta b ł ı it y

89

n

E

A

f th e r m

r o

an

,

d he n

c e th e e n e r gy

L

=

j

nue

is

o

is

c o n s ta n t

b ta in e d

w

(6 5 ) h e n th e se t e r m itr e m b a la n c e , _ O) s u pw n o w th a t a s m a ll



b a tio n c a u s e s a s lig h t im b a la n c e p e r tu r , 5 o th a t L B y E q u ia io n (6 5 ) nue e x ce e d# . th e to ta l e n e r8 y w ill in c r e a s e (É > O ) a n d s in E i , ce s n e g a tiv e , it fn e a n » th a t its a b s o lu te v a lu e w ill b e c o m e s m a lle r T h e r e fo r e b E y q u a tio n (6 2 ) o r (6 A ), th e a v e r a g e t e m p e r a tu r e w ill d e c r e a s e A t th e s a m e tim e th e s$ta r w ill e x a n d , p th e a v e r a g e d e n s ity th u s d e c r e a s in g A s a r e s u lt th e (a v e r a e r M e o f n u c le a f ) g h ic h is p r o p o f tio n a l to o s itiv e o w r e a c tio n s , w e r s o f p a n d T , w ill s lo w d o w n p p i l d r o p T h e p e r tu r b a tio n w ill b e r e v e r s e d a n d th e r m a l e u ilib r iu m an d L nuc w l q b ll t t a e r e d u s T n o r e h i e v l e l h i t s h e o re m , i£ y l e r m iń o t t w s ta , p f o v id e d b y th e v a th e s ta b iliz in g m e c h a n is m b y w h ic h s ta r s a r e c a p a b le o f m a in ta in in g th e f ī n a l ,

,

,

equ

ilib r iu

m

fo

r su c

h lo

n

g tim

6 2

S ta r s

es

Ca se s

o

a re sa

f th e r m

id to b e in

a

a s ta te o

f s e c u fa

r s tů

b iE ry

ı ty ıin s t a b iı

s e c u la r l i n rg u m e n ts le a d in g to th e c o n c u s o a tu r e d e p e n d e n c e o f th e in te r n a l e n e r8 y o f th e s ta r o n te m p e r s ta b ility w a s th e i tie m a l i n n e h O n ly if a c a n g h a E v e h e a t c a p a c ity o f s ta r s m o f e p r e c is e ly t e n e g l i r n , a ffe c ts th e e n e f g y s u p p y e in te m p e r a tu f e th a t n tu h e n e f g y in v o lv e s a c a n g h th e rm a l s ta b ility s e c u f e d

T he

c r u c ia

l lin k in th e

c

h a in

o

f

a

,

,

,

,

is t

e

T he

rm a

ı ty l in s t a b iı

o

f d e ge n

e r a te

ga s e s

e r a te e le c tr o n g a s m a in ly to th e d e g e n d h e n th e p r e s s u r e is u e h as lie s to th e internal e n e r g y o f t e g e T h e s a m e a pp it is in s e n s itiv e to te m p e r a tu r f a r o d l h E q u a tio n (6 2 ) s till h o s ( h e n c e a lth o u g d n a 5 3 ) i n o , (a s s h o w n in S e c t a p e r tu r b a tio ī ı f ] e n e r g y f e s u ltin g r o m e in [n te r n a s a e r d c e a n o n fe la tiv is tic g a s ), il a d r o p in te m p e r a tu r e t it w itt n o t e n ta a n s io n b u x e o t d p l a l l e to h w i L, > L itiv e to te m p e r a tu f e t a n r m o fe se n s f a i s i n o t d c tio n o f S in c e n u c le a f e n e r g y p r o u i h In s te a d o f a r e s to r a l n o t d im in s il w t u t u o p d e n s ity , th e n u c le a r e n e f g y h e te m p e r a tu r e w ill w ill e n s u e t i e q u ilib r u m m f o r a n aw y th is w ill c a u s e th e th e r m a l e q u ilib r iu m , a f u e f g y r e le a s e n u c le a r e n d e c n h a n th e e b ility is c a lle d a c o n tin u e to r is e d u e to fo r th S u c h a n in s ta e , a n d so t l a a c s e tio n to n u c le a r e n e f g y g e n e r a ,

W

e

ha ve

s e e n th a t w

,

,

ho w

e v e r,

in this

be

avo

id e d : th e g a s

c a s e th a t th e

de ge n

m a y,

e ra c

y has

ll e v e n tu a y ,

be c o m

A b e e n tw e d

l e s u ffic ie n t y

h o t a n d d ilu te d

s ts l s s o f s te lla r o u tb u r , n e n tire c a

Scanned by CamScanner

kn

o w rr a s /? o v tıe

p le s

ex am

o

th a t w e s h a ll e n c o u n te r

in C lm p tc r I I c o n s titu te w e l l kn ow ri r u n a w a y s w h ic h d e v e ı o p in to e x lo s i p o ns on t he s u b s e q u e n tly q u e n c h c d

n o n u c le a r

f s u c h th e n

a r fs a n

f w h ite d w

s u r fa c e s o

T he

,

la r in s ta b ility

d

,

,

a rc

d b y tc

p c t a tu r e s c n s iliv c n u c le a r r e a c tio n s iï r d e g e n e r a te m a tte r w a s ñ r s t s tu d ie d b y T s u n g D a o L e e (in 19 5 0 ) a n d L e o n M e s te l (rn 19 5 2 ) In 19 5 8 E v r y S c h a tz m a n p r o p o s e d th a t u n s ta b le b u r n in g o n th c s u r fa c es o f w h ite d w a r fs m a y le a d to r e c u lr e n t e je c tio n o F a s e o u s s h e lls T h is g avant G a rd e s u g g e s tio n th e n b a r e ly s u p p o r te d b y o b s e r v a tio n s b e c a m e in tirï ie th e v e r y IT l o dc l o f n o v a o u tb u r s ts (s e e C h a te r 1 1 ) p T o b e tte r u n d e r s ta n d th e a p p lic a tio n o f th e s ta b ility c r ite r io n , c o n s id e r a s t ar w h ic h b u m s n u c ı e a r fu e l a t its c e n tr e In h y d r o s ta tic e q u ilib r iu m , th e c e n tr a l p r e s s u r e a n d d e n s ity a r e I e la te d b y se c u

c a u se

ı n

,

,

d P.

4 cĮ p c

(6 6 )





(s e e

3

1o c

E q u a tio n (5 2 8 )) T h e r e s s u r e d e n s it a n d te m e r a tu p y p i t f u a o n t o t s h i h a e w c m a y b e w r itte n in g e n e r a l fo r m a s q

e

,

re

a re

lin k e d b y th e

,

山と

引队 a



凤 w

h e re

o

b ta in

S o lo by

n

a

g

d b

an

as a

lo

e n e rg y

g a in ) is a c c o id e a l g a s e s w ,

an

d O

ex

pan

a re

s s ) is



p o s itiv e coefficients C

4 /3

<

,

sgn

十b

td p c /p c ]

sg n

=

o m



(6 7 )

.



b in in g E q u a tio

[d T c / T ]

,

an

d he n

(6 6 ) a n d (6 2 )

n s

,

c e c o n tr a c

tio

w e

(c a u s e d

n

p a n ie d b y h e a tin g , w h ile e x p a n s io n (c a u s e d b y e n e rg y m p a n ie d b y c o o lin g a s r e q u ir e d fo r s ta b ilit y T h is is th e c a s e fo r h e re a = b 1 F o r d e g e n e r a te m a te r ia l o n th e o th e r h a n d a 4 /3 acco m

,

=

,

b «

,

s d p c /p c a n d d l c / h a v e o p p o s ite s ig n s T h is m e a n s th a t i s o n w h ic h w o u ld r e s u lt fr o m a n in c r e a s e in internal e n e r g y w o u ld b e p a n ie d b y a (s m a ll) r is e in te m p e r a tu r e , th a t in tu m w o u ld le a d to a fu r th e r cem en t o f L n c S u c h a s itu a tio n is o b v io u s ly u n s ta b le B u t s in c e th e te m u <

1 T hu

,

,

ac co m en

ha n

p e r a tu r e r is e s a s th e g a s e x p a n d s th e g a s m a y g r a d u a lly b e c o m th e c o e ffic ie n ts a a n d b th e fo r m e r d e c r e a s in , g a n d th e la tte r in ,

s ta

c a se

(6 8 )

,

a

b ility

w

dege n

e r a te s ta r

ill b e

r e s to r e

d W

e

id e a l (in te r m

i g)

c re a s n

,

in

w

s o

f

h ic h

in p a s s in g th a t g e n e r a liz in g E q u a tio n e r g y is e x p e c te d to c o n tr a c t a n d c o o l u n lik e

n o

th a t lo s e s e n

e

te

,

,

,

,

an

id e a l g a s

o n e

T h e t h in

C o

o n s id e r a

f

ra

d iu

s

R

th in ,

b e tw

she

ll

een

o a

f

m a ss

fix e d in

A

m

n er

,

s

h e ll in s t a b ilit y

te m p e r a tu r e T

bo

u n

d a ry

ro an

d

,

an

an

d d e n s ity p w ith in a s ta r o u te r b o u n d a r y r s o th a t ,

国画

Scanned by CamScanner

6 ı Ç* \ ¢*

・¢th ıım

,

\ N h th ņ

w

H 1只 r n ï ų n

l lw

ıIn ıt * b ı ı ı ty

Nw

ln t\\\t n l lh o s h c ı l (s e e E q u t\tio n (5 4 )) IF w y g i \W ı\\llu \t ¢X W t\ \ls tı \t r n \ņ u ľ h t n t n o w th e s h c Į ıw ilı e x pa n d t\s N M (n * W \\w Į W l \lw lłw t\ ľ }i n h u v ? lï 1 Il\l n g o l th e s e la e r s w iı t in l re s u ı y is \t\Ų \n lw \ Ĥ \\ [\\in lądh« ıP W ł \ tx u it l Ķ

\

m ¢ * N \\ h n

ł \I

\

\



,

,

,

ł \ï c c t u l

,

M h ititu tin ı idr

ł

th

\ \n

\īw

tł \tio n

(h

U

)

-

lllh r lu m

w t o

lh o p re s s u r e w ith in th e

ł \ re ı a tio n

b e tw

e e n th e c

s he

l ı ,

ha n ge s

W

" r

b uNĮ \ln th e r e s u ltin g c h ł\n g c In ı in g to th u ìt (6 7 ) Ie t\tı ı

hllłtin

,

1 1

)

T

te m p e ľ ł \tu lĘ

w e u s e th e e q u a tio n o

,

f s ta te in th e

.

\ th c n

nquitų th

m ıl s ta b ility w e

tc 11p c N tu f ¢ O l sincl b

-

L

e x

p a n s io

n \ 1 ıth e s h e

ll to

re su

lt in

d r o p in

a

0

.

Ohiously

Ib

ľ «

iuNcicntly

ı( th in s h e ı

0

/r

0 ) th e

4

s ta

b ility

co n

d itio

n

w o u

ld

i s s u po n ıis 10 11 th in its te m p e ra tu re n c r e a e h ı \tc d 11 th e s c ı ı ı y B e v io ı e a d to a n d th is m a y ı ' i h in it is n n id e a l g a s ) A e ķ p a n s lo n (e v e n il th t g u s w ı ıb e h a v e s r ttio n a th in s h e ı ı e a r e n e lg y g e n e ł h i ıe s p e c ï to n u c t w T h s u Una»ay h r m a ıin s ta b ility o f th in s h e lls \tc g a s T h e t e ? n c rı t d e " a s i g \) n u c h in th c s ł 11 o w ł \ı H iir m in 19 6 5 tin d R ic h a r d l ln Schwwzschild w Ł \s H n it Ħ) in tc u o u t lr y M u ı a c k th e iĘ o t) Zl w o r d o f ity (0 1 ı b iı t o l th e r m a ıs ta B c ïb ı \e w c ı e tw c th t s u b Je c w e h a v e n e g le c te d b r e g o in g d is c u s s io n s our ı ı ı a ı n r t u ı i c t\\ı tıo n w o u ltl b ? n o t o n ly th e e n e tg y m i8 h t a lk c t n o i tcmpcrł ï tuı n ? th ? p o s s lh illt lh t\l ł \ c han g y n p e ra tu ľ e SUiting ïe ı T h u t a n in e rc łï s e in h t nl nu x h e l ı u +i b n l c ì \ı g o la titm ıille \ h ig h e r L a n d th e ł h e ı J n \ï c b u l a ls o 1o Łl lu t\ h ig ı l c t l n o l o o 111 ı y L m uy n lr a n te e d Nuc in ig h t n o t b e g u ı ta b ility h ? r m n ıs ï s \ ļ In le t pllctl o \\Į ţ o n ic L 1 t ľ is e in s p ite th c lc m p c m tu lĘ o w ll c u u s c s iı ş l n ı 1 l \ ł I n S lm lla r ly l . Iıl Pluol h e a l w

,

n tu a

.

'

,

,

,

.



,

.

,

:

.

,

Scanned by CamScanner

Y

1, is Io ı tı ı c II s c x p s tı

f l ta r s

o

tltc o c ili c r h t c n h £ïn e

i th is n ì g

'

lt y ı

a ta b l

Tı to

6

l' h e ilt n o

o u t o

w

F th c

s he l

l

th a n is th e r a t e of p c ıa tu r e to tc tï ı e n s itiv e s # s ı c , l a i s x n hc he a l u ı A s it h n p p c rls , t iĮ r e d u e to a te m p e r a tu r o r q th a e e s in L n u c n h a g c h t w i id vaı d i n e t a c l n e r ls rc be n e g \r u n ìc n

colptud

io

p e r tu r b a t

n, nnd o ur

lb

r c g o in g ı

g

c an

be

八S S U

p

D yn a

n

d

g

r c s s u?

田t h e

6 3

u se

W

re

it y ic a l s t a b iı

m

S im ila r l re la te d

ity is D y n a m ic n l s ta b iı

to m o tio n s o

f

l in a s s p a 】c e s

in th e

s ta r , th a t

is , to

l l i s c a le , th e g a s p a ıtic e s a r e a w a y s in i s o n th c m ic ro s c o p c m ttc r o s c o p ic m o t o n ; ic m o tio n s o c c u r i e u ilib r iu tn n o m a c r o s c o p Io c a l m o tio n In h y d ro s ta l c q ıa n d o m l w ly In o r d e r to te s t th e s ta b ility o f r ilT ı p e r c e p tib ly s o m o re p lle c is e ly th e y o c c u h r e s p o n s e to s m a ll p e r tu r b a tio n s o f th e w e h a v e to c o n s id e r l c th is e q u ilib r iu m d th e o u tw a r d fo f c e e x e r te d b y th e b a la n c e b e tw e e n th e g ra v ita tio n a ıa ttra c tio n a n d l w ith a s p h e f ic a lly s y m m e tr ic c o n fig u r a tio n w e p re s s u r e g r a d ie n t S in c e w e e a i n T h e b a s ic q u e s tio n s h a ll c o n s id e t ra d ia l p e i tu r b a tio n s : c o m p r e s s io n o r e x p a n s o is w h e th e r a te m p o r a r y c o n ti a c tio n w ill r e s u lt in e x p a n s io n to w a r d th e o r ig in a l

b

o n e as

,

,

,

,

s ta te o r

A s im

in fı rthei

tio n

c o n tr a c

,

e s c a la

tin g in a r u n a w a y

f d y n a ir ıic a l p e r tu r b a tio n s to illu s tra te th e b a s ic p r in c ip le s in v

rig o r o u s tr e a tm e n t o

p le B u t in o r d e r p le s h o u ld s u ffic e

C

w

ith in

o

lv e d ,

a

a

s ta r

is fa r fr o m

h ig h ly

s im

equ

ilib r iu m

T h e p re s s u r e

19 ) a m

o n s id e i a

,

atany ,

ĺ

P

M

G

J

H

th

en c e

co n

d iū

o n

dm

m

(6 14 )

4 Jr r 4

,/ı

T h e d e n s it y

(6

p lifie d

in h y d r o s ta tic g a se o u s sp h e re o f m a s s M p o in t r (n ı) is e q u a l to th e w e ig h t p e r u n it a r e a o f th e la y e r s b e tw e e n /lz a n d M a s o b ta in e d b in te r a tin y g g th e e q u a tio n o f h y d r o s ta tic e q u ilib r iu m (5 1) a n d ta k i n g P (M ) = O exam

s o a s to c a

e s rw

a t r (m

) is g iv e n b y E q u a tio n



(5 2 )

け P

C o n s id e r ev e r w y

now

h e re

a s m a ll u i n fo r m b ta in e d fr o m th e o

r

If 8 «

I th e b i n o m ia l a ,

,



m d

r a d ia

,

o

dnı



r ig in a

l

lo

com

nes

l[6 15 )

b a

p r e s s io n

by

a sm a

(1

8

,

so

th a t th e n e w

ll p e r tu r b a tio

r a d ii

a re

m

n

' =

p p r o x im

r

Br

=

r

)

(6 16 )

a tio n

(I į

e

P: N

e

yı N 1 ī

n e

a Þ



1

1 1

1 /)

Scanned by CamScanner

e

6 3

be

can

u se

d T he P

A

ssu m

p re s s u w

de

n e w

n s itie s w

ic a ıs t b a ilit

a m

4 Ĵr

r

2

(l

,

a

d ia b a tic

a r ly , b y E q u s im ìı

ill b e

e

y dr

a tio n

-

p (1 + 3

c o n tr a c ti o n to

b e a d ia b a tic (a n d n e g le c tin g r a d ia tio n g a s p r e s s u r e w ill ' r e la te to th e in iti l a o n e a s (p /p )y , p o n e n t (in tr o d u c e d in s e c tio n 3 6 )

ex

(1 + 3 e )y

(6 14 ) th e

h

=

4

r

(1

e x p e c te d th a t a f te r th is p e r tu r b a tio d t in h y r o s a ń c e q u ilib r iu m th a t is + ,

,

to c a u s e th e s p h e r e to

(6 1 9 ) a n

(6 2 0 ) in to E q u

ex

co n

fo

th e c o n d itio n

en ce

d \tł o n fo r d y n

re w

(1 +

g a se o u

T he

'

ill r e la te to th e in itia l

co n

4e

(6 2 0 )

)

s s p h e re w

d itio

n re

ill n

lo

o

q u ir e d fo

r re

ger be s to ń n g

n

a m

r s ta

ic a į

s ta

'

P

ga s >

(1

(6 2 1 )

,

(6

h

p a n d b a c k to its

a tio n

P

H

(6 1 9 )

o u r c ase

P

d

n th e

q

.

P

H

)4

t is to b e ı

so a s

(1 + 3 8 y a )

'

4 Jr

is in

P

H

a

h y d ro s ta tic r e s s u p

n ew

,

P

m

(6 1 8 )

)

ew

o ne as

ilib r iu

93

=

P

equ

y

'

in g fu r th e r m o r e th e r e ) w e fin d th a t th e n

h e r e y a is th e

D yn

o r ig in a

w e th u s r e

l s ta te S u b s titu tin g E q u a tio

b le h y d r o

s ta

(6 2 2 )

tic e q u ilib r iu m

,

o th e r w o r d s , th e

in

o r

b iį ity īs 4 ya

T he is

sa m

e re su

re v e rs e

lt o b ta in

in th e

s

c a se o

>

(6 2 3 )

3

f e x p a n s io

d

It c a n b e

sho w n r

n s

q u ir e

) > P (1 + 4 8 )

+ 3 ya

2 1)

ig o r o u s ly th a t a

s ta r

in

w

n

,

w

hen

h ic h y a

>

<

4 /3

O

an

d

co n

d itio n

(6 2 1)

ìze r e is d y n a m T h e c a s e in w h ic h

e v e ry w

13 e v e r y w h e r e ) l if y a = 4 / b le (a n d n e u tr a lly s ta b e G lo b a l d y n a m ic a l in s ta b ility e x a m in a tio n u ir e s fu r th e r y a < 4 /3 s o m e w h e r e r e q ti e s ta r is n e g a tiv e T h u s 4 /3 )Łd m o v e r th e e n r l l a r i y a t e f is o b ta in e d if th e n g i h ig h th e s ta r w ill b e c o m e . h e r e P /p s r l a rg e l t i n e ffi c y if y a ・ \ in a s u ll th e s ta r w h e r e P /p is s m a in th e o u te r la y e r s 3 4 < / r ya u n s ta b le If h o w e v e ta b le c o m e u n s b e a s a w h o le n e e d n o t ic a lly

s ta

,

,

:

,

,

,

,

,

is e 6 ı T h e e q B c

,

m u s t a llo w

tin g e ffe c ts o

a

f

u a t io n

o

f

s ta te

,

so

lid ,

s e lf

-fä c e a t th e s u l

fin ite d e n s ity

e te m p e r a tu f

fo r

w

h ic h

a re

,

w

b d ie s g r a v ita tin g o h e r e th e p r e s s u r e v

ll ge n e ra y

,

s m a ll, s u c

h

e

su c h a s a n is h e s

q u a tio n

s o

f

Scanned by CamScanner

th e fo

lı c a s t in s ta le a r e u s u a y

n n

w

h e re

d im

t, a c o n s ta rł

K is

u r fa c e o is th e s

p

b le s v e n s io n le s s v a r ia

p re s su

re a n

d d e n s ity

(a ) D y n

,

In th e la tte r

c a se

,

e s tio n v io la

ūo

d

ly

an

d sho w

w

h e re

is

ask

b ility

f th e

s ta

h

c a ses

in S e c tio

f d y n a m ic a l

o

'

c

W

n a t a re

ń te ń o

>

,



4 /3

s ta

o r

,

s u l-fa c e

y i, 7 2

,

4 /3

<

d e n s ity is lirn ite d

it ¥ b iı

th e s te lla r c o n fig u ra tio n

Th a t is 1o Y a

n

y 2 P a s s to n o m n a liz e d Ą a n d P r d e n o te c e n tr a ]

th a t

72 e ith e r y i q u ir e s th a t f c e n tra l to th e a llo w e d r a tio o

5 4 /3 ? W '

e

s

th a t m a y

hav e

a lr e a d y

3 5

n

Reı a t iv is t ic d e s e n

e ra

te e k

tro n

gas

relativisticegenerate e le c tr o n g a s Y ı te n d s to 4 /3 T h e in s ta b ility e x p e c te d im itin g m a s s 4 /3 re s u lts in th is c a s e in th e C h a n d ra w k h a r ı th e lim it Y

Fo r

in

d y ı>

re

n o

e n c o u n te r e d s u c

,

-

x

an

p /p c ,

an

Ca s e s

h a v e to

w e

d e n s ity

/p c

r e s p e c tiv e

6 4 T he qu le a d to

p

-

ic a l s ta b ility

am

[(ř T (ŕ ľ ]

K

p (p ) =

a

a

-

(d e ń v e d in S e c tio n 5 4 ): th e d e g e n e ra c y p re s s m a ttr a c tio n o n c o n tr a c tio n

ly if th e s ı ı e ı a r m a s s is w ill e n d in c o lla p s e

Do

T he

d

fo

m

in a n t

h ic h y a

sm a

ra

can

lim ik F o

le r th a n S ı

d la t ı o n p re s s u

s i n

th e r a

g ra v ita tio n a l h ig h e r m a s s ,

n

d s to 4 /3 (a s s h o w n in S e « io n 3 6 ) is th a t o f ra d ia tio n p re s s u r e o r in te r m s o f th e p a ra m e te r þ in tr o d u c e d in S e c tio n 3 1 P + 0 In th e lim it þ= ı(id e a l g a s w ith o u t ra d ia tio n ) y a = 5 /3 a n d h e n c e a n id e a l a s w o u ld b e d y n a m ic a ll s ta b l g e u n d e r its o w n y g ra v ita tio n a l fie ld A s P d e c n e a s e s d y a e c r e a s e s a s w e ll te n d in to 4 /3 in th ı g O (p u r e e im it þ= P h o to n g a s ) A n o th e r w a y o f s h o w in g th a t a ra d ia tio n p r e s s u r e d o m in a te d g a s te n d s to b e d n a m ic ll a y u n s ta b le is b y y u s in g th e v ir ia l th e o r e m F o r u r e ra d ia fio n p P /P = u d /3 a n d h en ce b ra y E q u a tio n (2 2 3 a

se c o n

c ase

r w

te n

d o m in a n t

,

,

,

,

,

)

M

Q

b ility

g th a t th e to ta l e n e r gy e s u n bo u n d W e se e

m a

dm

= ,

p

m e a n in

be c o m

3

=

y d ifï e r

,

o

f

a

th e r e fo re

s ta r ,

E

(6 24 )

Q + U

v a n is h e s ; th a t is , th e s ta r th a t th e c o n s e q u e n c e s o f d y n a m ic a l itıs ta =

Scanned by CamScanner

Ex e

r c is e

S ho

6 2

o n c o r e sp

d s to

ilib r iu m th a t fo r a n a « lia b a tic e h y d r o s ta tic e q u p r o c e s s , s ta b ı

w

in im

a m

s ta te o

u m

lo

n

F th e

iz a t io

to ta l e n e r8 Y

ty p e p r o c e

n

(E

U + Q )

=

sse s

f p a r ti D ith c h a n g in g in w h ic h th e n u m b e r o f p a r tic le s is n o t c o n s e r v e d b u t c h a n g e s w e le s le d itio n s Io n iz a tio n (s e c tio n 3 6 ) p r o v id e s a ty p ic a l e x a m p le : a s in g s ic a l c o n h y p ht b y a b s o r b in g th e ń g n a y p r o d u c e tw o p a r tic le s a n io n a n d a n e le c tr o n a to m r h o to n A t th e t o f e n e rg y fr o m a c o llis io n w ith a n o th e r p a r tic le o r w ith a p am o u n d s to d im in o c c u r s w h ic h te n r e c o m E n a tio n im e th e r e v e r s e r e a c tio n sa m e t is f W h e n th e s y s te m is c o m p r e s s e d r e c o m b in a tio n ti l is h th e n u m b e r o p a r c e s f re d w h e r e a s if th e v o lu n e is in c r e a s e d io n iz a tio n is fa v o u r e d T h e r e o ic a l in s ta b ility

yn a m

,

o r

y a 5 4 /3 , is

a ls o

in

n e to o c c u r

p ro

an

y

s y s te m

o

,

,

,

,

,

en

han

ce

,

ł

,

,

d e n s ity (L e C h a te itiv e r o v id e a n in tu

f p a r tic le s c h a n g e s in in v e r s e p r o p o r tio n to th e lie r s p r in c ip le ) T h e fo llo w in g s im p le a r g u m e n t is m e a n t to p s te m s to th e e ffe c t o f th is p r o p e r ty o n th e v a lu e o f y a C o n s id e r tw o s y e x p la n a tio n f v o lu m e V a n d p r e s s u r e P in o n e th e n u m b e r o f p a r tic le s N is c o n o f p a r tic le s o h d u e to io n iz a tio n ty p e r e a c tio n s W e a s s u m e i h s e r v e d in th e o t e r t m a y c a n g e tio n a l to th e n u m b e r o f p a r tic le s i a n id e a l g a s a n d r e c a ll th a t th e p r e s s u r e s p r o p o r S u ppo se n o w l (fe g a r d le s s o f th e ir n a tu r e ) a n d in v e r s e ly p r o p o r tio n a l to th e v o u m e ' V In th e ń r s t s y s te m th e p r e s s u r e < th a t th e v o lu m e is s lig h tly c o m p r e s s e d to V ho w ev er N / V In th e s e c o n d s y s te m > s in c e N / V w o u ld o b v io u s ly in c r e a s e ' ' ' w o u ld H e n c e th e n e w r a tio N / V N < N w o u ld c h a n g e a s w e ll s a y to N ' N / V < N / V C o n s e q u e n tly th e p r e s s u r e b e s m a lle r th a n in th e fır s t s y s te m f th e p r e s s u r e o n d w o u ld in c r e a s e to a le s s e r e x te n t m e a n in g th a t th e d e p e n e n c e o th e

be r

nu m

o

'

,

,

,

,

,

,

,

,

,

v o lu m e

(a n d h e n c e d e n ,

s ity ) is

w e a

ke

in th e

r

se c o n

d

s y s te m

T h is

sho u

f y a p o s s ib ly s m a lle r th a n 4 /3 F o r a p u r e g a s fo r e x a 】T lp le a c c o r d in g to E q u a tio n (3 6 0 ) y a < 4 /3 b e tw e e io n iz a tio n (fo r x / k T 10 ) H e n c e in a c o o l a tm o s p h e r e o n ly a n ly s ta b le ld b e d y n a m ic a ı n e u tr a l o r a c o m p le te ly io n iz e d g a s w o u in to

a sm

a

lle r

v a lu e o

,

,

,

,

Ex

e r c is e

6 3

Sho w

io n iz e d h d r o e n y g

w

th a t th e r e

ill a lw

a

is

a

ys be dyn

c

ń tic a l te m p e r a tu r e

am

ic a lly

s ta

b le

,

an

a

bo

v e

w

te

n

g ly io n iz e d 5% an d 95 %

a lm

o st e n

h ic h p a

d fin d th is te

s la

s in

,

,

ld tr a n

m

r tia

p e r a tu

tir e ly

lly

re

Scanned by CamScanner



ıı・ ıM » ı ï

Th a

á

,着 ,

d lo p la c e m

e

P ï łP 1

r ite r io n S u h w t\rz «c h ilď « c

llio ll o l Figu ro 6 2 IIIu H IIl lly íyo ld i(ı i tl/// m o v iı)B ll m u s N c lc m d n ,

m

fb r s ta b ility

o in t 2 p o in t 1 to p

w

ith in

e c tio n a g a in s t c o n v

Co

.

W

In rv e

e

hyd

sc e n

ro s ta tic c q u

in S e c tio

5 5 th a Į th e

n

w

h ic h

ı n ay

bc

v io la te d

in

F

c a se s o

<

a fr e c t th e c o u r s e

n v e c t io rı

r a d ia tiv e

ilib r iu lï ıis lim ite d b y th c K

a

a s ta r

tic a lly ro c e s s e s d r a s tc r Į h ŕ lĮ b o th lh c s c p l u ı c t x e n p h o t i n htï ı ıs e c l lio n o l s [c lltrıo v o u

6 5

by

n u x th r o

u

gh

a

s ta r

in

re q u ir e m e n t

4 7r c G

f in te n

e n e rg y

m

,

s e n u c le a r

burning

,

w

he n F

=

qdm (5 3 )

g ly h ig h o 】 w h e n th e o p a c ity is v e r y h ig h B y E q u a tio n il h ig h n u x o r a h ig h o p a c ity le a d s to a s te e p te m p e r a tu re g r a d ie n t H O W e v e th e te m p e r a ľ u re g i a d ie n t ı ï ia y o n ly in c fe a s e u p to a lim it b e o n d w h ic h c o n v e c tio n y o c c u I s in v o lv in g c c lic m a c r o s c o ic m a i y s s m t o b o n t p ( u n o t a n e t m a s s flu x ) th a t c a iT ie s th c b u lk o l' th e e rie r8 y flu x W h e n th e to ta l flu x s a tis fie s E q u a tio n (5 4 ) (c o n v c c tiv e )th e i m a l e q u ilib r iu m is a c h ie v e d T h u s c o n v e c tio n m a y b e r e g a r de d a s a ty p e o F d y n a m ic a l in s ta bili ty a lth o u g h it d o e s n o t h a v e d is r u tiv e c o n s e u e n c e s p q In {h c t in s p ite o f b e in g a d y n a m ic p r o c e s s c o n v e c tio n a ff e c ts th e s tr u c tu r e o f a s ta r o n ly a s a n ec t iv e h e a t c a r r ie r a n d a s a m ix in g m e c h a n is m T h e c o n d itio n ľ th e o n s e t o f c o n v e c tio n (o r th e li i m tin g te m p e r a tu r e g r a d ie n ņ is d e te r m in e d b y a s im p le c r ite r i o n as w a s sho w n by K a r l S c h w a r z s c h ild i n 19 0 6 T h e S c h w a r z s c h il d c r ite r io n fo r s ta b ilit y a g a in s t c o n v e c tio n d e r iv e s fro m th e fo llo w in g a rg u m e n t: C o n s id e r a m a s s e le m ent Ą m S t a a s s h o w n in F i u a t so m e p o in t w itb in a g r e 6 2 D e n o tin th i s p o in t b g y 1 le t th e ł o c al v aı u e s o f be c o

m e s e x c e e d in

,

,

,

,

,

,

,

,

,

Scanned by CamScanner

竹 ―



S A

* 3 s d ie

W

ııl ic lı

イ S c h i ıď$

d ¢n s lty Fi ln

s

p w



*

an

d 即

1e w e ia*ï ¢ w

p

dd ını «

ba

i

a n

d

¢\ w

d e ıı# it F

ity 明 目tl iı

龋 ıh c 内 自n d

e # s ım c n

h in th lı

G a b e R ic

d iq w

crlıeri 细



a

e ın ıw

p P

$m

a ¢e

置in t

八 \ tM

e

a ı

lı4 ın

r ır m ¢

u



邮 個

c ı》 冒

p n eM

T ht e



m n a ıp e w ı

\

¢ııe

»

m

k



t= « » i* » qq ı=ı =d«w «ıæ =

ı* e

ııb a ı

m

n n «

ı *

ĺ t d ¢ı h ıı h

営蛔

S ııP P n ıt th e

m

ï

* ¢w w

m

e

m

ı ı o ı

.

d ıııııiııiıc e c p« ı

m

d be p o e ı d ı

a ıı ıb

M

e re n o ¢

h ıı ıno a « ew n ıe t

Scanned by CamScanner

s ta

The

6

lit y bı

98

th e

y A s and

c u rv e s

in te r s e c t

w

io

ith A

£ £ ŢX b ility

s ta

an

d

n u ı

ľ

1s



ltip ly in g b o th

s id e s

by p y

It is

n o te w o r th y

For

an

id e a l g a s

b o th to te m p e r a tu

re

,

e

° s ta r

d

w

W

j

Ž0 0

be

*

w

ith in th e

th e c o n d itio n fo

r

.

(6 2 6 )

..

l v a lid ity

ne

P

b b u ıu

p ro v e d b y s e in 19 6 7

n w as n o t

o

C o m b in in g E q u a tio g iv e n c o m p o s itio n d itio n fo r c o n v e c tiv e s ta b ility in th e fo r m

m a y a ls o

,

p

"

a

h ic h

n s ity

de

ha v e

w e

P

co n

to th e

lu s lo n N co nc

tio n

d ia u o n p ıc g lig ib le r a w he n c e a n d to d e n s ity ,

an

rs

o rld s T e sp co ı



fo r

f s ta

ite r io f th is s im p le c r fte r it c a m il s ix d e c a d e s a e th o d s u n t

a th a t th e g e n e r

th e m a tic a l m r ig o r o u s m a

-

/P

o

e

in to

u

,

,

r

,

(6 2 7 ) T

(6 2 7 ) a n d (6 2 6 )

n s

w

,

e o

b ta in th e

w r itte n a s

r e c a llin

g th a t th e te m p e r a tu r e a n d th e p r e s s u r e g r a d ie n ts a r e n e a tiv e W e h a v e th u s g o b ta in e d th e u p p e r lim it fo r th e m a g n itu d e o f th e te m e r a tu r e p g r a d ie n t a llo w e d b e fo r e c o n v e c tio n s e ts in

6 6

it

m ay

be

a tm o s h e p re c o n v e c ti ve

Ca se s

e q u a ll a y p p lie

B ut

can w e

in s ta bilit i y n

d to

be

o

f co

in te r io r s

m o re s e c p

s ta r s ?

n v e c t iv e

ific

an

in s t a b iı it y

d fo r ,

a b o u t th e In p a r tic u l a r h o w is ,

co n

ex am

d itio

p le

,

to

n s th a t m

r e s tr ic tio n

th e E a r th

'

s

y le a dm to (5 3 4 ) c o n n e c ;te d a

n

h

m

o

o

bl

C O ]

a

Scanned by CamScanner

I

in S e c tio

n 3 6 th a t d u r in g io n i z a tio n th e a d ia b a tic e x o n e n t is p i f n r e g io n s o r th h r e o re e T d e s ta r w h e r e e r e w h t e g a s is p a r tia lı io n iz e d th e lo y o n v e c tiv e s ta b ilit c f r o i n i s o t i m o r e d iffic u lt y d n to s a tis fy A t th e s a m e tim e co a y b e c o lT te d y n a m ic a ll m s i n o y u n s ta b le if 4 3 h e s e re g

W

e

hav

e se e n

,

,

t

ya

,

ya (

/

<

) b u t th e

a d ia b a tic e x o p n e n ts th a t a p p e a r in c o n d itio n s b 2 8 d c o i e f m fe r e n t fu n c tio n s o f e ) a n d (6 p B o th a d ia b a tic e x p o n e n t s te n d (6 2 6 ) d 4 5 /3 fo r 芦 争 a n to /3 fo r 芦 台 0

in

v ï h ic

h

c a se

ya

=

,

to

Ex e

r c is e

n e n ts

in

6 4 co n

F o llo w in g th e p r o

If w

e n ow

d th e a iı fo r

u se

tiv e

re o

f S e c tio n 3 6 d e r iv e th e ,

n s

=

q u a tio

K

F

a

n

4 JT

<

c

G

d ia b a tic

ex

po

fu n c tio

an

d

r a d ia tio n

tio n

(5 3 ) fo

r

th e te m p e r a tu r e g r a d ie n t

(5 1 )fo r th e p r e s s u r e s ta b ility (6 2 9 ) in th e fo r m e

a

,

as

n s

,

th e r a d ia tiv e d iffu s io n e q u

h y d r o s ta tic

conv ec

du

(6 2 6 ) a n d (6 2 8 ) fo r a n id e a l g a s th e ir v a lu e s fo r þ O åa n d 1

d itio

l u la te o f þC a c

ce

4

H

g r a d ie n t

(T )

(1

,

w e o

b ta in th e

co n

d itio

n

(6 3 0 )

þ)

h ic h im p o s e d a n u p p e r lim it o n th e p r o d u c t h t co n c o u ld n o lo n g e r h o ld W e n o te t a r a d ia tiv e e q u ilib r iu m in s q u a r e b r a c k e ts o n th e ń g h t h a n d s id e ditio n (6 3 0 ) is s tr o n g e r s in c e th e te r m F f tio n a r is e s b e fo r e th e u p p e r lim it o r K is s n a a lle r th a n u n ity T h e r e fo r e c o n v e c T h e tw o c o n d itio n s c o n v e rg e a s P te n d s to z e r o (c o n d itio n (5 3 4 )) is r e a c h e d it a n d lo w a d ia b a tic e x p o n e n t c o m b in e In th e c a s e o f io n iz a tio n th e h ig h o p a c y t r r e g io n s o f f c t is p a r tic u la r ly im p o r ta n t in th e o u e to in d u c e c o n v e c tio n T h is e r e fo r h e liu m a n d h y d r o g e n to b e l a r e s u ffic ie n tly o w s ta r s w h e r e te m p e r a tu r e s o f h ig h te m p e r a tu r e lla r in te ń o r s e s p e c ia lly in z o n e s o n ly p a r tia lly io n iz e d In s te i th a t m a y in d u c e c o n v e c tio n s t th e d o m in a n t fa c to r w h e r e th e o p a c ity is c o n s ta n i te n s e n u c le a r burning is e x p e c te d to f e s u lt fr o m n a M g h e n e rg y flu x S u c h a flu x b e e x pre sse d a s a p o w e r r a tio n r a te m a y A s s u m in g th a t th e n u c le a r e n e r g y g e n e e to tr a n s la te it s h o u ld b e p o s s ib ı ^ " m la w o f th e fo r m (5 7 ) q = q o p T w ith n » ı i itin g v a lu e fo f n T h is l r burning in to a m th e c o n d itio n o n th e in te n s ity o f n u c e a 1y b u t r e q u ir e s l tic a ı c o m p lis h e d a n a y is b y n o m e a n s a s im p le ta s k it c a n n o t b e a c fo r l tio n o f a lim itin g v a u e tio n s T h e q u e s s o lu tio n o f th e s te lla r s tr u c tu r e e q u a in r e la tiv e ly s im p le 3 0 s ; fo r e x a m p le u s g 9 1 h e t i n d e s n h a s a lr e a d s d y b e e n a d re ń b e d in C h a p te r 5 ) C o w lin g o d e ls d e s c m h e t f o t s m o d e ls (m o r e e la b o r a te v a f ia n c o n v e c tiv e ly s ta b le n t o p a c ity , n o f o r a c o n s ta : s i n o i t o b ta in e d th d n o e fo llo w in g c 4 w h ile fo r l in g b e tw e e n 3 a n d n u m be r y a d s e e c c o n fi u x e g r a tio n is p o s s ib le if n in e x c e s s lu tio n is p o s s ib le fo r n n o s u c h so 7 3 ) a K ra m e r i n o , t c S e i s o p a c ty la w ( ı a b o r a te d b y R o g e r u rs u e d a n d e o b le m w a s p r o f a bo h e t o s 5 p u t 8 In th e e a r ly 1 9

T his is s im ila r to h ic h K F a bo v e w

co n

d itio

n

(5 3 4 )

,

w

,

,

,

,

,

,

,

,

,

,

,

Scanned by CamScanner

6

to Tı

m y lc r

C

o om

w

on

ld

nol

In

dw

p a c ity

e n c ma

lı y

5

tio n n in s e c rv c s e e c hı

be

is

v e ry

to

d o m in a te

lo w

w e sho u

c o n c lu s io n

"

a

e f i\ h ig h tc m p

,

ld

an d

,

o cc u r

le s ta n t lb th c s im p ed o n s a b t 6 th ıl ,

s ta b ility

se c o n

lik e ly to

m o fe

is

is e c tio n th a t c o n v

lin d

d 1o s u r p ıis c

re s s ttr e d e g e n e ra c y p

tiv e o

o

O Ï

n v e c tio lh n l c o n in d ic ł\to s

30 ) d itio n (6

in a n t w

w e s ho u

tslı ı ts

ty ı ı bı

f th c e n e r s itiv ity o gy tm e s e n

Do

iln r ith s in ì

s tn

d,

do

m

tco nvec a g a in s

l n u c le a r n o s ta b e

to t c o n v e c tio n n o te x pe c

o w in a n t in ı

w

rd m o

he n de l

,

a s s s ta r s

m

tio n is r e g a in e d T h is is

bu

r n in

g is p o

s s ib le u n

in te r io d e v e lo p in th e

rs o

de r

f w h ite

a r fs

C o n v e c t iv e

e n e r gy

h d e n g th m e t o t h e m ix ın g ı

tra n s p o r t

r v a n T E q u a tio n (5 3 ) is n o ro n g e d ia tio n flu x , w h ic h i h t h a n d s id e is th e r a e a r in g o n th e r g l a f x u h e t t p h p a t e th e s e n s n tin g to o n ly a s m a ll a tio n (5 4 )), a m o u th e to ta l flu x F (o f E q u n o w d iffe r s fr o m t b e s u p p le m e n te d o r r e p la c e d f F H e n c e E q u a tio n (5 3 ) m u s u n k n o w n fr a c tio n o i f c o n v e c tio n S in c e c o n v e c tiv e m o t o n s a r e b y a n o th e r o n e th a t ta k e s a c c o u n t o tin g th e c o n ti l th e r e a r e o n ly a p p r o x im a te w a y s o f e s m a c le a r ly n o t e n tir e ly r a d ia d im e n s io n a l s te lla r m o d e ls T h e m o s t c o m m o n ly v e c tiv e flu x fo r s p h e r ic a İ o n e d b y L u d w ig B ie r m a n n in th e 1 9 3 0 s b a s e d o n a d o p te d m e th o d w a s fir s t p r o p o s e le n th w h ic h h a d b e e n in tr o d u c e d b y L u d w ig P r a n d tl a th e c o n c e t o f m ik in

w h e n c o n v e c tiv e

e n e rg y

l ce tl a n s p o r t ta k e s p a

,

,

,

,

,

g , g p fe w y e a r s e a r lie r a s th e d is ta n c e tr a v e r s e d b y a m a s s e le m e n t w h ile c o n s e r v in g its p r o p e r tie s b e fo r e it b le n d s w ith its s u r r o u n d in g s T h e a r g u m e n ts fo r e s ti ,

,

m a tin

g th e c o n v e c tiv e

Of c o n

vec

tio n

,

flu

x c o n s titu

a n a p p r o x im a te m e

te w h a t is k n o w n a s th e m ix iï ıg

th o d

fo r

c a lc u la

tin g c o n v e c tiv e tr a n s fe r

p r ia te p a r a m e ? z a tio n S in c e th e m ix in g le n g th , w h ic h w £c , c a n n o t b e d e te r m in e d fro m fir s t r in c i le s it is ta k e n a s p a p p ro

p

p a ra m

le ï ıg tìı tìıe o r y

,

e

sh a

a

fr e e

by

an

ll d e n o te b y ,

a

d ju s ta b le

e te í

In th e m o tio n s

c a se o

C

f c o n v e c tiv

o n s id e r a r is in

e tr a n s fe r ,

th e e n e lg y

is tr a n

sm

itte d b y tu r b u le n t m

a ss

m a s s e le m e n

g t a t a r a d ia l d is ta n c e r (m a s s m ) w h e r e d th e d e n s it y p T h e b a s ic a s s u m tio n is th a t th e m a s s p e le m e n t tr a v e ls a d is ta n c e C a d ia b i a t c a lly a t s o m e v e lo c it y u c , u n til it r e a c h e s P r e s s u r e e q u ilib r iu m w ith it s s u r r o u n d in s d a n g r e le a s e s its s u r p lu s h e a t W e n o w e s tim a te th e d iffe r e n c e s õ ( ) b e tw e e n p r o p e r tie s f o th e e le m e n t a n d th o s e o f its is g iv e n b th y e d iffe r e n c e b e t w e e n th e c h a n g e in te in th e s u rr o m p e r a tu r e th a t h u n d in s o a s o c c u rre d v e r th e s g m a ll d is ta n ce c an d h t e c o rr e s o n d i n g a d ia b a tic p th e te m

p e r a tu r e is T

,

an

,

Scanned by CamScanner

6 6

e s

o

f i

c ha n g

e

th a t h a

s o c c u lr E

d

iıh in tl ]c

w

吕ア

芸) 二



,一

(6 3 1 )



iJa r fo

a s im

ï jsin g

h e r e th e tm

P

d ı n p

fo

rm

/(d

th e ı em ı *

r

p

/ d r ) (M h e ig h Ļ w h ic h ix in g le n g th in u i n n

c a le p re s s u r e s

g th e m d is e ħn e x ı k n

s a r in

a

(i



łe ı s

h e re

w

w

ıifíiıs

th e

a s th e m

(6 3 2 )

ń

s id e

w

ith

a

in

m

i

is tı ıe

C o fnh i sl th i 加电t h e e ts o

o w n

)

r aı u re

t

s

e n

ix in g ı m g th pa

gt

s c a le

,

d im

a

u s

s

e n s io n le s s

M

p a ia

ea

iııe ie r

r a m e te r .

£c P w

h ic h ís th e

fro m E q u a tio

T he he a t

r e īe a ie

=

ld r )

(6 3 4 )

ŁP Ig p y

p a r a m e te r o f th e m o d e l T ic ll yp a y a 6 2 ( 7 ) th e d e n s ity d e lic it is r e la te d t o th e

sm a

.

n

,

d W

u n

o f te n J p e r a tu r e

it

m

a ss

d d e n s ity M u ltip ï y J n g b y th e v e lo c ity o r th e c o n v e c tiv e h e a t Øu x an

,

,

he a t

a £c o in s ta n t

\ın

be r u n ı

ūe m p e n

p r e s s u re

H e ııc e

.

u u re

su

th e

a m

F in a lly rp ı rıs b y f

o u n t o

is

cpóT

an

d p c p ã T is th e h e a f r e l p e r u n it v o lu m e o b ta in th e a v e r a g e r a le o f h e a tin g p e r u n it a r w

w e

H

T he

d p

s o le

a s s e le n a e n t r e le a s e s

m

/(

c



,

w

he r e

cp

is

th e

he a t

c a\

ity

,

p 吣 门沾T

a

fu

n c

ńo

n

(6 3 5 )

' w h e r e g is th e a c c e l y b e e s tim a te d b y u c = į i i l i th e lo c a l g ra v ita tio n a l e r a tio n w h ic h b y th e A r c h im e d e s b u o y a n c y p r n c p e s , H ence a c c e le r a tio n g , r e d u c e d b y th e fa c to r 18p /p l

c o n v e c tiv e v e lo c ity m a

,

,

,

Uc

W

he m

iĺ ph\e

=

ha ve

w e

th e n n a J sp e e d

Į tłm

\ðT

=

l r \Ł .

=

Ua

ĺ p lp }A ðT lT \

is th e W e n o te th a t d E q u a tio n (6 3 4 ) to e lim in a te g Ļ c d ) S o m e tim e s h a lf th is h ic h is o f th e o r d e r o f th e s o u n s p c e r ta in fa c to r m a y b e o f ta n Ļ s in c e th e u n e «l b u t th is is u n im p

y is a s s u m , p e d in to th e fr e e p a r a m

e te r ( ť

d 6 34 ) C o m b in in E u a tio tıs (6 3 5 ), (6 3 6 ), (6 3 3 ) a n ( g q

,

H

c



p

(6 3 6 )

,

u se

(w

v e Jo e it

.

čp

T マソソ卢

以下酊了」 ー

{

d In T

\d ln

p

w e o

b ta in

3 /2

11 ノゴ

a

2

Scanned by CamScanner

d s ta

The

6

it y b iı

o2

T he

to ta l e n e

5 E q u a tio n (

tu r e m pe ra te s th e te 3 ) th a t r e la

co n a m o re

by

ic a te d rp ł

f s ta

g ra

rs

su m

F is th e

it tim e pe r u n

e d n s o rt rg y tf a p

o

d

o

f th e

ra

d ia tiv

e

p a r t g iv e

fıu

x

is

e n e rg y

he d ie n t to t

re

h y dro

n

s ta tic e

q

ac ed pı

h ic h

w

o n e

a

by

e an s

m

p o ly tr o p

t A d ia b a t id y

ace H re p ı

w e b a tic ity ô T / T s u p e r a d ia ta k e d b y G M /R a n a n d p /p E q u a tio n (6 3 3 ), ,

ce

=

.

M P by 37 ) E q u a tio n (6

by L

I in

/R

/R

2

,

W

,

3

T by U h ic h y ie ld s cp

,

/M W

T

ith

o su m

o f

m

a r i2

c o n v e c

t iv

depen ds o n th e v s u s t a in to m a in t a in

de pe

rn u st

w

f th e

o

10 " o

g n iz e th e h t e r m a l (K

e re c o

s, a n

f 10 3

d th e

f

o

ht ha n d

s

id e

a s th e r e c

2 6 0 )) o f th e o ltz ) tim e s c a le (E q u a tio n ( e lv in H e lm h o tio n (2 5 6 )) o f th e d n a m ic a ] tim e s c a le (E q u a

se c o n

d

a s th e

to

ip r o c a l rd e r o f

d

y

s

tia lly

c o u tse

w

T

p ity

te m en s

e sse n

o rd e r

c o n c lu s io n

In

s

fir s t te r m

h r ig th e p r o d u c t o n t e

o

h ic h

c le a r ly s h o w s th a t

go o d

v e ry

s u r fa c e

,

w

in

ĻK )

a c o n v e c tiv e z o n e

p p ro x im a tio n T h is a p p r o x im h e r e P /p « G M / R W e n o te a

th e te m p e r a tu

a tio n

is

ho w

ever

no t v a

lid

re

cı o se

th e s te lı ar

to

th a i a s s u m in g

an

a

d ia b a tic

p e r a tu r e g r a d ie n t le a v e s F u n d e te r m in e d th r o u g h o u t th e c o n v e c tiv e z o n e It is ly th e tin y e x te n t o f s u p e ra d ia b a tic it th a t d e te r m in e s th e r a te o f o n v e c tiv e c y e n e rg y tr a n s p o r t T h is is r e m in is c e n t o f th f e a c t th a t it is th e s li h t d f m t te m

p r e c is e

ho m

g e n e ity in th e ra d ia ū o n fie ld th a t d r iv e s th e s te lla r in te r io rs (s e e A p p e n d ix A ) o

c o re

A iıd n o n u c le a r e n e rg y

fr a c tio n

T he ș in c e

assu m

o

F th is

p tio n d y n a m ic a l

c o tre

g e iıe ra ū o is g iv e n b y 司 雯目巫) 罈 ヨ

n

o u ts id e

g

ra

d ia tiv

th e c o r e

f a d ia b a tic it l y e a d s to a o ıtr p y o p ic s ta b ilit r y e q u ire s y > 4 3 a / a n d s in c e

,

e

ene

sho w

par

e

u re

ro

rg y tr a n s p o r t in

th a t th e r n a s s

o

,

q u a tio Y a is a t m e

n

o

f

o st

s ta te

5 /3

,

N

o w

a s ta r

f

ith th e m

g r a d ie n t m u s t b e v e r y n e a r ly a d ia b a tic (y H y a ) T h u s in s te a d o f E q u a tio n (5 3 ) Th e te m p e r a tu r e to a g r a d ie n t m a y b e re p la c e d b y th e a d ia b a tic o n e in d e e p c o n v e c tiv e z o m w

n

e ra

in

冒 歹



Scanned by CamScanner

hy

e ta tic ro s

i q u ilib r u

m

m u s t s a tis fy

4

3 ic h w h by

a

5 ya

<

(6 4 0 )

<

3

'

h c o n fig u r a tio n o f a s ta r is to s th a t if t e n le a n in d e x n m a y o n ly v a r y b e tw e e n o e th e

p o ly

u

p

be

p p ro 1 5 and 3 a

x

im

a te

ly d e

s c r ib e

d

,

6 7 e th e tm a r iz T t) s u rï

qu

e s tio n o

Co

f s ta b ility

o

n cı u s io n

f e q u ilib r iu

m

in

a s ta r

(w h e th e r

ra

d ia tiv

e

t s ta b ility te r , le t u s s a y th a h r a is e d a t th e b e g in n in g o f th is c a p i v e t c e v on o in t to or c a t a n y g iv e n p p a r tic le s a n d p h o to n s th e a b ility o f th e g a s n o d s s de p e n x e r ts , s o a la y e r s b y m e a n s o f th e p r e s s u r e it e l i e ig h t o f th e o v e r y n g w e h t in re s u s ta h is e n d , th e p r e s s u i s ib le p e r tu r b a tio n s T o t a c t b a la n c e d e s p te p o s x e i n a t i n to n ta it S e n s itiv ity h b o th o n te m p e r a tu r e a n d o n d e n s y d s t r o n g ly e n o u g n e e d d to p n lu s t u n aw ays, an d in o r d e r to p r e v e n t th e r m o n u c le a r r r e is r e q u ir e t u a r e s to te m p f in s ta b ility in s t a r , a d d itio n a l c a s e s o a v o id c o lla p s e T h e r e a r e t o s a o s u r in th e d e n s ity i le , b u t s in c e th e y o c c v io la tio n o f th is p ń n c p i l n g fr o m t u s e r l l i a y ll d e a l e s se n t o p , w e sh a de v e ı i o r c o n ń g u r a tio n s i t r l e n i a c e s h n e i n w p o f e v o lu t o c o u rse a s th e y a r is e w ith th e m

)

Scanned by CamScanner

The

evo

sc

H

a v in

g

an sw e red

f th e

is

b y th e (s lo w )

se t

i

e v o lu t o n

d e c r e a s e fr o m tio n o f a s t ar

he

th e tw o

tu r e o

o

ı u t io

b a s ic q u e s tio

f s ta r s W

r a te

o

f

th e c e n tr e o u t w a rd w

sse s

s id e r in

g th e

P o s itio n

re c a

c o n s ìJ m

W

f

eac

e

n s

po

n

o

f th e

d

a

l

re

n u c le a r

e s c a le

(th e

n

h a n g e s th a t

o ccu r a

t its c e n tr e

To

f

o

s te

fu e l N

c o n c lu

lla r

o w

th e r a te of

,

d e th a t th e

co re

)

,

a re

e v o lu

ith th e

w

o u te r

evo

lu tio

b ta in

s im

p lifie d p ic tu r e

o

a

n

,

e v o lu ti on

o

f th e

s ta r

o

f

th e te m p e r a tu

re a n d de n s ity a r e th to d e te r m i e o n l n e an y p r o p e r tie s r e u i y o th e r p h y s ic a l q re d q u a n tity If w e d e n o te th e c e n tr a l te m ,

h a p te r 2

fu e l th e ,

c

a

-

re

n u c le a r

g io

rs

t th e th e e n d o f C

m a y th e r e fo re

c e n tr a

h

se

ll th a t th e tim

p tio

ill b e le d b th e th e y

th e c o r e is g r a d u a lly d e p le te d o

Pro \

e

f s ta

o

t ic p ic t u

a

m

n

te m p e r a t u re a n d d e n s it y

T h e a ir p

[T (t )

,

p c (t )]

th e o n l y p r o p e r ty th a t d is ti n g u is h e of an s th e e v y o th e r s ta r f o lu tio n a o th e s ry am e co m p o s itio n is its m a ss

c o iT e s po n

tr a c k o ,

f

d s to

a

w e m a y ex

s ta r

a

in

o rd e r

pe

r a tu r e

p o in t in

fm

p e c t to

m

o

th a t

b ta in

ı 04

Scanned by CamScanner

7 ı

p a ka v y e n tr o

py

an

d G io

S

an

,

cha

Pa c

t ・r ı za

t io n o f

(ı o g T ı o g

S h a v iv in 19 68 T h e p ro g r e s s in tim d th u s p a r a m e t r ic lin e

p

) pı a n

e

ıo 5

ra

[T c (, )

s

,

T h e fo llo w in g d is c u s s io n , w h ic h fr o m v e r y s im p le a r u i? is in g g

w

ill

P c (S

)1 W

e w a s si m u ı a te

e re o

b ta in e d fo

e v e n tu a

m e n ts w as ,

lly le a d t o a in s p ir e «l b y th e s e

d b y d e c re a s in g th e r d iffe r e n t v a ı ues o f

m o re c o m

pre h e

rı s iv e

p ic tu r e

w o rk s

A ll th e p r o c e s s e s th a t a r e b o u n d to o c c u r in a s ta r h a v e c h a r a c te r is tic te m i a n d d e n s ty r a n g e s a n d h e n c e d iff p e r a tu r e e re n t c o m b in a tio n s f o t e m t e r a i u r d e d e n s ity a n t h r e m e t n p e p r e v a ilin w ill d e g s t a te o f th e s te lla r m a te ń a l a n d th d e o m in a n t p h y s ic a l th a t s h o u ld b e e x p ro c e s s e s p e c te d to o c c u r T h u s th e (T ı a n ) e m a y b e d iv id e d p p in to z o n e s r e p r e s e n tin g d if fe r e n t h i p y s c a l s ta te s o r r o c e s s e O s p u r fir s t s te p w ilı be to g e t a c q u a in te d w ith th e te iT a in th r o u g h w h ic h th e e v o lu tio n h t f a h l t l s o t e e s ar p c e n tr e a r e w in d in g ; th e s e c o n d s te p w ill b e to id e n tify th e tr a c k c o r r e s p o n d in g to e a c h s te lla r m a s s ; fin a lly b y fo llo w in g e a c h tr a c k th r o u g h th is te r r a in w e s h a ll b e a b le to tr a c e th e c h a in o f p r o c e s s e s th a t m a k e u p th e e v o lu tio n o f a s ta r ,

2

,

,

,

)f

d

,

,

y

7 I T he

(T

s ta te a n w

,

p

) p la n e

Cha

w

d d iffe r e n t

h e r e th e

co n

d itio

ra c

t e r iz a t io

n

ill b e d iv id e d in to n u c le a r n s a re

p ro

bo

u n

o

f t h e (lo g T lo g p ) la p ,

zo n e s

do

m

in a te d b y d ifr e r e n t e q u a tio n s o f la r in te r e s t w ill b e th o s e r e g io n s

O f p a r tic u le a d to d y n a m ic a l in s ta b ility A

c e sse s

d to

d e n s ity a n d te m p e r a tu r e ty p ic a l o f s te lla r in te ń o r s s p a n lo g a r ith m ic s c a le s w ill b e u s e d fo r b o th

Zo

T h e fo llo F ig u r e

in g 7 1 T he w

a rg u m m

fo r b o th c o m o n p o f th e fo r m

en

o st c o m en

ts

n es o

e

q u a t io

n

o

m

an

y

s th e r a n

o rd e r s o

fm

ge s o f a g n itu d e ,

f s ta t e

o f C h a p te r 3 a n d le a d to l l d s te a r g a s is th a t o f a n id e a l g a s n s ta te o f th e io n iz e d le c tr o n s H e n c e th e c o m m o n e q u a tio n o f s ta te is

a re

m o

f th e

n e

ts : io n s a n

b a se d

o n

th e

m a te

ńal

e

p



三p T



K

o

pT

,

口马



A t h ig h d e n s itie s a n d r e la tiv e ly lo w E q u a tio n (3 2 8 )) th e ir c o n tr ib u tio n to th e d e g e n e r a te a n d s in c e te m e r p a tu r e s th e e le c tr o n s b e c o m e th e n b e a p p r o x im a te d b y Pre s s u r e is d o m in a n t th e e q u a tio n o f s ta te m a y , W

h e re K

o

is

(

a c o n s ta n t s e e

,

,

P

p



K

w

r

Scanned by CamScanner

Ħg u

7 I M

re

a p p in

g

f th e te m p e r a tu r e d e n i d s ty ia g r a m

o

s ta te

(s e e E q u a tio n (3 3 5 ))

,

to th e o th e r

s id e o

f

is ,

o

f

h ic h th e

w

h ic h

w

c o u rse

e fr e c

,

a c c o r d in

g to th e

p la c e s E q u a tio n (7 1) T h e tr a n s itio n fr o m g r a d u a l w ith th e c h a n e in d e n s it g y a n d te m

f d e g e n e r a c is l c e a r l im y y p o r ta n t w h ile id e a l g a s la w p r e v a ils T h is b o u n d a r y m a y b e d e fin e d b th th a t th e e y p r e s s u r e o b ta in e d fr o m E ,

lo g P a s tr a i h t g

lin e

w

ith

=

a s lo

a bo v e

re p re se n

(7 1) b e

n

1 5 lo g T +

pe

o

f 15

K \ p 5 13 lie s

,

K

>

q u a l to th a t

e

C O n s ta n

a s sh o w n

o pT

(to th e le ft o f th ) is lin e T h e id eal as g

t tw o d iff e re

o

f

o n e s t a te

p e r a tu r e

,

t o

q u a tio

h ic h is

q u a tio n

re

s id e a n

w

e

o

o n

th e o th e r

q u ir e m e n t b ta in e d fr o m re

t,

(7 3 )

in F ig u r e 7 1 T he

e le c tro n

,

zo n e

,

la b e lle d I li e s b e lo w it ,

n t s ta te s o

in te r e s te d in th e b e h a v io

ur o

f

f e v o lu tio

n

,

j

n o t u st t o th e e le c tr o n

a s ta r r a th e r ,

p re s s u

re

(in

th e

th a n th at o f an h y p o th e tic a l e le c tf o n

Scanned by CamScanner

Fo f eq

s tilıh ig

io r1 uat

h e r d e n s itic ti

o f s ta te

,

c

he n

w

rc ı a tiv i« [ic c llb e t»

P

K łp a s tr a

fi e s h ic h d e n

ith

a s lo

pe

o

im p o r ta n t ro le th c ,

'

=

K

(1 A ) een

,

ilFi

pT

o

th c

id e a l g a s

b e fo re , fT o

m

an

To n e

d th e

th e r e q u ir e m e n t

,

ig h t lin e lo g p

w

an

K t p 4 /3

=

E u a tio n (3 3 8 )) T h e b o u n d a r y b e tw (s e e q tic d e g e n e r a c y z o n e m a y b c o b ta in e d M a tiv is

w

p la y

h a n g e s to th c fo r m

f3 T hu

s th e

bo

3 lo g T +

=

d a ry b e tw

u n

c o n s ta n

(7 5 )

t

th e id e a ıg a s z o n e a n

een

d th e

e le c tr o n

h a n g e s s lo p e b e c o m in g s te e e r a s th e d e n s ity in c r e a s e s p d ı t r o n c e g e n e r a c y r e g io n th e tr a n s itio n fr o m n o n r e la tiv is tic to e e is tic d e g e n e r a c y o c c u r s w h e n th e r is e in p re s s u r e w ith in c r e a s in g d e n s ity re İ a tiv in e d b y th e lim itin g v e ı H e n c e re la tiv is tic d e g e n e ra c y o c ity ( be c o m e s c o n s tr a b e c o n s id e f e d w h e n s h o u ld zo n e c

de ge n e r a c y W ith in th e

,

,

K

a a t is

,

T his is

a

bo

ro u

\

p

5 l]

»

K

?

p

ö

3 ı

T lo g p ) p la n e ) l h h ig h d e n s ity le v e l (a h o r iz o n ta l lin e in t e ( o g r a c y z o n e is i F ig u r e 7 1 w h e f e th e r e la tiv is tic d e g e n e g h ly in d ic a te d n v e a

,

la be lle d IU

l b e e n n e g le c te d Its c o n tr ib u tio n to th e to ta p re s s u re h a s d e n s itie s ı t h ig h te m p e r a tu re s a n d o w o f ta n t h o w e v e r a i m b s e m o e e c s s r r u e p p d d to th a t o f th e g a s a n d s h o u ld b e a d e (th e lo w e f r ig h t c o m e r o f th e d ia g r a m ) h u a tio n o f s ta te e d o m in a n t w ith t e e q E v e n tu a lly ra d ia tio n p r e s s u r e w o u ld b e c o m c h a n g in g to In

zon e

I

ra

d ia tio

n

,

,

,

,

p

(se e E q u a tio n (3 4 0

re

ig h t lin e

11 7 )

4

n eg

li lig ib le fo

r, s a y ,

PP m _

d

rl

=

7 1 ) in th e fo r m

lo g p a s tr a

aT

s u r e to b e T a k in g th e g a s p r e s

Pre s s u r e (la b e lle d IV in F ig u

a g a in



=

3 ]o g T +

3 (w ith o f s lo p e

c o n s ta n

a c o n s ta n t

t

d iffe r e n t fro m

(7 8 ) th a t in E q u a tio n

(7 5 ) o f c o u r s e ) ,

Scanned by CamScanner

o n tı T h e e v o lu

7

o

f ıt « r t

ı0 8 n es o

Zo

T h e fo llo

w

in g

w

is

e n e rg y

h ic h

n rc

n ts a rgu m e

m

d ia tc d

aw ay

ıtc r in m ł

th c

b a s c tl o n



n g b u rn ı

oa r n u cı

f

c tu pı

c tı a ıc h ・ın «

-

l

l « h u p te r '

o

u t lu m in th c s tc lı lh ıtt is o ı

I

I A

nucı ¢a

r

A ı th o u 吕h ıte ı la r

o » ily

ı h ig h s e n s itiv ity o l n u c c a r re a c tio n e to th c ı r ic te d D u t s e ī i e t u i es s q b d c lin c d ľ o ľ c w h n u c lc a : in b u r gni n z o n /liV S /lo tt / m ı\y c ı H të e n c e a n łm w ı u i a r ld [h c ra te o f n u c ı m \ car r a te s to te d o l th c th t c s h o o n o n e si e s r t a i s n e l c a s k e t a i d b l t p h r l l e s a d n o t c c T i e s hc , h o th e r s p ro c e s ib le im d o n t c m e d n e g lig l d e a n [ i l c o T ) n cd burning m a y b e a s s u l p p o g he ( g itu te s a lin e in t ro c e s s c o n s t h c a e f r p o d l d a c e r ta in th ï ìe s h o e n e r a tio n q e x c e e l n u c le a r e n e g y g p re q

T tit q m s c r ib e d liı

be

m ay

a

p p r o x im

o 1 J kg

sa y,

in

a te

d by

q

t h e th re s h o

T he

ld g iv e n b y q

ex o e

gg ic tr a n s fo

qm

-

in

( 10

la w

er

po w

a

'

s

o

ı ı ï

T

a re

In

ox

m o st o

f th e

an

c a se s m

d

-

ıe a c

h p ro c e # s

rm

(7 9 ) ,

is

r m a tio n o

y g e n burning i d l tt n F ig u r e 7 2 p o e ,

) S in c e fo

"

f h y d r o g e n in to th e ir o n g r o u p e le m burning in to h e liu m e ith e r b y th e p

h d ro g e n p ń s e s fiv e m a jo r s ta g e s : y b u 】n in g in to o r b y th e C N O c y c le , h e liu m

burning

'

g

g

e rg

f th e fo

qo p

-

3

burning

ic o n s iı 1

an

c a rb o n

d

n

>

1

,

b y th e 3 c e

T h e fiv

r e a c tio n

e c o rr e s p o n

d he n

an

ce

th e

e n ts c o m

p ,

c h a in

c a rbo n

d in g th re s h o ld s

(n e g a tiv e ) s lo p e in

l p th a t th e th r e s h o ld s a r e a lm o s t v e r tic a l lin e s S tr ic t y th e th r e s h o ı d d e fin e d b y E q u a tio n (7 10 ) s h o u ld b e a s tr a ig h t lin e in r e a lity th e v a lu e s o f th e p o w e r s in E u a tio n (7 9 ) c h a n e s li h tl fo r d iffe r e n t te m q p e ra tu re g g y

E q u ŕ ttio n (7 10 ) is

s o s te e

,

,

\ s ; th is is th e r e a s o n w h y th e lin e s in F ig u r e 7 2 a r e n o t p e r fe c tly s tr a ig h t F o r h y d r o g e n burning th e s lo e is m ild e r a t l o w te m p e r a tu r e s c o r r e s p o n d in g to p , th e p p c h a in (n H 4 ) a n d b e c o m e s s te e p e r a t h i h e r te m he g p e r a tu r e s , w h e re t C N O c y c le (n H 16 ) b e c o m e s d om i ra n

,

,

n an t

N

u c le o s y n th e s is

by

e n e r g y re le a s in

in to h e a v ie r n u c le i h e a te d to v e d r y h ig h te m p e r a tu r e s a l e d is in te g ıa te b y e n e rg e tic h o to n i s n to h e ı p iu m n u c le i T h is e n he s e r g y a b s o r b in g p r o c e s s ıe a c e q u ilib ń u m (c a ll d e a s in th e c a s e o f ili s c o n b u r n in g n ttc le a r s ta tis tic tı/ e q ııilib r izł m ) w ith th e r l e a tiv e a b u n d a n c e o f ir o n to h l e iu m n u c le i d e te r n r in e d b y th e v a lu e s o f te m p e r a tu r e a n d d e n s it A th re y s h o ld m a y b e d e fin e d fo r th e p r o c e s s o f ir o n p h o to d is in te g r a tio n a s a s tr i in th e l p ( o g T lo g p ) p la n e b th e r e u ir e m e n t q y ones en

ds

w

ith ir o n Ir o n

g fu s io

n o

f lig h te r

e le m e n ts

,

,

,

,

,

,

Scanned by CamScanner

\

p

#

F

lkA

u

L

Ų

t

.

L o g [7 1« 11

R\

re

7 2 M

th a t th e n u m

ho w

n

a

p p in g

be r

in F i\

o

o

f th e te m p e r a tu r e ?

f h e liu

re

m

an

d ir o

n s ity

n n u c le

d ia g r a m

ibe

a

acc o

p p r o x im

7 2

rd in g to

a te

ly

e

n u c le a r

p ro



c e sse s



q u a l T h is th r e s h o ld

乙 く

Zo he

n e s o

f in s t a b ilit y



fo llo w in g a r g u m e n ts a r e b a s e d o n th e m a te ń a l o f C h a p te r 6 T h e c o n d iń o n o f fi ti ll a m íc a l s ta b ility is y a > 4 /3 (S e c tio n 6 3 ) W e th u s e x p e c t s te a r c o n \ r a o n s

ic a tfy tłlzs ta b te in th o s e f e g io n s f h e ll g T lo g p ) p la n e w h e r e e co m e l i i ti re d u c e d to 4 /3 o r le s s S u c h r e g io n s a r e th e fa r e x tr e m e s o f th e r e a t v s c w h e re e d o m in a te d z o n e N a n d o f th e r a d ia tio n p r e s s u r zo n e m , e n e ra c y i t i i zo n e o n d t r a h e t s n o g 3 A n o th e r is th e ir o n p o Ya te n d s a s y m p to tic a lly to 4 / tń c te d r e g io n s w ith th e c e n tr e o f s ta r s r e s li e re y a < 4 /3 A s w e a r e d e a n g lie o u ts id e th e i i a tio n o f h y d f o g e n a n d h e l u m s ta b ility c a u s e d b y th e io n z d u c tio n w h ic h is i it th a t w e c o n s id e r P a r p r o ļ e s o f te m p e r a tu r e a n d d e n s y ta b le z o n e w ith ? ll d e fin e s a n a d d itio n a l u n s ty p e p r o c e s s a s w e , o n iz a tio n e s m ? k e d th e W ith a ll th e s e u n s ta b le z o n 4 /3 , a ï i s h o w n in F ig u r e 7 3 tr d d o n tw o s id e s o m p le te ly b o u n e e be c o m e s c ◆e p a r t o f th e (]o g T , lo g p ) p la n im p o s e d H e n c e s e v e f e c o n s tr a in ts a r e e r a tu f e s m g h d e n s itie s a n d a t h ig h te p e a r burning re c a ll th a t n u c ı f s ta r s W e fin a lly th e p o s s ib le e v o lu tio n a f y tr a c k s o H e n c e th e t h e th e f f e la tiv is tic o r n o d jn za

m

,

,

,

,

ロ ら , 、



,

e iT n a

d e n e r a te g a s e s ł ı y u n s ta b te in e g

,

( \

w

Scanned by CamScanner

The

ı u t io

evo

n

f s ta

o

7 3 0

re

n

f th e

s ta

th r e s h o

burning

n u c le a r

th e b o u

u tlin e o

b le

ld s

d a ry in to th e d e g e n

7 2

e v o lu

The

t io

an

d

u n s ta b le z o n e s

f F ig u

o

re

e ra c y z o n e

,

H

a v in

e a c q u a in te

g be c o m

7 2 hav

c m a tı

c tu pı

re

in th e te m p e ı ıtu r e d e n s ity d ia g r a m

b e e n d is c o

e

n tin u e

d

a fte r c r o s s in

g

II

p a th o f th e (lo g T ìo g p

n a ry

he

[T (K )]

Lo g

Ħg u

sc

a

rs f

ce n

)

t r a l p o in t o f a s t a

a n pı

r

in t h e

e

(lo g T ìo g p ) p la n e , th e q u e s tio n w e n o w f g iv e n m a s s M m a y a s s u m e a n y c o m bi n a tio n o f te m p e r a tu r e a n d d e n s it y v a lu e s , th a t is , m a y b e fo u n d a n y w ı ı e r e in th is p la n e o r w h e th e r th e s e v a lu e s a ľ e in s o m e w a W e now y c o n s tr a in e d b y M r e g a r d th e (lo g T lo g p ) p la n e a s a (lo g T t lo g p ) la n e r e f e iT in g to th e s te l c p , la r c e n tr e A s s u m in a g p o ly tr o p ic c o n fig u r a tio n (E q u a tio n 5 10 ( )) fo r a s ta r in h y d r o s ta tic e u ilib r iu m , th e c e n tr a l d e n s it q y is r e la te d to th e c e n tr a l p r e s s u r e b y E q u a tio n (5 2 8 ) a sk

is

w

h e th e r th e

c e n tr e

d

w

o

f

ith th e

a

,

s ta r o

,

,

,

Pc

T h is

i

r e la t o n

s ta b le c o n

is

on

ly ,

su c H a s e l e c tr o n

(4 Ĵ r )" 3 B . G M

2 /3

p

y3

w e a kl y

ń g u ra tio n s fo r

as co n vec i ton

=

w

d e p e n d e n t o n th e p o l tr o ic i y n dex p h ic h n v a r ie s b e tw e e n

dege n e ra c y S ( e c tio n 6 6

(s e c tio n 3 3 )

) A lth o u g h

,

15

or on

a s ta r

an

d 3

n

,

(7

1 1)

1y e s p e c ia ı

fo r

(s e e S e c tio n 6 6 )

,

th e m a c r o s c o p ic s c a le

in h y d r o s t a tic

e

q u ilib r iu

m

,

an

d

su c h

is

ot /ł

Scanned by CamScanner

L o g [ï (K )]

ı ig ir e 7 4 R e la tio

p e ] fe e t i

f tw

ld c s

l d e n s ity

n tm

d ıe s la b k id e ll g a s

h in » ?iı

m

n o

&n

d de ge n e m

to c e n tn ıl te m te

p e r a tu re fo

f d iffe r e n t

r s ta r s o

m a sse s

g ils z o n e s

p o ly tr o p e (e v e n if its c o m p o s itio n is h o m o g e n e o u s ) r e la tio n (7 1 1 ) il g o o d a p p ro x im a tio n to h y d r o s ta tic e q u ilib r iu m fo r o /ıy c o n fi u r a tio n g ,

N o te th a t s im p ly b y d im e n s io n a l a n a ly s is o f th e h y d r o s ta tic e q u a tio n th e c e n tr a l ' /Ĵ Ŝ m E s s u ï E m u s t b e p ro p o r tio n a l to G M p a te d to th e c e n tr a l d e n s ity a n d te m p e r h a d d itio n th e c e n m ıl p re s s u re is r e ı ,

,

u re -

c

b y th e

an e

w e

q u a tio n

e q u a tio n

o

f

e q u a tio n

h a v e d iffe r e n t

(7 1 I)

C o n s id e r

,

w e m a

a s ta r o

h e re E q u a tio

n

fm

y

e

lim in

ass

M

f th e (lo g Ą lo g p c ) C o m b in in g e a c h o f th e m w ith s o f s ta te P c to o b ta in a re la tio n b e tw e e n p c a n d T c

W ith in th e d iffe r e n t

s ta te

a te w

ho

(7 1 ) h o ld s T h e

z o n e s o

,

,

s e c e n tr a r e la

l p o in t is fo

u n

tio n b e tw e e n T c a n

d in th e id e a l g a s

zo n e

d p c in th is

is

c a se

o

f

he ı b rm

Pc

=

壁 生 ĄJT B G

3

M

2

(7 12 )

'

f g iv e n m a s s th e c e n tr a l d e n s ity v a r ie s a s th e c e n tr a l t a l te m p e r a tu r e e m p e ra tu re c u b e d F o r s ta r s o f d ifr e r e n t m a s s e s b u t th e s a m e c e n r i s s O n lo g a r ith m ic s c a le s e c e n tr a l d e n s it d e c r e a s e s a s th e m a s s s q u a re d n c re a e y in e w ith a s lo p e o f 3 T h u s d ifre n e n t m a s s e s e la tio n (7 12 b e c o m e s a s tr a ig h t ı ) i o e l n e d iffe r e n t a r a lle l lin e s w h ic h in te r s e c t th e te m p e r a tu r e a x is a t n te r v a ls p 0 I 1 IO a n d 10 0 M o a r e P ro p o rtio n a l to lo g M T h e lin e s c o r r e s p o n d in g to M h i l P ıo tte d in F ig u r e 7 4 th e s e m a s s e s b e in g s u c c e s s iv e p o w e r s o f 10 M o , t e n te l v a s be tw e e n th e lin e s a re e q u a l e a n in

g th a t fo

r a

s ta r o

,

,

,

,

,

,

Scanned by CamScanner

o n o u tı Tho evo ı

7

1 12

c a tı ıc h e m

f s ta r s

U n tio II lin d [ C ı v o I1c r o u n d in l R t i n o l m p b ta in c r a te th e c e m ı5 , w c o ıı ) w iıh /ı = u n tio n (7 E « n f ï o l r Ą =

Pc

w

4 7r

K

a tio n d a ıg t\s rc ı u c c s lh c i c re p ı

h ic h

c tu pı

pe

b (7 2 ) h o ld » S U » titu tin g

n

I

is in d e p e n d e n t (7 ı2 ) H c ıc p c

o

r7

and

,

l m E q u tltio n (7 13 ) th c 7 4 S tr ic tly , ro i n F ig u r e d t e t l o flb c ts in c r e a s e p in c r e a s e s w ith m a s s M , t r c la tiv is tic e u a le d , b u m a s s s [ı h c t s a d viry ho u ı o g p ) p la n e ı T , ı c e n tr a ıd e n s ity s s in th c ( o g ı s ta b le re g io n r c th c o n y ï I a d n I a s n e z o th c p o w e r ım e r g e a t th e b o u n d iı 7 12 ) a n d (7 13 ) w s r e la tio n s ( F o r r e la tiv e ı y lo w m iıs s e , ts in F ig u re 7 4 h d a s he d se g m e n II, a s s h o w n b y t e d n I a s e n o z n e e t w b e a ry h lr ıa s s W e h a v e s e e n h a r a c te r is tic o l e a c i o u s b e n d in g p a th c r e s u ltin g in a c o n t n u ar d to in fin ity a s th e s te lı l d e g e n e r a te s ta r s te n s in s e c tio n 5 4 th a t th c d e n s ity o it M c n th e h ig h e s t m a s s th a t c a n itic a l C h a n d r a s e k h a r lim m a s s a p p r o a c h e s th e c r r e s s u r e T h u s th e i m b y e le c tro n d e g e n e ra c y p b e s u s ta in e d in h y d r o s ta tic e q u ilib ı u b n d a t h ig h e r a n d h ig h e r d e n s ity i t in c te a s in g m a s s e s w ilı e p a th s c o r re s p o n d n g o f la tiv is tic d e g e n e r a c y la n e , d e e p e r in to th e re g io n o re v a lu e s in th e (lo g T c lo g p c ) p h ic h ill b e r e p r e s e n te d b y a s tra ig h t lin e , w It is e m y to s e e th a t th c lim itin g c a s e w n e ll z o a c r n e d e h e t e i y g w e e n p a th s th a t b e n d n to w ill a ls o m a r k th e d iv is io n b e t l th a t th e b o u n d a r y b e tw e e n th e id e a l I W e re c a ı i a n d th o s e w h ic h re m a in n z o n e le c tro n g a s z o n e , c lo s e to its re la tiv is tic p a r t, h a s a g a s z o n e a n d th e d e g e n e r a te e in th e id e a l g a s z o n e h a v e a s lo p e o f 3 o p e o f 3 S in c e th e (lo g T c , lo g p c ) c u r v e s sı a tiv is tic d e g e n e r a c y th a t c o in c id e s w ith th e re ı a s w e ll th e re e x is ts a v a lu e o f M as

,

bo

u n

d a ry T h is

m a ss

is M

c h, w

b ta in e d b y e q u a tin g th e r ig h t h a n d s id e s h ile th e b o u n d a r y b e tw e e n z o n e s I a n d III w a s

h ic h

w as o

f E q u a tio n s (7 4 ) a n d (7 ı1), w b o ta in e d b y e q u a tin g th e r ig h t h a n d o

th e b o u n d a ry b e tw e e n z o n e s I a n d III m

in th e (lo g ı o g p c ) p la n e , In c o n c lu s io n , a s ta r

(lo g

,

a re Į w o

lo g p c ) p la n e c h a ra c te r is tic

fo r M

,

w

o

h ic h

f fix e d

w e s ha

sha pe s o

f 4 IM

f E q u a tio n s (7 I I) a n d (7 1) H e n c e e r g e s w ith th e p a th c o f r e s p o n d in g to M c h

s id e s o

m ass

h a s its

ow n

d is tin c t tr a c k in

ı l re le i to in th e fo llo w in g te x t : s tr a ig h t

ı in e s fo

r

M

>

M

ch an

as

W

T h e re

M

d kn ee

th e

s h a pe

d

c h In g e n e r a l te r m s , w e m a y u n d e r s ta n d th e r e la tio n s h i b e tw e e n p tr a c k s c o rre s p o n d in g to d ifk r e n t m a s s e s a s fo ll o w s W ith in c ľ e a s in lla r m a s s , t s e g th e g r a v ita tio n a l p u lıto w a rd th e c e n t re b e c o m e s s tl o n e r H e n c e a h ig h e r p r e s g s u re is re q u ir e d to c o u n te r b a la n c e g r a v ity T h is m a y b e a c h ie v e d in a n id e a l g a s b y a h ig h e r d e n s it o r a h i h e r te y m p e r a ttir e A h i h e r d e n i g s ty im p lie s h o w e v e r , g , s m a lle r d is ta n c e s b e t w e e n m a te r ia l a r tic le s h i w p h f c u r th e ı e n h a n c e th e , g ra v i ta tio n a ] fie ld In fa c i i s n c e th e h d r o s ta tic , y p r e s s u re is p ıo p o r tio n a l to a ìıig lıe r P o w e r o f th e d i o n es

<

M

en s

ty tlm

n

is th e g a s p r e s s u re (4 3 /

as co m

p a r e d to 1),

a

h ig h e r

Scanned by CamScanner

7 3

Figu r e 7 5 S c h e m te m

T h・

a

e v o lu t ı o n o

fa

s ta r

ı

as vı ew e

tic illu s tr a tio n o f th e e v o lu tio

it p e r a tu r e d e n s y

tr a c

n

o

d fr o

f

m

s ta r s

ı tl

cen

3 Iı

tre

a c c o r d in

g to th e ir

c e n tra

l

ks

te m o w e r d e n s ity o r a tigher a n ce T hu s a ı ly w o r s e n th e im b a ı d In th e c a s e ilib r iu m if th e s te lla r m a s s is in c r e a s e e a r e r e q u ir e d fo r e q u r t u ra e p la y s a fa r le s s im p o r ta n t r o le B u t n g a s th e te m p e r a tu r e p o f a d e g e n e r a te e le c tf o h l to a lo w e r p o w e r o f th e d e n s ity t a n s u r e is p r o p o r tio n a n o w th e h y d r o s ta tic p r e s d d 5 /3 ) s o th a t a h ig h e r d e n s ity is n e e e e d to is th e g a s p r e s s u r e (4 /3 a s c o m p a r ta r fo r e q u ilib ń u m in a m o r e m a s s iv e s W h e r e d o e s th e e v o lu tio n a f y c o u r s e n s w e r is T h e q u e s tio n w e n o w h a v e to a a tr a c k ? l d th e c e n tf a l p o in t a lo n g f

d e n s ity

w o u

ld

o n

,

,

-

,

'

,

'

o

a s ta r

ea

7 3

The

e v o lu

t io n

o

fa

i e s ta r, a s v e w

d fr o

m

it s

ce n

tre

lb e it s c h e m a tic w e o b ta in a fu ll a n e p ic tu r e C o m b in in g F ig u r e s 7 1 to 7 4 in to o h o o se a m a s s i u re 7 5 W e m a y n o w c h o w n in F g s s a i n t l o v ie w o f s te lla r e v o u , lu e o f M ), a n d fo llo w th e ig u r e 7 5 b y th e v a F i n d k e f a M , id e n tify its p a th (m its d is c o v e r w h a t it e n c o u n te r s o n a lo n g it to t i n o ) jo u r n e y o f th e (lo g ï c , lo g p c p u ch itie s a n d te m p e r a tu r e s a r e m w he re de n s d s l u o c , w a y S ta r s fo r m in g a s e o u s i o in t is o n th e r e fo r e , th e s ta r t n g p l l a r in te ń o r s ; t e s i n lo w e r th a n th o s e p r e v a ilin g w ith o u t a n a s ta r r a d ia te s e n e rg y b e g in n in g e h t t A th e lo w e r a r t o f th e p a th have p ts a n d h e a ts u p (a s w e th a t it c o n tr a c i ch m ean s h in te rn a l e n e r w e c r u o , gy s ,

,

,

,

,

Scanned by CamScanner

自 The

7

쁘 l th e c e n tr a

p o in t

a sc e n

to th e

p

p

jo u n le y c h a in

d in g

c o r te s p o n

p a rt

ds

a lo

n

o

f s ta f s

w

g w m

h ic h

w e

re c a

o

f th e

tr a c e rı

l p o in t a lo

n

ı g 4 M

一 a

s tr a

fa

s ta r

lıto b e

l tio n o th e e v o u is p o in t in h t t A d l h th r e s o

burning n r s t n u c le a r b a la n c e T h e

u t io n ev o ı



ic t u r e m a t ic p a sc he

to a v e r y co m e s

lo

ig h t lin

e

o

\

f

˜

一 一

h y d r o g e n is

n

g pa u

se

w

一 一 ˜ 一

e

d o n th e lo w e r h o ld is c r o s s e e th r e s h t s e s s a t bu m f r h ig h m e x p e c t s ta r s o w h e re a s o ld th e r e fo r e W e sh o u ı e c c O y to th e C N





b e tw e e n th e id e a l g a s u n d ary a t th e b o h t n i o t c e h e p r e v io u s s f 3 (r e g a r d le s s o f s lo p e o It w a s s h o w n in t n e has a a b ility z o t i s n e r u s s f th e W M c u r v e s h r a d ia tio n p ľ e s lo p e s o zo n e an d t e h e s a in e a s th e i f n itio n ) t d e i t s f r o d te d i b o u n d a r y T h is m e a n s th e c ń te ń o n a o p a c h e s th s i t a b ly a p p r o v e i n w M d e a se s, t H e n c e a s th e m a s s in c r iv e ly m o r e im p o r ta n a n e s p ro g re s s s su re b e c o m e r i n t o i d a p a ta r s r i n p re s su re th a t in m a s s iv e s te d b y r a d ia t o i e a s ta r d o m in a re s su re S n c s a s t e h a i p f n g d m o e v e n tu a lly t th u s e m e r g e s o r t e u p p e r lim i u n b o u n d) a n i n m o b c e g l is d y n a m ic a lly u n s ta b e ( a r k e d b y th e c u r v e b o v e ) 10 0 M o a s m r so m e w ha t a o r a e ( n h l u y s te lla r m a s s r o g

砷 一



,



厢 一



,



,

ge

m a

y

a ls o

b e in fe iT e d fr o



n ı th e



lla r m ld d o e s n o t e x te n d t o te m d r o g e n burning th r e s h o h ï l T he 】 y r a i d a l ) o T g g pc (lo g c f M 6 7 2 ) T h e h ig h e s t v a lu e o ū m e s 1 0 K (s e e F ig u r e a fe w s b e lo w r e t u a e r p b e n d in g in to th e d e g e n e r a c y th is th r e s h o ld , b e fo r e fo r w h ic h w M s till to u c h e s ll m a s s lim it, m a r k e d V u u in b e r e g a r d e d a s th e lo w e r s te a r a p re s s u r e z o n e m y n n o r an y l w th is lim it w ill n e v e r ig n ite h y d r o g e F ig u r e 7 5 0 b je c ts o f m a s s b e o d h e a t u p a n d w ill th e n c o n tr a c t m o r e w ill ń r s t c o n tr a c t a n h o th e r n u c le a r fu e l; t e y f t s se e ff S u c h o b je c ts d o n o t fit in to o u r d e ń n itio n o s a r ( o w ly w h ile c o o lin g o sı lim it fo r a s ta r is s o m e w h a t b e lo w C h a p te r 1) B a s e d o n F ig u r e 7 5 , th e lo w e r m a s s lo

A

w er

lim it fo

r

th e

s te

a ss

ra n



,

。 。

,

O IM

が 、

o

W h e n th e h y d r o g e n s u p p ly in th e s te lla r c o r e is fin a lly e x h a u s te d th e lo s e s e n e r g y a g a in , a n d th e c o r e c o n tr a c ts a n d h e a ts u p T h e c e n tr a l p o in t r e s u ,

s ta r

m es

w ill s o o n c r o s s th e d e g e n e r a c y p a th F o r lo w m a s s s ta r s M d p re s s u r e b o u n d a r y a n d b e n d to th e le ft in to a h o r iz o n ta l lin e T h e p r e s s u r e e x e r te b y th e d e g e n e r a te e le c tr o n g a s h a s b e c o m e sufficient fo r c o u n te r a c tin g g r a v ity

its

c lim

T he

b

u

p th e V

c o n tr a c tio n

M

,

s lo w s

do w

n an

d th e

th e r m a ıe n e r8 y , te n d in g to a c o n s ta n t d e n s ity

h ig h e r th e

d ia tin g th e a c c u m u la te d d r a d iu s ), d e te r m in e d b y M T h e

s ta r c o o ls w

(a n

h ile

ra

m a s s th e h ig h e r w ill b e th e fin a l d e n s it a n d th e lo w e r th e fin a l r a d iu s y F o r h ig h e r M V M w ill c r o s s th e n e x t n u c le a r burning th r e s h o ld H e liu m n o w ig n ite s in th e c o r e a n d a n o th e r p h a s e o f th e r m a l e q u ilib r iu m is e s ta b lis h e d m a r k in g th e b e in n in g g o f a n o th e r p a u s e in th e jo u r n e y o f th e c e n u a l p o in t W e n o te th a t a m o n g th e W M p a th s th a t c r o s s th e h e liu m burning th r e s h o ld th o s e c o rT e s p o n d in g to lo w m a s s e s d o s o v e r y c lo s e to th e d e e n e r a c b o u n d a r g y y W e ,

,

,

,

Scanned by CamScanner

ıı 4

in C h a p te r 2

s <)e n

e v o lu t io n o

The

7

\n ł

d

a g a in

a sc he m a

f s ta r s

in C h a p te i 6 ) H

t lc p ic t u

re

in th e (lo g r e c a ll to b e a

lo g p ) c p ltin e t s r a ig h t li ne

ence

,

l p o in t a s c e n d s a lo n g 4 ım w h ic h w e oF l c ro s s t o w a i h ig h e r te ıììp e r a tu r e s a n d d e n s itie s E v e n tu a lly , it w iı s lo p e 3 the ï i t n u c lc a ıburning th r c s h o ı d A t th is p o in t in th e e v o lu tio n o f a s ta r h y d r o g e n i s ig n ite d a t th e c e n tıţ a n d th e s ta r a d ju s ts in to th e r m a ıe q u ilib r iu m w ith L n u c a n d L i th e c e n tr a

n

b a la n c e T h c th a t r

n o te

jo u m

y o f th e n ia s s e s W m

lo w

e

c e n tr a l p o in c ro s s e s

t a lo n g W M c o m e s to a v e ry lo n g p a u s e

th e th re s h o ld o n th e u p p e r

h e r e a s fo r h ig h m a s s e s th e th r e s h o ld is p a r t c o r re s p o n d in g to th e C N O c y c le W e s h o u ld th e r e fo r e h y d r o g e n b y d iffe re n t p ro c e s s e s a c c o r d in g to th e ir m a s s e s to th e p

It w zo n e

th e c

H

an

p

h a in

c

w

p a rt

,

c o r re s p o n

c ro s s e d o n ex

W d in

e

g

th e lo w e r

p e c t s ta r s to b u m

a s sho w n

in th e p r e v io u s s e c tio n th a t th e b o u n d a r y b e tw e e n th e id e a l a s g r a d ia tio n p r e s s u re in s ta b ility z o n e h a s a s lo p e o f 3 (r e g a r d le s s o f

d th e

ń te r io n

p te d fo r its d e fin itio n ) th e s a m e a s th e s lo p e s o f th e ŲıM c u r v e s a s s in c r e a s e s W M in e v ita b ly a p p r o a c h e s th is b o u n d a ry T h is m e a n s s ta r s r a d ia tio n p r e s s u r e b e c o m e s p r o g r e s s iv e ly m o r e im p o r ta n t a n d in a te s g a s p re s s u re S in c e a s ta r d o m in a te d b y r a d ia tio n p r e s s u r e

ado

e n c e a s th e m

,

,

th a t in m a s s iv e

lly d o m is d y n a m ic a lly u n s ta b le (b e c o m in g u n b o u n d ) a n u p e r lim it th u s e m e e s fo r th e p rg s te lla r m a s s r o u g h ly n e a r (o r s o m e w h a t a b o v e ) 1 0 0 M k d b m h a s a f e y t e c u rv e o V M in F ig u r e 7 5 e v e n tu a

,

,

,

m ax

A

lo w

er

lim it fo

th e

s te

lla r

a ls o

b e in fe r r e d fr o m

th e lo g p c ) d ia g r a m T h e h y d r o g e n burning th r e s h o ld d o e s n o t e x te n d to te m 6 p e ra tu r e s b e lo w a fe w tim e s 10 K (s e e F rg u r e 7 2 ) T h e h ig h e s t v a lu e o f M fo r w h ic h W M s till to u c h e s th is th r e s h o ld b e fo r e b e n d in in to th e d e e n e r a c g g y r b e s s u r e z d o n e d m ay e re g a r e a s th e lo w e r s te lla r m a s s lim it m a r k e d W p M h in F ig u r e 7 5 0 b je c ts o f m a s s b e lo w th is lim it w ill n e v e r i n ite h d r o e g y g n n o r an y o th e r n u c le a r fu e l; th e y w ill fir s t c o n tr a c t a n d h e a t u p a n d w ill th e n c o n tr a c t m o r e s lo w ly w h ile c o o lin g o fF S u c h o b je c ts d o n o t ń t in to o u r d e fi i i n t o n o f s ta r s s e e o g (ı

r

m a ss

ra n

ge

m ay

,

,

,

,

m

(

C h a p te r 1 ) B O ıM o

a se

d

on

F ig u r e 7 5 th e lo ,

W h e n th e h y d r o g e n

lo

s e s e n e r g y a g a in

its

lim b

,

an

su

d th e

w er m

p p ly in th e c o re c o n

a ss

lla r

lim it fo

r a s ta r

is

so m e w

h a t b e lo w

is fin a lly e x h a u s te d th e s ta r tr a c ts a n d h e a ts u p T h e c e n tr a l p o in t r e s u m e s s te

c o re

,

p th e W M p a th F o r lo w m a s s s ta r s W M w ill s o o n c r o s s th e d e e n e r a c y g p r e s s u r e b o u n d a r y a n d b e n d to th e le ft in to a h o r iz o n ta l lin e T h e r e s s u r e e x e r te d p b y th e d e g e n e r a te e le c tr o n a s h a s b e c o m e s u ffi i g c e n t fo r c o u n te r a c tin g g r a v ity T h e c o n tr a c tio n s lo w s d o w n a n d th e s ta r c o o l s w h ile r a d ia tin g th e a c c u m u la te d th e r m a l e n e r g y te n d in to a c o n s ta n t d e n it s y (a n d r a d iu s ) d e te r m in e d b g y M T he h ig h e r th e m a s s th e h ig h e r w ill b e th e fin a l d e n s ity a n d th e lo w e r th e fin a l r a d iu s F o r h ig h e r M , ŲıM w ill c r o s s th e n e x t n u c le a r burning u ir e s h o ld H e liu m n o w ig n ite s in th e c o r e a n d a n o th e r p h a s e o f th e r m a l e u ilib r iu m is e s ta b lis h e d q m a r k in g th e b e in n in f h o a t n o e r i g a u g p s e n th e jo u r n e y o f th e c e n tr a l p o in t W e n o te th a t a m o n g th e 4 ıM p a th s th a t c r o s s th e h e liu m b u r n in th r e s h o ld th o s e g c o ìT e s p o n d in g to lo w m a s s e s d o s o v e r y c lo s e to th e d e e n e r a c b o u n d a r W e g y y c

u

,

,

,

,

,

,

Scanned by CamScanner

7 3

rn a y

S ī1a S ı

T on

p e c t to

ex

e n c o u n

e v o

w

ı u tı o ı lı

f

o

a

s ta r , as v ı *w *

te r s o m e f o n n

e a ts

p h ic h h a v

h e s to r y r e e g th o s

T he

its e lf e

a

fte

r th e

burnt h e liu

f th e

o

e x

m

d ı ro

rm o n u c lc a r

it s

m

ce n

Iï 5

tre

in s ta b ilit in y

f su ch

s ta r s o

h a u s tio

n o f h e liu m th e lo w e r m a s s s ta r s d e v e lo e ı p e c tr o n d e g e n e r a te c o r e s , fin a l d e n s it y (a n d r a d iu s ) is r e a c h e d

c o n tr a c t ,

lin g C o n tr a c tio n s to p s w h e n th e d b y th e th e ]r ıa s s M W e h a v e th te m e d u s id e n tifie d t as w o c la s s e s o f c o m p a c t o n e in c lu d in t a rs s s t a r g n i s o f v er l g co o y lo w m a s s m a d e y of p r e d o m in a n tı a n d a n o th e r in c lu d in g m o r e m a s s iv e s ta r s c h e liu n ı o m p o s e d (a t le a s t l t a r y) o f p d iu m burning p r o u c ts c a r b o n a n d o x y g e n he ł in e b e tw e e n s ta r s th T h e d iv id in g ı a t e v e n tu a ll b y e c o m e d e g e n e r a te a n d c o o l b t o c a je c t s a n d th o s e w h ic h r e m a in in th e id e l s co m p a ff a g a s s ta te d u e to th e ir o e r a tu r e s e v e n w h e n r e a c h in m g h ig h d e n s itie s c o r r e s p o n d s a s w e h a v e h ig h te p _ M c h c o n tr a c tio n m a To W i c h In p r in c ip le fo r M se e n . y g o o n in d e fin ite ly o n d f n a m ic a l s ta b ilit o e li n r H d y e o w r e v er w M y c r o s s e s th e c a r b o n burning he b o a rrd

o o s ta r t c

ì in e

,

,

,

t

,

th r e s h o a

ld

v e ry

y de ge n h ig b ı

s ta n c e s c ir c u m

d e to

b n or ca r o fa te is h o w

e r a te

lm of o r a

(

n a tio n

ev er

o n

s id e r in g

)M

o st

m

a te

,

ch

e rac

ńal N

(s e e S e c tio n 6

,

o n w e a re c

de ge n

n e a r th e

u c

2)

th a t is

,

y

le a r

burning

d

ld

an

bo

u n

sh o u

n e

g lig ib ly

sm

is th e r m

re s u

lt in

a

th a t c a r b o n

a lly th e r m

u

n s ta b le

ig n ite s ın de r su c h

u n

o n u c le a r r u n a w a

y

ly s m ic c o n s e q u e n c e s S u c h a t s in g le is o la te d s ta r s o f fix e d m a s s th a

d to h a v e

ly h y p o th e tic a l fo r th e s in c e th e p r o b a b ility o f a

is

ch

T h is in d ic a te s

zo n e

a

ll In

re

c a ta c

h a v in g b e e n b o m w ith a r c o lla p s e d u e to a lity , s te 1ı s ta r s

a m

a ss

c a rb o n

Scanned by CamScanner

Tïï e

7

e w

u t io ı

o

n

f

a sc

s s ta r

1 16

o td e r s

o

iu m a g lı t

f

B e tw

de

o

f

s ta r s

liv e d s ta te a n d lo n g tl fo r d s D iffe re n y p ro c e e

d e to ir o n

. \in

an

o

i n E v o lu t o e ra l in g e n a sse s n t in

o s ta rs

h e rm le a d s to t

n a tio n

M

ee n

0 \M

o nu

f d iffi] re

lit in s ta b i y c le a r

ctu pı

a t ic

hem

d

M

Ļ T ho

re

10 0 M o

-

n ìn x

u n

se

d ı

ho u th a t s

de

e n

Ą ll S t an

i

r th e c r itic a

d in

d e v e lo p s in to i n (o e x p lo s o

lla p s e

c o

ı* \

S ta rs

h ig h ly

a

ir o n c o r e o f th e t h e a tin g n e u e se o r i subs q c o lla p s y n th e s s o h ic c a ta s tr p a i n d te d to e n

lM

r

u n s ta b l e b o th ) S ta r s o f

s t a t e x pe c

m o n am o n

g

o

b s e r v e d s ta r s

a re

th e m

a in

se

qu

e s en ce o n

,

m e n tio n e

d in C h a p te r ı

r n in g s t a r s a c o r r e la tio n h y dro g e n b u to w e hav e f th e k in d th a t d e fin e s th e r a tu r e o th is in fe r e n c e tiv e te m p e n d e ffe c a i t s o i n y n Iu m d o n e in th e n e x t s e c tio n T h e e x is ts b e tw e e T h is w ill b e ra m i a d R g H c e in th e to th e h o ń z o n ta l p a r t m a in s e q u e n e s p o n d in g s ta r s c o r r i act co o ln g m o c e h p t f o i h tfo r w a r d It w ill b e id e n tific a ū o n d w a ıjs is q u ite s u a g e d w h ite v r e b s o h e t w ith o f v M tr a c k s d in g to o b s e r v a tio n s o n e d is ed acc o r in C h a p te r 9 In d e l i t d a e e r o i m n d p u rs u e s o n e s a n d m o r e m a s s iv e h ite d w a r fs : lo w m a s tw o ty p e s o f w tin g u is h e s b e t w e e n h th e c o n n e c tio n b e tw e e n i c o m p o s itio n a lth o u g o ty p e s d iffe r n t w h e t l o s a s e n o ; f th e in te r io r is d e b a ta b le W n e r e d o o s iū o n a n d th a t o th e o b s e r v e d s u r fa c e c o m p ld b e a s s o c ia te d w ith e s s th a t th e y s h o u th is p ic tu r e ? M a y w e g u r e d g ia n ts fit in to h th e c o r e c o n tr a c ts f llo w in g h y d r o g e n e x h a u s tio n w e n th a t p h a s e o f e v o Į u tio n o is o d e ? T h is p u z z lin g q u e s tio n w ill b e a d d r e s s e d to w a r d th e n e x t c o r e burning e p sh o w

th a t

fo

r

,

,

,

,

,

s h o r tly

(S e c ū o n 7 5 )

F in a lly te r m e d

b e te m

,

o

p lo s io n s ith p o s s ib le

s te lla r e x

b se rv e d

fy p e I a n d fy p e ı[ w p te d , e v e n a t th is e a r ly

a s s o c ia te o n e

,

ty p e

w

ith

su

pe

m

are o

o va e

b d iv is io n

s

f tw

(T \ĵp e ıa İ b ,

o ,

d is tin

ct

)O

e tc

ty p e s

n e m ay

d e r s ta n d in g o f s te lla r e v o lu tio n to d e to n a tio n a n d th e o th e r w ith ir o n p h o to d is in te d e ta il th e p r o p e r tie s o f e a c h o b s e r v a tio n a lly a s , in

s ta g e

c a rbo n

su

our u n

g r a tio n B y a n a ly s in g in m o r e w e ll a s th e o r e tic a lly w e s h a ll s h o w in C h a t , p e r 10 th a t th is , in d e e d , is th e c a s e

fo

7 4

T h e th e o r y

O b s e r v a tio n a lly th e m a in , th e lu m in o s ity a n d th e f e f

ec

o

f th e

m a in

se

qu

r

to

k

so

ı N

e n ce

f

se q u e n c e

o

tiv e te m

a n a

is d e fin e d b a n e m p ir ic a l r e la tio n b e tw y p e r a tu r e o f a g r o u o f s ta ľ s c a lle d a c c o r d in p ,

r

h

自自 由

Scanned by CamScanner

C

a tio n h a s th e fo rm s e q u e n c e s ta r s T h is r e ı m a in

lo g L w

h e ıe th e

e a t la tg

b e tw

L

s lo

pe

is

sha

llo

_

lo g

a

ír

+

c o n s ta n

th e ı ow er end

(7 ]4 )

t,

(lo w L ) a n d b e c o m

e s s te e p e r

p ro p e rty o f m a in s e q u e n c e s ta r s is a n a p p a r e n t a n d lu m in o s ity , a ls o in th e fo r m o f a p o w e r la w

c o rf e la tio n

cr

w e r at

n o th e r

A

een m a ss

L

1 6 in C h a p te r (s e e F ig u r e ( ) c e s ta r s a r e se q u e n

th o

I) O

o(

ur

s e s ta r s th a t b u m

M

(7 15 )

v

i th e o r y is th a t m a n

h y p o th e s is b a s e d

o n

h y d r o g e n in th e ir

c o re s ,

th e ir c e n tre s ly in g

t ? e n burning th r e s h o ld in F ig u re 7 5 w h e r e th e p a th s V M in te f s e c g th e h y o g ld W e th e r e fo r e h a v e to p r o v e th a t fo r s u c h s ta r s a c o r r e la tio n o f th is th re s h o 14 ) e x is ts a n d a n a d d itio n a l o n e b e tw e e n m a s s a n d lu m in o s ity , lik e th e ty p e (7 a Įo n

,

i n c o r fe la t o

(7 1 5 )

C o n s id e r

s ta r s th a t

hav

be g u

e

burning

n

h y d ro g e n

a t th e

c e n tr e

an

d

a re

in

i t b e u n ifo r m q u ilib ń u m W e m a y ta k e th e ir c o m p o s it o n o b itio n th a t w e h a v e a lr e a d y a s s u m e d to e h i ii l th ro u g h o u t, e q u a l to t e n t a c o m p o s u ilib ń u m ll s ta r s (s e e C h a p te r 1 ) P r o v id e d th e y a r e in r a d ia tiv e e q s h a íe d b y a tio n s ń b e d b y E q u a tio n s (5 1) (5 7 ) W ith th e fu r th e r a s s u m p d th e if s ? u c tu r e is e s c f r th e s a k e d ia tio n p r e s s u r e a n d (b ) a n a n a ly tic o p a c ity la w ( o bl o f (a ) n e g lig i e r a th e s e e q u a tio n s b e c o m e i s h a ll a d o p t a c o n s ta n t o p a c ty ) o f s im p lic ity w e

th e r m a l a n

d hy?

o s ta t ic e

,

,

,

,

d iii

4 ĵr

r

4

1

dr =



P

=

,

(7 17 ) i

pT



(7 2 0 ) ,

0 5 m < M T (m ) a n d F (m ) in th e r a n g e m ) ( m p ) p ( to b e s o lv e d fo r r (m ) Is it p o s s ib le n ly fr e e p a r a m e te r w h ic h is th e o fo r a n y v a lu e o f th e m a s s M lu tio n s w ith o u t a c tu a lly te ń s tic s o f th e s e s o to le a r n s o m e th in g a b o u t th e c h a r a c iffe r e n tia ıe q u a tio n s ? A s in o th e r c a s e s f n o n lin e a r d t o e d s s o lv in e i t l a c i h g t s com p h d im e n s io n a l d a l m a y b e learned fr o m t e s a gre a t e ofco m p le x p h y s ic a l s y s te m aı ı a ly s is o f th e e q u a tio n s ,

,

,

,

,

,

Scanned by CamScanner

u t lo ı evo

The

7

n o

f s to f s

e bı v a ıia

l 8 e

d e fin e

a

io n le s s cns

d im

r

N ) P (n l) P Ü m ) r ( s n i o t T h e fb n c

,

he a sc

-

,

c tu pı

re

l 11 a s s c tio n a ı th e ln ı

(7 2 1)

jii

=

T (ï ıl)

ľ

c m a tı

be

n a y th e

F (m ) m a rid

re

a c e d by d i pı m en

,

,

ie n ts c o e ffic

Ted s ta 】

h e r e th e

w

r

=

f\ (X ì R

P

=

Jł(O

P.

P



JJ (9

P.

T

=

l4 (x )T

F

=

Î 5 {JO

.

.

F.

d im h a v e th e

'

s o e n s io n

f th e

i n (7 16 ) to E q u a t o (7 2 3 ) in

,

N

In

a

by

e x t,

p h y s ic a

su

b s titu tin g

t lo s s

th e i a n d re p e a t n g an

s re la tio n

l e q u a tio n th e

u A d o p tin g (w ith o E q u a tio n s e p a r a te

d im e n s io n s

na

lity

(7 2 7 ) in to

c o n s ta n t o

G M

fo r E q u a tio

b ta in

h a n d h e n c e in id e s m u s t m a tc , th e tw o s

tio lity ) a p ro p o r o f g e n e ra

p ro c e d

w e o

fu

n ay n ity , w e ı

2

8) 7 ı a tio n s (? 2 0 ) ( (7 17 ) th e n E q u ,

n

,

,

f:

di

J2

-

\

=

m

la $+

&x o

q u a tio n s d e fin e d in th e e

c o e fric ie n

,

=

丁。



(7 2 9) P P.

示 云

(7 3 0)

l3 l l e n tia lin e a r d iffe r b e e ı' th a t h a v e v a r ia b le fu n c tio n s f : 5 na ı d im e n s io < 1 b y E q u a tio n s (7 2 2 ) (7 2 6 ) T h e fL 7 26 ) a th e r ig h t h a n d s id e o f E q u a tio n s (7 2 2 ) (

f E q u a tio n s (7 2 8 ) (7 3 2 ) w fo r th e n o w in d e p e n d e n t o f M

th e le ft

P.

3 15

d f°

n

on

d (7 19 )

d

o

(7 2 1)

to

e

ha v e

a se t o

f

n o n

,

ra n

ge O

<

x

ts th a t a p p e a r o n

Scanned by CamScanner

7 4

d ta in e

Iir ııc rio

m

th e o p p o

f th ı

ı n ıı n n

qw

ıı9

n «ı

o f M e s te lltT r m a çŢ M b y s o lv in th h i t n e r h o s t o f E u a ti g c s e t o F c tlg e b r a ic a tio n g u q o n s (7 2 eq 8 ) (7 3 2 c ) i l t o u e a i b o a m i t n s i a n d th e n n g th e = o ı q u tio n s o f th e aı difle re n g e b r a ic e u a ti q o ns w e h 6 2 t 7 c m , a f ) r i p o le s o f a n y o b ta in fro m E q u a tio n s (7 2 2 ) ( y p h y s ic a l c h a r a c te r is tic f t c r e o ) a (te m p e r a tu re , d e n s ity , ny vaı s u re , ue o f M T h e im pres o r t a nt co nc l p u s io n is th a t th e s h a p e r o ltle s a s a fu n c tio n e o F th e Fr o f th p a c tio n a l m a s s is th e s a m e in a ll s ı a r s , th e

ob

as

ıı s

e d ìıo n to lo e r t ls c a lı gy pr o p y B y s o lv in g o n ly th e s im p le th e r e fo r e d e r iv e th e d e e ra

f r e la tio n s b e tw e e n th e s t a r r e d q u a n titie s w e n y p n de n ce o f h i p y s c a l p r o p e r tie s o n th e s te lla r m a s s u t a c tu a lly s o lv in g th e d iff w ith o e r e n tia l e q u a tio n s s u b s titu tin E u a tio n s (7 2 8 ) g q i t E 9 2 n o u i 7 t a ) o n d 7 { q 3 ( 0 ) w e o b ta i a īr se t o

,

n

,

G an

d in s e r tin g th is

T h u s Ħu

x es at a

c u b e o f th e e n c lo s in

in

th a n

g,

(x

Fo

,

f 1M

1 ) flu

=

o x

,

T he o r

,

l

n a

ill b e

r e la tio n

,

f d ifr e r e n t d tim

de pe n de n

n

II

an

d

m

R w

h ic h

o

,



oc

,

a s s , to

be

d e l d is c u

p a re d

c o m

e re c a

lıth a t

a

d in C h a p te r 5 (7 3 4 ) im p lie s L o c M 3 R 4 s se

a tio n s

(7

2 8)

47 3 0 )

(7 3 6 )

,

-

,

,

,

,

,

a d iu s w

ill b e

,

a lm o s t p r o

burning b y

th a t in

a

d e ge n e r m e

ith

w

d ii c o r re s p o n d in g to a g iv e n fr a c tio n a ım a s s in s ta r s o f d ifre r e n t T h is h o ld s in p a r tic u la r fo r x 1 th a t is fo r th e s te lla r r a d iu s R H e n c e la r g e /ı s u c h a s n H 1 6 c o rr e s o n d in to C N O c c ı g y e h y d ro g e n burning th e p ,

en

o

,

r e la te s r a

m a sse s or a

.

f lO M

In p a r tic u la r th e a l to th e m a s s c u b e d

(s e e b e lo w ) W

ll th e n

as w e

a s ta r o

s u r fa c e

fx

r e la tio n C o m b in in g E q u a tio n s (7 3 4 ) a n d (7 3 2 ) a n d s u b s titu tin E g qu y ie ld s th e d e p e n d e n c e o f R . o n th e m a s s M in th e fo r m

ce o n

ńcal

a s th e

(7 3 5 )

p

e r e ta in th e

la r g e r in

e s

p r o p o r tio

th a t d e r iv e d o b s e r v a tio n a ll fo r m a in s e u e n c e t s ars y q s im ila r r e la tio n e m e d f h e r i t o m l e s m e s ta n d a rd m rg

If w

a s s e s r e la te

m

x a c ro s s a s p h e

o th e r v a lu e o

in o s ity

m

hav e

w e

3

M

o(

lu

een

,

a th o u s a n

p p lie s to a n y in o s ity w ill b e

b e tw

(7 3 1)

d ia tiv e flu

e a

th e lu m

n

s ta r s o

ra

,

L

T his is th e d e s ir e d

in

m a ss

a ss w

sam

in to E u a tio q

p le th e

r ex am

y h a lf th e to ta l m

a s ta r o

su r fa c e

in tu m

,

g iv e n fr a c tio

a s s r a tio

m

sa

r e la tio n

M

th e p

ll c a s e s th e a te

po w

s ta r s

er o

ra

(w

f th e

p d iu

s

m

ass

Fo r n

h a in th e d e p e n d e n c e is in c r e a s e s w ith in c re a s in g c

h ite d w

m ass

l to th e

p o r tio n a

,

a r fs

)

T he po w

,

=

4 th a t a p p r o x im w ea

ke r R

m a ss,

ņ

in

o(

M

a te s

3 /7

w

hy d ro e n o te

c o n tr a s t to c o m

pact is in v e r s e ly p ro p o ıt io n a l to (7 3 6 ) is a lw a y s s m a lle r th a n u n ity

,

w h e re th e ra d iu s

e r in re la tio n

Scanned by CamScanner

ı2 o

Tı »

?

(g

(7 2 9 1

f s ta rs

a tio ) In se r tin g re ı M y w ith m a s s o f d e n s iı

3 (h e d e n s ity d

ce n

d e n s e r th a n

« H Ħi a n e

T h a i s h o *d s fo

e

r

m i

W ? m ) in

m a

re a d y

y be

e

d

T a k in g ı o g a r ith m

w

h ik fo r

T b es e

a re

tpp p e r

pa n

au o w

Ĥ o

bm

n

(b ) fo r n

rm

s on

u s in

g

b o th

p re s s u re Ą 4 a n d n - 16

e

d

o

f th e te m e r p a¢ u re

f o lır h y p o th e s is th a t E q u a tio n s 7 ( 16 ) In th e r e la tio n b e a in s e q u e n c e s ta r s t

m

2

4 tr R

k

(E q u

p e ra tu r e

L

r e la tio n s

(7 3 5 ) a n d (7 3 6 )

s id e s , w e

_

cr

,

h a v e fo

r n

lo g L

_

5 6 lo g T

lo g L

_

8 4 lo g T e ff +

+

tr

=

tio n

a

to o

(1 3 )) th e

w e en

r a d iu s

b ta in

4 t,

(7 3 9 )

c o n s ta n t

(7 4 0 )

c o n s ta n

16

=

th e c a lc u la te d s lo

(h ig h L

an

lo w

er

o n th e

p e s fo r th e lo w e r p a r t (lo w d M ) o f (h e m a in s e u enc i

q

p a rt

an

d

m uc

h

lly c h a ra a

e

n

L

a n d M ) a n d fo r the l ( o g T e ff ı o g L ) d ia g ra m u ppe r p a r t a s th o s e d e ń v e id

th e

,

s te e

a tio n a

O ıh e r

an

c r u c ia l te s t o

fo t th e

e fre c tiv e te m

lim in a te d

)

la r m a T h u s ııa ith in c r e a s in g s te ı n o fı ow t i n r s t i a c t o d n o n a e A r e n g g n e r* ı s ta r s a t a y c st a rs b v io u s fro m F is u re 7 4 c e n H e (x - O ) is o

b e ta k e n to d e s c r ib e

m ay

n in o s it) a n ı

R

lï a r

M (・) in g c n e ta 】fo

aïe n o w

h

(7

d e c e o l t h e

? ı

i*

« «

a tiı

w

m ias s iw

r th e s le

(7 3 6 ) in to E \

n

ıæ

P ・ c( M

s in

p k

tk

a sch * m

-

co

as n 4

v a r la ū o n

d b ta in th e

e

w

.

priipk

\ In

m

don o ı ı n oı

pe r

o n

th e

,

e

ń s tic s

o

f th e

m a in

se

q u e n c e a r e a ls o r e a d il e x la in e d T he y p o b v io u s l r o p o r tio n a l t i y p o ts m a s s ı n the n n ıı e q u ilih rilłm th e ¢a ı e o fc o n s u m p tio n f th e n u c e r h : i e s qu to th e r a te o f e n e ï g ! relt*e L H e n c e th e d u r ti a o n o f th e m a in s e u e q n c e (h y d ro g e n b u m in u s lıge f * ıı s h o u ld ro u h l g y Jsa lis fy nw

ı e a r e n e rg y

re s e r v o ir o

f a s ta r is

,

r h«s o c w

lï e rc

speı ı t

w e

by

ha v e

:

,

M

r

«

M

(7 4 1\

d æ la tio n (7 3 5 ) T h e la ı g e r th c s te lı s ta r ¢»n th e m ar m ł \s s , th e s h o r te r th e lin n a in tie u e n q c e (b u rn i n g h d ro n ı y s e n ) T h is e x ı tin s w h y ı u iw

p

e n se m

b le b e c o n ie s

g n u lu a lı y s ho

n e r, (ı s s tlı r s th a t a re

le s s

an

d le s s

m a s s iv e

le a

Scanned by CamScanner

The

7

20

(te n d in g (7 2 9 ) w

w ltï t io

e

ip le

as n

v a r ia e o b ta in th e

tio n o

1 in p ń n

to

c

o o

>

s in c e

s iv e s ta r s n s e r th a n m a s

?

m a s s a re

T h a t th is h o ld s fo

Ex

e r c is e

T

M

o n

M

m ass

(7 3 7 )

T h u s s ta r s o f lo w te lla r m a s s ith in c f e a s in g s o d e g e n e r a te s ta r s c o n tr a s t t a g a in in at an y x f o m F i\ r e 7 4 O ) is o b v io u s r x =

w

d e n s ity d e c re a s e s

3 th e

>

n

ith

,

(

n tr e r th e s æ lla r c e

h e p r e s s u fe n ]6 and n -

an

ft n de n æ o 7 ı D e ń v e th e d e p e b fo r ıı = 4 (a ) in g e 】ıe ra l fo r m ( )

d y fo

th e

r



M 2

o(

p

w

(7 3 6 ) in t o E q u a tio n

r e la tio n

) In s e r tin g

f d e n s ity

p ic t tır e

t ic s ch e m a

a

f s ta r s

o

n

i 1te t o f o

c ru c

r

d

s is

h y p th

o

f th e te m p e r a tu

th t E q u

a tio n s

re

(7 1 6 1ı

w h r e la tio n b e tw w s ta r s In t e a in s e q u e n c e k n to d e s c f ib e m e t b a e o 2 a m ) y di (7 2 (E q u a tio n (1 3 )) th e r a u s 4 tr R c T a tu r e L = Iu m in o s ity a n d e fï qe c tiv e te m p e r 6 to o b ta in l tio n s (7 3 5 ) a n d (7 3 ), R m a y b e e l i m i n a u s in g r e a re a

e a re n o w

.

T

L

T a k in g lo g a ń th m

w

h ile fo

r n

s o n

s id e s , w e

b o th

lo g L

=

lo g L

=

§仪

'

(7 3 8 )

T

h a v e fo t

n

=

4

5 6 lo g Ħ +

c o n s ta n

t,

(7 3 9 )

8 4 lo g T

c o n s ta n t

(7 4 0 )

16

=

Ħ

+

h p e s fo r th e lo w e r p a r t (lo w L a n d M ) a n d fo r t e i u p p e r p a r t (h ig h L a iıd M ) o f th e m a in s e q u e n c e in th e (lo g f i , lo g L ) d a g r a m r o n th e u p p e r p a r t, a s th o s e d e r iv e d s h a llo w o n th e lo w e r p a r t a n d m u c h s \

T he se

th e c a lc u la te d s lo

a re

,

o

b s e r v a tio

n a lly c h a r a c te r is tic s o

f th e

m a in

q u e n c e a r e a ls o r e a d ily e x p la in e d T h e n u c Į e a r e n e r gy r e s e r v o ir o f a s ta r is o b v io u s ly p r o p o r tio n a l to its m a s s In th e r m a l e q u ilib ń u m th e r a te o f c o n s u m p tio n o f th e n u c le a r fu e l is e u a l t th o e r a te o f e n e r g y q r e le a s e L H e n c e th e d u r a tio n o f th e m a in s e u e iıc e h d r ( y o g e n burning) s ta g e q t M s s h o u ld ro u g h l s a tis f y y O th e r

se

,

,

,

M rM s C C w

h e re

spe n t

w e

hav e

b y th e

a n e n se m

b le

u s e d r e la tio n

o

f s ta r s b o m

a

b le b e c o m

it T h is is th e

es

g ra

re a s o n

M

l7 s t e lla r m

(burning h y ?

t th e s a m e tim e

,

o

4 1)

a s s , th e s h o r te r th e tim e

g e n ) T h is

ex

th e m o r e m a s s iv e am o

p ļ a in s w h y in ı eav e n g th e m

W ith th e a s s a e f p g o tim e th e m a in s e u e n c e o f th is q s h o r te Ļ a s s t a r s th a t a r e le s s a n d le s s m a s s iv e le a v e th e d iffe r e n t e x te n t o r ( u p p e r e n d ) o f m a in s e u e n c e s q

d u a lly

fo r

cc

(7 3 5 ) T h e ı a rg e r th e

s ta r o n th e m a in s e u q en ce

th e m a in s e u e n c e e ie r a rı q e iı se m

T

,

Scanned by CamScanner

7 4

d in g to

c o r e sp o n

C h a p te r I W e hav

s te

e c o n c lu

T h e th e

ı la r

ded

c lu s te r s

in p a r tic u la r , fo e n c e s ta r

qu

se

)

M

caı cu

ce n

w

he re

w e

e

su

qu

tr a l te m p e r a tu

d e c re

s

b s titu te d

n

4,

l

m a ss

ı a te it

m a in

its lo

se ca

4

H

in

qu

10 6 K

×

en c e

s ta r

a

M

R d ia g r a m

th e r e fo r e c a lib r a te r e la tio n

an

accu

to a p o s itiv e

g M

s ta r s

po w

er

p e r a tu r e w

f ig n itin g c c o rd in g to o

o

f d iffe

T h is h o ld s

ith in

(7

c

h a in in

w

m

,

a in

a m

s te

lla r

ge n e kn

o

m

a s se s

burning ow

(lo w

42)

te m

in to h e liu

th a t th e

su

a n tly v

ia th e p p c h a in d e ta ile d s tu d ie s o f its in te r io r W

m

re n t

,

p p r o p r ia te to lo w

d fr o

p a b le r a te ly A

r s ta r s c a

,

p p ly in g to th e p p burning h y d r o g e n p r e d o

tio n in th e H

d in

e n c o u n te r e

Ļ/7

a

,

hav e

te m p e r a tu r e w ith i n

ith d e c r e a s in

æ

fo

m o re

(th e h ig h e s t te m

re

a se s w

_

a

T h e lo w e s t te m e r a tu r e p p e r a tu r e s ) r e q u ir e d fo r h ? y

is T m

ı2 1

e n ce

age s a s w e ,

th a t is a s M ,

,

Tc

hav

in im

m

/(ıı+ 3 )

4

M

O(

h ic h th u

w

,

a

to

,

.

m a in s e

th e b a s is o f th e s c h e m a tic p ic tu r e o f s te lla r e v o lu tio n

o n

(7 3 6 ) th e

/R

r th e

f the

f d ifr e r e n t

o

(F ig u f e 7 5 ) th a t th e r e s h o u ld b e h y d r o g e n W e m a y n o w a tte m t p E q u a tio n (7 3 3 ) a n d r e la tio n m a s s e s v a r ie s a s

o py o

n ,

m

is fr o

e m

a m

a

y

(7 4 2 ) (7 4 3 )

T he

co n

d itio

fo

n

r

h y d r o g e n ig n itio

n

Tc Z Tm th u s b e tr a n

m ay

s la te

d in to

a co n

d itio

n o n

in

th e

m

a ss

(7 4 4 )

y ie ld in g M

m

0 1M

in

o

fo

d in g to th is m a s s ith th e a id o f L o a n d M

c o rr e s p o n

it w

th e e s tim a te d

r

ay

m o

L

Ex o

e r c is e

f th e

!x

m a in s e

e r c is e

le ń v e īs tim

C a lc u la te th e

7 2

an

7 3 u

qu en

U s in g

la te d fr o

m

r e la tio n

10 7 K

T h e lu

m

in

o s ity

(7 3 5 ) a fte r c a lib r a tin g

in i

e

u re ffe c tiv e te m p e r a t

c o rr e s p o n

d in g to th e lo w

er en

d

ce

i n b E u a tio n (5 3 7 (w ith L E d d g v e y q d itio n L 5 L E d d f m a in s e q u e n c e s ta r s lu m in o s ity o a n d th e th e m a s s f th e m a in s e q u e n c e r end o t th e u p p e a tu f e a r e p

,

th e c o n

i fo p p e r lim t

a te th e

c a lc u

×

,

m

J

be

1 5

o

ective

r

te m

Scanned by CamScanner

n ı

t» ra o n o rı tı

ņ v o lu

\e Tı

7

tt? r\ m l h c tw tı tı ı \¢ 1o ı 4 ı ľ lH d ı nn 7 q ı li*Ð Ĥ X » ľ rl*ņ r l w ı ı ı ı l llı\ u p n u ly \\Ñ» \\in n # N u rņlo n t o ı , ,

po w

K

u p l? d h d ı\\ı \ ı ri (\ı e p \' n \ ı e r tı

n lln n \c N llt

l

\ u

T¢ eı m w ı

\ılo \e n n lc ln ı

hlh

t\pnı ly ın w

,

ly pn c ı

o

tl rı tı

/

¢中e ttf th e m a in d th o $t ı tu ı u itĻ ity la w ) 7// (lh o K ılıl11( rl+ p

M

nnp

r

w ı [ı

tł w e ı £

\u

\s s n \ı

m

ln u

H

ľ

\n c o n c lu s lu n

'

ı6 ) IIn

t (1' lg u le ı

llTc lc n l o p u u ily In w

ı o r t\ u M \\n c c x tc n l

w c

,

hav o

1:u rth o rm

Hu c ee c d u d

il w

o re

ll ll»

n

o n

,

ił ı houÆ h

ltr th e ł

l ]e n t n l l l f u r th e l 3 J# In d e p Ģ m « th e p o w e r i* lT 1 e r ittu re , tlv o ı y In w le p ıe ltı

園 闻目ワコn c ln tlu tilly ı

罗庙

ı

o c po w o l ı lı

c Io p l ln ı

1\p p ru

ı ch«mntı c p ıc *u r

a

-

,

lıN ı

5

b u l ilic

in

ex

o n

t to th e lo w e r p a r

lı p pc r

o u

o n th c u

ld « till re m

p pe r

a in m u c h

lb a tu r e » o l th e o b # e r v e d m p o i$itio n lt th c in itia l c o u n t th Ł

p la in in g

ta k u in to t\c e o

c

p a rt w

3

in o H t

h e m a in # e q u e n w c r H la n d w h y t ı# ltll # , w c t\lH o u m ı o l llı m o ı \ h iı t l c i t c t r s t is n o y m rf$ a re th o ĥ e m tin » e q u e n c e s h c h y p o u ìc H is th a t ı T i l e n \ l h n u t h ı c t l or i5 ı\ s tl ip ru h a » th u « tu r n e d in to 1/ıe t ıe y

m a in s c q u c n e c

u

lm

( m u

\ rc lu ı

b \ır n h y d ro g e n in

s im s th a t

ht

tiv c ly » m i\ll c o le i\p p lic #

S tıic tly th c th e o r y

v ť cfN p /Tc Q

,

u e /īc e , i to lh c z e r o a g e m a n $ e q h ld b e a r in m in d th a t it

l h o m o g c n c o lIs A n d w e p o s itio n is lr u y ı ro c e d u r e e m p lo y e d » lc i\n d q u ite g c n e ra p n th c # im ı ig n o ıe s ? o n v o c tio n ĺļ u l w h y c £i o t b e a p p lie d to b u r n in g ? T h c ıc a s o n w h y it c a n n b c u p p lic u o n ly to h y d ro g e n it ı i n i# th a t th c c r u c ia l h o m o g e n e y o th e r ilages o l c v o u l o ) o th e r ty p e s o ıs ta i s ( d at li iŕi n o lo n g e r v a i ı ta te h o lh o l c o m p o s itio n a n d o l p h y s c a s a s s u m p tio n u tio n t\r y s ta g c ti adv an ced cv o ı

w

h e n th c

so o rc ı

Ex un

d

#

7 5

4 b u t tu k in 8 in to

n

qu e nce

T hc

\n \c sı

s e r v e to s ta r o

ith

w

0 u tı ı ne

7 5

r

d im c n s io lm

R c p c l\t th c

m n le c u ln r w e ig h t /A se

o u

co m

lm

D

o

f th e

s ic d ia g i i m

n l th c a c e o lı

c r iv c

I o s p c c \ Io

M

te m p e r a tu ıc r

:

lb

de pe n du

u s in

g th o K

ìc e o

e fs o r a lT ı

'

l tc tn p e i lltu ľ c

p a c ity la w

ean o n th e iTı

in g la w s o l s le lı w p r o p e r tic £ o n th e m a in th c s c a ı

/ı fls

w o

ı ıa s M

s tr u c tu re o

f s t a r s In ı a te

evo ı u t io n a r y s t a

th a t w a ķ u s e d to d e s e r ib c lh c e v o lu tio

decrihc lh c v lr ılc ltu m i\s s

l a n a ly s is

n o

ıa

l' s ta r s

ge s

m a

y

so aı

c o re

(ln ) ım

v o s ta r t\l tl g iv e n e v o lu tio n a r s ta e C o n s i? g y i i i h i t v e n o i n 11 t / o cal t w n h w e y g a v e th c v a lu e o f th e ı p d lh c v a lu e o l th c lo c a ıd e n s it y p (m ) w h ic h d e fin e a p o in t

g io n \ T he c o l

re

,

co ı T e spo n

d in g to

t

o

r an

in th c (lo g T , ı o g p ) p la n e Jo in in g th c p o in ts

W

P in t o 1 h y d ro g ĺ

r a

ues d ilT e l e n t v a ı

P Scanned by CamScanner

7 !

s t r u c t ııp ıof

ıt ır ı

ı n ı ıu

ıv o lu t ı o n a p y ıt \

23 ı

L IL I

10

) 一

i

莲 中

ヨ ー

7

Lo g

Ħg u

re

ph a s e s

7 6 S c he

m a tic

illu

fo r

o s ta r

(A B C D E ) a n d

lO M

a

s tr a tio n ,

,

o

,



8

f th e

s te

,

9

10

ロ 中 ロ

[T (K )]

lla r

fig u r a tio n in d iĦe r e n t

co n

h ite d w

a w

a rf

e v o lu tio n a r y

(W D )



o

f m b e tw

O

een

th e s ta r in th e

W

o n th e

d M ,

; th e

b ta in

o th e r

an

p a r a m e tr ic

a

) p la n e O

p

10 6 K

b ly b e lo w

a c ro s s th e

w e o

,

(lo g T lo g

c u rv e

M

c o n s id e r a

an

n e en

d

o

is

lo

a v e ry

s tr u c tu r e o

f



th e c e n tr a l p o in t ı ie s h a r a c te ń z e d b y a te m p e r a tu r e d e n s ity H e n c e s tr u c tu r e lin e s r u n

th e s u r fä c e

d by

lin e th a t tr a c e s th e

f th e ı in e

w

c

仁 ヌ

(lo g T lo g

p ) p la n e to w a r d th e lo w e r le ft c o m e r T h e e x a c t s h a p e o f , th e s e lin e s m a y b e c o m p ı ic a te d (o n ly p o ly tr o p e s w o u ld b e d e s c ń b e d b s tr a i h t y g lin e s o n lo g a r ith m ic s c a le s ) a n d m a y c h a n g e w ith tim e a s th e c e n t ra l i t p o n n ıo v e s N e v e r th e le s s th e y w ill in v a r ia b ly le a d (m o r e o r le s s ) m o n o to n ic a ll a lo n g V M y fr o m th e c e n tr a l p o in t to w a r d lo w te m p e r a tu r e s a n d d e n s itie s





,

A

p le is g iv e n s c h e m a tic a lly in F ig u r e 7 6 fo r B C o f s tr u c tu r e lin e s la b e lle d A w ith o r ig in s

n

ex am

a se ū e s

se ń e s o

f p o in ts (la b e lı ed 0 m

ay

b e ta k e n

B ?

g n iz e lin e A s c r ib e s th e s ta r

c o re

W

e n o te

th a t th e

P o in t o u ts id e th e hydr o g e n

c o re

burning

r e g io n

T he

b e y o n d th e

c o re

at a

its e lf

,

c o n ,

w

,

,

) ly in g a lo n g th e

ı a te r

d itio

n

g th e

n a r y tr a c

1o

h ro

in

a in

a she

m

o

.

n o

f th e

s ta r





se

,

r s e c ts

th e h y ? o g e n

lt o u ts id e th e h e liu

burning s h e ll c o n s titu te s d e v o id



by

o

ı o g ic a l o f F ig u r e 7 5

at a c

k 9

f lO M

q u e n c e s tr u c tu r e T h e n e x t lin e s ta g e w h e n h y d ro g e n h a s b e e n d e p le te d in th e s fo r h y ? o g e n burning a r e n o w fu lfille d a t s o m e

h e r e A in te

c o n tin u e s

n ow

lu tio

ev o

s ta r o

a

to r o u g h ly r e p r e s e n t th e e v o lv in g s tr u c tu r e o

a s o u tlin in

e re c o ,

,

,

T h e s e lin e s W

,

f e n e rgy

a c

s o u rc e s ,

m

burning th re s h o ld

h e m ic a lly h o is

T he

c o re

c o n tr a c tin

m o

g

ge n

an

r e la tiv e

T hu

ly

co o

e o u s e n v e lo

d h e a tin g

u

s

l

( :

v

pe

p

Scanned by CamScanner

12 4

7

T bı

ıv o lu tlm

ï łc g n r d ln p ıh l» p ill rlc u ln r h is b n o k

hc m

d

\n ł

w n lı cd

th e

n c a re «l ł uı u re

s n fc

ï y w c tiı ıa a o n m ı

m

So

fu r th e

w c

a w m tin

A

lo o

,

g

k

,

o

ï mo m lh e h lg

re \ trll*

lily łļ w s c lw

ı thı mı tłp k ııır ı ttr tlrï

e m rı p lll( :r》ı w

b l(山 w

iï r/ q « h ll¢l v

e rn u y

r rM

In

In

Zp d

»k ił re ¢)f ilie r ł

f14 1v n n rl l(v u lrttltn t tıl rh p

h llil: Srmf

w /w

in C h a p te r 9 n g [h c c o n lm c tio ı

Nc ł ı w

ltt * lr ¢ll1# e r lh lln iba lr wl*b Iıl r

e llr lu * lly

r iN k u n cl 8 o o 11, rh c re b u ll» n

h a ll ta k e th e

us

ho »e

w

ı

p ltï ı*e , M

u rlo Jtn ry cvn ı

lł u ıIb r lh o lıe

a \\ ln

f ıta r ı=

rnum

m

h tm

ttr « ,

l

e r ic ŕ il u a k u la ı jo ft+

,

q u ił» i b ta tic a lly , n ıl a lim e w a le w h ic h ı s m u c h lo n g e r th a n th e d y m i n ı ic a l lim e » c a Je th e v ir ia J th c cn e m ım y be a s s u m e d 1o h o ld P ro v id e d th e a m o u n t u l e n e r i l l i ( o d u r o h i) u r n g thi h a j gy g a n p w is n e g lig ib le w ith r e s p e c t to th e to ta l » lc lla r c łtc r gy (th a t i# [h e n n a l e u ilib r i , um q is m a in ta in e d ) th e la tte r m a b c a tt» u m e u 【 i o r e Jr m n c o n b ta n l A # d itı c uM td i y ssu m

n o

f th e

c o r e Io o c c u r

,

n

,

S e c tio

2 8

de r

c ir c u m

[h c g ra v ila tio n a J p o le n [ia l e n e r gy a n d the th e rm a l e n e r g y a re e a c h e o n « e r v c d C o n # e u e n [l c o n ı ra e tio n u f th e c o re m u » l q y, b e a c c o m p a n ie d b y e x p a n s io n o l th e e n v e lo p e Jio iw ı u c o n w w e th e g r a v ita tio n a l i l t o t e n a h A e n c i h Į t i l t c b lT i h a c m e, eat ng o t e c o re m u ø£ıe » u lt in c o o Jin o r p r8 y ¢ th e e n v e lo p e fo r th c th e r m a l e n e r8 y to b e c o m $e r v e d Jn p a rtic u la r th e urftee n

un

,

h

suc

» ta n c e »

,

,

,

(e ft æ tiv e ) te m p e r a tu r e dmps th e b la c k b o d y ra d ia tio n lh u » » h iftin g to th e re d T h e s ta r a s s u m e s th e a p p e a r a n c e o l' a ï e d g lm l (R ( i) In o r d e r to g e t a ro u g h id e a o f th c a iï 】o u n t o f e x p a n » io n th a t m i h t ta k e ı g p ace ,

6

m

d is ta n c e

2 at a

S u p p o s e th a t

o n e

c o n se rv ed

d ř2

m o v es

in

am o u nt

e x e r c is e

o m

d is ta n c e

e a s ily v e r ifie

/r o

a re r e la te d

w a rd

(7 2

,

p

]0 %

7 2, 6o

by ř 2

fa

th e o u tw a rd o n e i8 m o r e th a n

e le m

a ##

m l

e n ts

s ta r a n d re g a r d n ı(r ir) a s a

th a t th e g r a v ila tio n a ıe n e r8 y o Į

ří )

0 9 ), th e

=

lm

,

and

p o in t m

iu$#

to w a r d th e c e n tr e , to a d is ta n c e r n a n d th e

(2

=

1 13 ) W h e n th e in w

=

o

d th a t th e d is ta n c e #

f ro (ř i

o

c o n # id e r tw o e q u a

th e c e n tre

c le m e n t m o v e s

It is

72

-

h

ro

o th e r o u tw a rd , to a

an

p Je

a v e r y s im

do

w e m ay

a rd

3 0 % (72

m e a +iu r e d in u n

j

w

e

=

fin d th a t

1 3 3 ),

an

is

s y s te m

one

=

/

r ı no

e le m

l

m

b o u t th e

sa m e

0 8) ho w d ilfe re rıc e in c r c m

ev er

i$ 2 0 % (ř J

d th e

he n

w

o th e r m o v e s o u tw a r d

dispJment

f th e

itfi o f r o , ř l by

a

=

,

,

r2

g to in /iih iry a s r i a p p r o a c h e « /h tt (th e o r ig in a l d im a n c e t h is e x e r c iıe a h o u ld b n o t e ta k e n to o lite ra lly th e g ra v ita tio n a l e n e rg y js c o n # e r v e d g lo b a lly n o ¢b y s e p a r a te m a s s e le m e n tß th e m o tio n o e c u r fi w ith in th e m a s s o f th c s ta r a n d n o [ o u tßid e it a n d s o fo r th N e v e r th e le « s th e o , g e n e r a l c o n c lu « io n th a t it w iu i m m n i ı e n d in

,

,

em

p h a s iz e

ex

p a n s io n o

th a t a m

f th e

o

d e r a te

e n v e lo

pe

am o un to

If th e to ta l e n e r8 y d o e s n o t r e m

(L n u c ex

>

L

p a n s io n

on u

f c o re

c o n tr a c

tio n m a y e n ta il a

ific a n t s ig rı

js tr u e a in c o n s ta n t a # a tis u m e d ,

b u t r a lh tr i n »

th e a v e r a g e ), th e n it i# e a # y to lte e th a t th e e lfe c t o f e n v e l\

po n

c \ e c o n tn w tio n

w

ill b e

a

ll th e

m o re m

n » id e r a

b Je

T h e re fo r e

Scanned by CamScanner

«Ħarsinb*O«ıı*

7 5

g iu

e ttı

e n s io n s th a

d im

t ı

tm

t

l g łĮ tm

.

s ı 1\4\

! m a c h s h tų \\tl n t s u r n Ħ u s w c m p to tzıl e n e r g ! o l th c s tłlr trr«ses a w h lı m ı c h c c o re c o n ı L ) w e m n n o tdn w a n \ < ı u c tin tte t r ıc x m ı \ı sı o n : th c c m t ı he r o N m ł \y th e n c lı o r omain u n chı ın g tx l o r e v e n ü ìn t e n « t ï Tų ) \ lc p c n d ın g n n th e d in + re n c e t e n th e e n e rg y đro p n ĵ s u ltin \ h ì m c o tĘ c o n t g ı m c rio n t\n tl th c tw le m ı ıc n c tl y L ) O nı v d e ta iı ı ï d s te lla r e v dm p (L n w l o u tio n c iì n l lı p tm ıo n s c tm p r o v id e th c ttıre tin ì m th r a s to th e d e w a n s \\ ¢ cn n nl uilibriunt (its tr e n d łtn d e x te n t) B u t

pro v

id e d L

a re d

e qt o u

m o

ra

ue

ig n itio

p a iıd w a

th a t

n w as

d e d in

×

he n th e

p re s e

f

a

e x h a u s te

H

d in th e

e \ ìo lv in

S c hn



ces

fo

K

io n

g

m m

c

re

c o re

in n c o n tn ł cı

,

at

d

re

T (1 ]ï ı iıtıc l

,

,

u

p

fo r p o s tu ı a tin g

th e th re s h o ld te

m

pe

se

d U l is

s ho w e

p

a r a [e



ille d łľ £lo p e s '

d by

a

gatl )

Rïıe s ta r s

d

d o n e d u ń lıg th e b r ie f p e iio d

Hole

e s tim

s

p r e d ic tio n

d th r e s h o ld

a te

to uN a n

j h e liu

b r a n c h T he y

te a c h e s

p a n s io n

sı e lln r m (x le ls

)u s

tile ï łīa in s e q łte ı\c e

ı\e (łr

d S c h \s c h i l d fo

hea t t

an

Th e

1 1

o

f

p la y

e n \Ę lo

u n

d , to

'

cou

f

re s o n a n t

p e r a tu r e fo

r

Th e e n v e lo p e s

o r r a th e r s p e c u

p lņ "ic aıp m

a ï łe s s e ï ıtia

a re s o n a n t e ire tg y

f its

o

th e ir d is a p p o in t

de d

a

p e s T h is

o

te m

ig n itio n

m

c o n c lu

10 s K

×

ld s ĺ a r t ī o s s ïı o ïł

p tłta rio n

t r o te

c e s = ııo ı

' ,

ld h a v e b e e n

le v e l in th e

p e r a tu r e fo r th e 3 ce p ro c e s s to

a s to

so

a se c

c a r b o n n u c le u s

a

b o u t 10 s K !

p e ra tu ııe is fin a lly tìe a c h e d a t th e c e n tr e c o re o f th e s ta r is d e s c ń b e d b y lin e C in F ig u re 7 6

te m

s tr u c tu r e ex

an

d g ia n

e m Ę lo

an

d ı

m

th e ū m e

t and

ge n «

m o

c o re s h o u

g

h ild in ł g ji2 In d e e d an

ltic h is

w

th e kr p r o c e s s

r

S a n d a ge

ig n itio n

o n e

ith

g in h o

Tz i th e c t )w

R d itıg r a

l ıe m p e ra tu lıù

e n t

ps T he

d a ry

se c o n

d th a t

j

b se r v e d

o e n e rg y s o u r c e s a r e n o w

d

f

c o n tra c tin

c o re s a iıd e x

V n ie n th e h e liu m

n

a r tin

c o ï ıig ı ır m

10 8

n t c o tn

le v e l r e d u

c o n tr a c tio n s to

o

th e c e n tra

In d e p e n d e n t u g u m th is

Tw

u n

M

a

c o re s c o n n a c

th e c o n tr a c tio n o ..

fo

s s o lu tio n

y b e y o n d th e

w

th a t a s ta r w

n o te th a t th e s e c a lc u la tio n s \ LĘ í E

n2

h ile th e

Th a t w

e

in irio ï

f

r ig ï ir in tile

S a lp e te r

en

L\ n s

o

(s e e S e c tio n 4 5 ) T h u s

c h a ï a c te r

en

n ı th e

ı ntìesting to

b e t\w

um

saūı y c ıa im

c a \c u ı n tio n s o

c o n s is te d

o th e p id h ł

t is

n

d e ls

M

T h tłs -

y

t

g e n b tım in g s h e ll h

m

,

g ia n

t b y A lla n S a n d a g e a n d

T he

ı c

w e m a

T h e tirs t d e ta iı ed

N o te

.

,

L

n ue

o v e in ı ı

e \o

if th c

ı

h o \\ t v e r .

o ite d : th e pı

m a in o n e

H e liu

ll

a ro u n

h y d r o g e n burning in a n o th e r p h a s e o f c o re

a

s he

m

burning in

th e c o r e ,

d it W h e n h e liu

c o n tr a c tio n a n

d

e n v e lo

pe is

ex

m

is

p a n s io n

ev en m o re p a n s io n f th e s ta r a t th is p o in t u ro n o u n c e d turning th e s ta r in to a s u p e ıg ia ıłı T h e s tr u c t r e o de s c r ib e d b y lin e D in F ig u re 7 6 : o u ts id e th e c a r b o n o x y g e n c o re re s u ltin g fio m liu m burning w e fin d h v o burning s h e lls w h e te D in te r s e c ts th e h e liu m burning c tiv e ly T h e c o m p o s itio n e s ho ı d a n d th e h y d r o g e n burning th r e s h o ld re s p e la y e r e n c o LĘ is a h e liu m x o p in g th e c a r b o n o y g th e s ta r is s tr a tifie d e n v e ı f th e h e liu m d b th th e h e liu m burning s h e lıb e tw e e n th e m T h e o u te r o u n a r y o ll w h ic h s e p a r a te s th e h e liu m la y e r y e r is d e fin e d b y th e h y d r o g e n burning s h e

s e ts

in S in c e th e

c o re

is

no w

m o ne co n

de n se d

E n v e lo

pe

ex

,

,

Scanned by CamScanner

Scanned by CamScanner

P

Fig u r e 7 7 R e la tio n n u m e r ic a l c a lc u la tio

fro m A

K

o v e tz

F ig u r e 7 5

o

d

w

a s s o c ia te

h e liu m

,

o

n s o

Y

O

f

b ta in e d

c e n tr a

f th e

ig n itio

n

at

l de ev o

d D

o n th e

b a s is n o

th e c e n tr e

n s ity to

lu tio

n

o

3

c e n tr a

f s ta r s

o

l

f

P r ia ln ik (2 0 0 9 ) M

aro n an

ith th e ig n itio

CN 0

P

,

C + C

a

te m

p e r a tu

re

v a r io u s m

o n

N

o t

o

b ta in e d fr o

a sse s , a s m

R

o

y A s tn o n

a rke

So

c

co m

m

p le x

d (a d a p te d ,

395)

f s im p le a r g u m e n ts L e a v in g a s id e th e d e v ia tio n s i f a n u c le a r fu e l (in p a r tic u la r th e e x p e c te d e x p lo s v e d is c o v e r s ta r ), w e m a y b e s u r p r is e d to o f th e 1 M o

o

to l O M o e n d th e ir liv e s a s w h ite u h th a t s ta r s a s m a s s iv e a s 8 M o a n d p e r a p s p M ch! l d w a r fs W e h a v e e x p e c te d th is to h a p p e n o n ly b e o w th e c o n s e r v a tio n i T h is p o in ts o u t th e fa lla c y o f o u r a s s u m p t o n concerning ld h a v e s u s p e c te d th is a s s u m p tio n h o f th e s te lla r m a s s d u ń n g e v o lu tio n W e s o u l s io n s o f th e s ta łıd a ld to b e w r o n g e s p e c ia lly fo r m a s s iv e s ta r s fr o m th e c o n c u t th a t m a s s lo s s m o d l (S e c tio n 5 6 ) O b s e r v a tio n a l c o n s id e r a tio n s to o s u g g e s h o la r n e ig h b o u r h o o d , w ith m u s t o c c u r S e v e r a l lo w m a s s w h ite d w a r fs in t e s k n o w n If s ta r s c o n s e r v e d a c c u r a te l d e te r m in e d m a s s e s (0 4 M o o r le s s ) a r e lo n g y th e ir m a s s e s it w o u ld fo llo w th a t th e G a la x y is o ld e n o u g h fo r s ta r s o f 0 4 M o o r le s s to h a v e e v o lv e d o fr th e m a in s e q u e n c e W e s h o u ld th e n e x p e c t to e n c o u n te r a t le a s t s c e s e n d in g a t lu m in o s itie s b e lo w th a t o m e s ta r c lu s te r s w ith m a in s e q u e n In fa c t , th e c o rr e s u c h c lu s te r s a r e k n o w n p o n d in g to a m a s s o f 0 4 M o , b u t n o s te n d to c o n s id e r a b ly h ig h e r Iu m in o s itie s a in s e u e n c e s o f a ll k n o w n c lu s te r s e x q ,

,

,

,

,

,

,

Scanned by CamScanner

The

7

ı u t io

evo

n o

f s ta

rs

ız B

(c o r re s p o n d

o 7M

abov e n ia s s e s

in g to

o

a

sc

a

hem

a tin g ) in d ic

t ic p ic y

a

yo

i it a se kh ar l m

N

Leo

ow

hen

w

to c o n

n

M

e s te

T he span s

o

f th e

g e s is im p e d o m e so m e w h c lu s io n s

s ta

ld b e c

o u r c o n

c lu d e th a t s ta r s lo s e

Sh o r tco

m

fo

a in

s h o r tc o m

r t h e d iffe re n t p

s ta r a t e a c

h

s ta

im p o s s ib le (s ta tis tic a ll e a s a c c tır a te l re p r o d u c w e

f

th e ir tr e n d s

lin k th e p r o b le m

s ta r s w e

ı 1abo v

e th e

u n

de

r s ta n

th e o c e a n

19 6 5

j

W /ıite D l T h e T he o ï y q f

w e m us

d in g o f th e o f e v o lu ū o n

w a l s

f i d e te c t w h ite d w a r s n d e n s e a b le to pe s are h a v e to w e r f s r a d w th e w h ite s tr o n g e r : e n t is e v e n c lu s te r o f th e s a m e

te le s c o

de m

m o

th is a r g u m

c lu s te r s

g lo b u la r

f

o

a r f th u s w h ite d w c o o lin g n in to a s e ttle d o w n fa te o a c i t o s a s s i m a f th e u lt m te fs w ith th a t o f w h ite d w a r o m ń o h e f t g o

adays

burning

oe

lu

ı ¢łë

sho u

u s ic h fo r c e s s w h c lu s te f t s d e l ce a s its o se qu e n is a b o u t a s o ld e m a in a v in g th a f te r Į e l l r a i u y c t r m a ss pa

C ha n ?

gc

u n

7 6

re

ta r s n se qu e n c e s m a s s e s th a n m a ı

b s t a n ū a lly in th e c a s e o f th e e v o lu tio n a r y is c o n s id e r a b le H e n c e h e r e r a d ia tio n p r e s s u r e m a s s iv e s ta r s w a s th e in itia l m a s s i c r e a s in g ly s te e p e r s lo p e s F ig u r e 7 5 s h o u ld h a v e n p a th s v M in be c o m e a s s iv e th a n M c h m a y ta r s in itia lly m o r e m M in c r e a s e s T h is m e a n s th a t s d in g to lo w e r a r d p a th s c o r r e s p o n i w p a th s s h iftin g q u ic k ly to w w h ite d w a r fs th e r h t a t de sc ń bed l t o i i r a b e in g v e r y s m th e e v o lu tio n a r y c o u r s e a n d lo w e r m a s s e s l ic tu r e r e m a in s v a lid f a b o u t 1 M o T h e r e fo r e th e g e n e r a p e a r lie r fo r a m a s s o ill e n d u p a s w h ite d w a r fs a n d a s s b e tw e e n s ta r s th a t w e x c e p t th a t th e d iv id in g m 1 4 6 M o T o d e te r m in e o v a e is , in r e a lity , h ig h e r th a n s ta r s th ? w ill b e c o m e s u p e m f th e n e x t o s s is r e q u ir e d T his w ill b e th e s u b je c t o h o w h ig h a m o d e l o f m a s s ı su c

c

h

a s th a

Su

n

o n

ly

m u c h m o re su

h a p te r

Ex

s ta r s c o r e

(b y

gro w

m ean s o

M

L

th a t M n o tin

a

_

.

s

in

m a ss a s a re su

(0 )

A

w

m a ss o

0 (b ) F in d th e

0 , ( )

d

a rf

=

g iv e n

o x y ge n

o

fa

s ta r o

burning

f in itia l m

T he

ass

M

c le a r p r o

n u

o

T he

c e sse s

Q p e r g r a m o f burnt m a te ń a 1 T h e š ta r lo s e s m a s s in d ) a t a r a te p r o p o r tio n a l to its c o n s ta n t lu m in o s ity

M

o

Q

=

) a n «l a

f th e

m ass o

c o re a s a

f th e

5 -

u

1 0 ı4 J k g IO 14 k g J

'

pe

as a

c o re m a s s w

p p e r lim it o f M

×

fu n c tio n

e n v e lo

( ) W h a t is th e c

(d ) C a lc u la te th e

h ite d w

c a rb o n a n

lla r

a s te

lt o f n u c le a r

f e n e r8 y

し (a )F in d th e

g th a t M

v a n is h e s ?

a w

f

h y p o th e tic a l e v o lu tio n

o n s id e r th e

C

7 6

e r c is e

r e Je a s e a n a m o u n t o

.

th e

fr o m

t e m a n a tin g

o

(fr o m

fo r

w

o

f tim

e

fu n c tio

M n o

h e n th e

h ic h th e

tu r n in g

.

(t )

,

f tim

e

e n v e lo

s ta r w

in g

a s su m

M

pe

,

(t)

m a ss

ill b e c o m

e

s o la r c o m p o s itio n in to

!

n o th e r

h īc h h a s

p ro c e s s M a t h a s b e e n . E g le c te d is n e u m n o p m i. i. . In d e n s e c o a m a rk e d c o o lin la g e c t A s th e ń s e in ï e m ı Je ra M re b e w e e n

Scanned by CamScanner

7 6

S h o r tc o

m

in g s

o

f the

s im

e s te ı ı pı a r

ev o ı u t io n

p ic t u

29 ı

re

s ta g e s is im p e d e d b y n e u tr i n o co o ı in g , th e s lo e s o f th e 4 I M c u r v e s bu r n in g p h o e s m e w m t o a c s t b e e e d l p e r th a n 3 H o w e v e r th is e ffe c t d o e s n o t a lte r a n y s ho u l s io n s ur co n c u ,

o fo

T he

m a in s h o r tc o m

in g s

f th e

s im p le p ic tu re a r e (a ) th e to ta l la c k o f tim e f if d t e r e n h e t r o c e s s e s a n d (b th i p s fo r ) e g n o r a n c e o f th e o u tw a r d a p p e a r a n c e s pa n h c t a t e s a B a e o th fa c to r s r e d g e s ta r n er a co m o f th p a r is o n w ith o b s e r v a tio n s i i l l t t t s a c a y a s w e ll a s in d iv id °s s ib le (s to o

u a lly

im p

du re p ro

ce as

a c c u r a te ly

d th e ir tre n s u n de rs

po

s s ib le th e o

w e m u s t r e s o r t to

d e ta ile d

b s e r v e d s te lla r s te lla r m o

f th e p ń n c ip le s in v o lv e d w e f e v o lu tio n a r y c o m p u ta tio n s th a t w

ta n d in

oce an o

as

g

o

,

o u r m a in

d e ls H

a v in

g

q u ir e d a b a s ic th s a il th r o u g h

ac

pe c t a sm o o s h a ll r e a c h in C h a p te r 9

m ay ex e

p u r p o s e is n o t o n ly c h a r a c te r is tic s

) S in c e

Scanned by CamScanner

8

M

lo

a ss

fr o

ss

ta

s

m

rs



吕 づ



四 日

勺 园

8 ı O bse It is

p h o to n s d ia tio n

ra

is

kn

m e a s u re

s o la r m

d in

pe r y e a r

a sse s



o m

a w



in d W

e sh a

ll d e a l w

a ss m

p r e s e n t d is c u s s io n to s te lla r In d ir e c t e v id e n c e fo r m th e o r e tic a

l in d ic a tio

m

e re

is h o

w e v e r,

o

f th e

o u te r

la y e r s

n

fo

d de n

an

y ta k e tw e x p lo s io n , o r a ith e x p lo s iv e m a s s

itte d S h e d d in g o f m h ll s e , u s u a lly fo llo w in g a n is

lo

a ss

m

ss

o w

t re p e

n o

f

ce o t io n a l e v id e n

d itio n to th e o u tĦo w o f lo s e m a s s In a d le d g e d fa c t th a t s ta r s i le s B u t u n lik e th e flo w o f fl w o f m a te r ia l p a it c th e r e u s u a lly is a n o u t o in th e in te ń o r , th e flo w o f m a s s i e rgy g e n e ra t o n w h ic h is s u p p lie d b y e n t th a t is u s u a ll s s d e c re a se s a t a r a e y l n is h e d A s a r e s u lt th e s te lla r m a

ac

an

rva

r

d ir e c t

w

o te

fo

o

a

d by rm

tin u

co n

,

w

h e r e th e

s: a

su

dde n

o u s

flo

w

g a tiv e s ig n e je c tio n o f a m a s s

F ig u

lly r e fe r r e d to a s 10 , a n d d e v o te th e

u su a

in C h a p te r

j

e e c tio n

n e

in d s

a ss

b r o u g h t in th e p r e v io u s c h a p te r a n d b a b le o c c u r r e n c e w a s m e n tio n e d in C h a p te r 5 lo

ss

its p r o b s e r v a tio

w as

l e v id e n

fo

r c o n tin u o u s r a p id e x p a n s io n lla r p h o to s p h e r e th a t m a r k s th e o u te r edge a n d in to th e in te r s te lla r m e d iu m T h e m o s t c o m m o n is e x h ib ite d b y a c h a r a c te r is tic s h a p e o f s e c tr a l lin e s k n o w n p a s P C y g n i lin e s n a m e d a fte r th e , s ta r P C y g n i o n e o f th e b ń h te s t in o u r G a la x y d is c o v e r e d in 1 6 0 0 g s ta r ,

o

o

n a

f s ta r s b e y o n d th e

ce

s te

,

as a n ew

,

誣 .





卜 月 ぜ

(s e e

u

pco

p r o file co m

po To

m

co n

in g C h a p te r s 10 a n d 1 1) w h e r h e t ey s is ts o f a b lu e s h ifte d a b s o r p tio n c o m po

n en

tan d a

A p C y g n i lin e r e d s h ifte d e m is s io n e n

t

d e r s ta n d th is e c u lia r p p r o file , im a g in e a s h e r ic a ll p y s y m m e tr ic o u tflo w fr o m a s ta r A s s u m e th e s t a r e m its r a d ia ti o n a t so m e st w a v e le n th À T h is r a d ia tio n is s c a tte r e d b g o (a t re ) y th e o u tflo w in g a s a n d h g s in c e th e r e s p e c t to a n o b s e r g a s v e lo c itie s w it v e r r a n e fr o g m u to + u w h e r e u is th e e , th e e m is s io n lin e w ill x p a n s io n v e lo c ity. a pp e a r s m y m e tr ic a lly b r o a d en ed s h ifte d r e d s h ifte d a n d b lu e o n b o th s id e s o f 入o a s a , r e s u lt o f th e D o p p İe r e c t th e lin e o f s i h t o f th T h e r e io n a lo n g g u n

e s ta r

t

ill s c a tte r th e

h e r e th e a g s r a d ia tio n out

w

,



p ro m

nen t

th e o b s e r v e r ) w

#

in

a re

v e lo c it y

w

h ile th e

is p o s itiv e s ta r

is

g d i t r c ( e e d to w

o ccu

ltin g th e

a rd

r e g io n

13 0

Scanned by CamScanner

r

8 2

Fıg u

w

re

he re

8 I L in e

v e lo c

r a d ia tio n

,

E x a m p le s s p e c tr u m

s p e c tr u m

itie s

a re

o

The

m a ss

f P C yg n i

,

g a tiv e T h is w ill s h ifte d a b s o r p tio n

f P C y g n i lin e s a r e o f th e s ta r P C y g n i is o

a

3ı ı

o ns q u a tı

h e r e P C y g n i p ro file s

w

n e

th a t is , b lu e

ı o n

sho w n sho w n

a re a

p p a re n t

in d e p le tio n o f o n ly b lu e s h ifte d p e r p o s e d o n th e b r o a d e n e d e m is s io n

re s u lt su

in F ig u r e 8 1 w h e r e a p o r tio n o f th e lin e ; th e ty p ic a ıp r o file s a r e a p p a r e n t fo r th r e e ,

hn es

f a P C y g n i lin e a n d il d h h d p lic a te d w a y th e a n a ly s is o f t e e ta e s a p e o its in te n s ity e n a b le s th e d e r iv a tio n o f th e g a s d e n s ity a s w e ll a s its v e lo c ity a n d b e lo w th e s e le a d to th e e s tim a tio n l h ra d ia l d is ta n c e fr o m th e s ta r A s w e s h a l s o w tim a te s a r e a ls o p o s s ib le b a s e d o n o th e r o f th e m a s s lo s s r a te M a s s Į o s s r a te e s l d l i h kin d s o f s p e c tr a l lin e s W e s h a ll r e fr a in fr o m s p e c tr a l lin e a n a y s s e re a n o n y r e d m a s s lo s s r a te s v a r y o v e r a v e r y w id e m e n tio n th e s ig n ific a n t r e s u lt th a t m e a s u 1 4 14 d e p e n d in g o n s te lla r m a s s a n d M o yr 10 to 10 r a n g e o f v a lu e s : fr o m e v o lu tio n a r y s ta g e In

a co m

,

,

,

,

-

J

The

8 2 T he

o u tw a r d

r e fe r r e d to a s

s ta tic e u q

d u r in g

a

flo

w

o

f

m a ss

is g e n

m

fu ll s o la r

an

d

ec

r e ta in s

lip s e

,

m a ss

e r a te

o s p h e re

th e s te lla r a tm

ilib r iu

,

w

its

,

s iz e

h e n th e

lo

ss e

d in th e w

q u a t io

n s

o u te r m o s t la y e r s o

h ile th e b u lk

o

f th e

f th e

s ta r m

s ta r , u s u a

a in ta in

t, fo

s

lly

h y d ro

r e x a m p le T h is is b e a u tifu lly a p p a r e n d d is c o f th e S u n is o c c u lte d a n th e c o r o n a

,

Scanned by CamScanner

h ・ M

8

ss

lo

a ss

from

s

ta f s

ı3 2

T he

J

n

T hu

w a rd o u t

H

an

4 71

=

d p a s s in g

e r v a tio c o n s

.

w

n

r e th e s 2 u x , (1 r

he

/

In

w

ha

n t in c o n s ta

h ic h im a n d is th u

w

8 2 T io ta l s o la r

re

bec o

C

ity

m u st

ec

lip s e

be

v an

o

fA

is h in g ly

o n s id e r m a s s o u tflo w

sm a

1 1 19 9 9

st

\

u

in F ig u

a s sh o w n

m e s v i s ib le

v e lo c

E

F

s p e n a

k

m

M

F ig u

9 9 9

1

3

re

8 2 T hu

F d E sp e n a k ) (P h o to g r a p h b y r e

b a se

s a t th e

f th e

o

w

in d

re

g io n th e

ll

in th e

o u te r

la y e r s

o

f

s ta r o

a

f

a ss

m

M

,

u n

d e r th e

d w ith th e to ta l f th e s e la y e r s is n e g lig ib le c o m p a r e a s s 1J m p tio n th a t th e m a s s o i a s s u m p tio n o f s p h e r ic a l s y m m e tr y in tr o d u c e d in m a s s o f th e s ta r T h e b a s c h e n c lo s e d in a s p h e re o f C h a p te r İ s till h o ld s h e n c e th e flo w is r a d ia l T e m a s s an d s in c e it is a llo w e d to flo w c e v a r ia b le r a d iu s r c a n n o lo n g e r s e r v e a s s p a ,

,

,

th e c o n s e r v a tio n la w s a p p lie d to

be vo

a d a p te d to

lu m

e

m

a ss

e n c lo s e

V

flo w

d in

a

T h e e q u a tio n s o f m a s s , m C h a p te r 2 n o w h a v e to b e

M

C V

o n s id e r a s m a an

d V + dv

ll

m ass

c a se

it is

sph e re o o m en r e fo rm

a ss c o n se rv a

f

tu m

t io n

4 ìr r 2 d r )

,

r a d iu s r

an

u la te

v o lu m e e le m e n

(d v

fixed

In th is

d

e n ts in C h a p te r

s o m e tim e s c o n v e n

e n e r g y c o n s e r v a tio n

w

ie n t to

in d e p e n d e n t

a s th e

2

ill h a v e to a

e

q u a t io

d v b e tw

een

n

ra

o

f

d ii

co n

r

t in

an

d

r

,

ov er w

n

g iv e n o lo n g

te c

rs o ır ı

h an ge

d e ń v e d in U

se

E

u

d

le r

it y

+ d

r

,

o r v o lu m e s

h ic h p h y s ic a l r o e r tie s m a b e ta k e n p p y T h e m a s s c o n ta in e d in th i a s u n ifo r m s v o lu m e is d v O v e r a s m a ll p e ń o d p o f tim e ô t th e c h a n e in m a s s w ill b e g (p d v ) = d v p T h is c h a n g e w ill b e c a u s e d b y m a s s flo w in g in to a n d o u t o f th e v l o u m e e le m e n t L e t J b e th e a m o u n t o f m a s s th a t c r o s se s a s h e ri c a l s u r fa c e p ūm e o f r a d iu s r p e r u n it _

a

n

s p a c e v a r ia b le

th a t w e

u

o n se rv

s e c t io

d o p t th e

d

th e

t

e le m

c

Fo

r

s

d is ta l

In p a

,

Scanned by CamScanner

)7 8 (

p

rd

r

2

T

=

u

p d 1

M G

h dn a O

ecn e

p la id a r ( tn io

n ev

i

n

it

em

a ig y n a t

p lla

sw o

u

dra h n

oe

o ts r ń ( L y b d e n ia tb

f yb

, h t )e v ita v ń e d o sa i d e s s e rp x e e b t h

fo e ta r e

m e r a s tn e m e le s s a

fo

y tic o le v

ees

(

w a

e ht

fo

dn o ces

l

n a ir e lu

E

e

e v ita v ir e

h t( e c a p s

d la r o p m

iS )e v ita v ń e d

e gn a hc

fo

e ta r e

s ' n o tw e

N

m o rf

it a

n o

u

qe

em

,

e c n a ts id

la id a r h tiw

e

g n a h c to

n

iA

_

f o tn se o

d ,

)3 8 (

,

,

hw

sa e re

ht

f

ssa m

e

y tis n e d la c o le h t e r e h w

h t fo

ecne

g r e v id

e

,

sw o

eca

ps

h t( tn e m

n o

ita lu c la c

e

ht

,

sa

p

2

uo m a e

ht o t

s i ta

,

o m

fo

o

u tn e m

m

r r r4

qer

u tn e m

m

r e sn o c

s e r iu

no ssa m

fo

n o

ita u q e

e

ht

33 ı

e v itis o

p

e

O

,

o

a

)3 2

n o

n o itc e S

ita v r e s n o C

M

e re

o c

na

h t s id c ih w p s i J ta h t s e il m i h

h w y r e v e la u q e

su



O

=



ßy d a e ts r e d is n o c

ı la h s

a ts n it n i tn n llo f ta h w I

em

hT

sw o

ew

n o m re t

dn o

ces e

oc

e w ht e r h

v a

ta 十 三 3 ð pa

=

}

d + V (J

h t g n ik a t y tic o ı ev

c e

ht

V /t d n a 0

t )V (J

sa n w o n

{ å t im

k

o s la

il e h t

q ı ııo

w o

n

ıs s a m

c

hl

s

ıh T

,

es n o ita v r

rto c

ot

ı 1ı g n is s a p d

su

ra hT d

i

p siv d

=

,

sn o ı ta u

f d e su

J

=

h t tn a ts n

ita u q e y tiu n itn o

tb o e w

lô)v

)1 8 (

n o itc e r id

n ia

,

,

,

ro

on g i d e x if r e n o l ga e le s s a m n e v i

n

e

h t tc a f n i , s i e d is d n a h tfe l e t h

)2 8 (

ht

fo e g n a h c re t s e ititn a u q fo s m

a ta

su s n ia m e r

e

y tr e p o f p

ig n a r g a L

u

-

)5 5 7 1 n i r e u E

t

"

na

it a v

n o

ro "

f

de v ń e d

'

y so s sa m it tin u r e p r a ts e h t b t l

,

h t fo

u E s reı

tn a ts n o c

)4 8 (

n

lf y d a e ts

yJ tic uo lle v

u

g n iv o m a fo g i tn io p n e v i

et e

w on ecn

,

l ti

t sd a e

=

am s i tn e m e le s s

ig

nev



+

o

E

s ' r e lu



)5 8 (

n

qe

ita u

r a lu c itr a p n

ĉ ,

n o

,

?



a

u

Y d 1

n ııL

itr e p o r



山 p

)0 ðt

se

e ra

o c tn a ts n

t a /u

=

i

u

c 】 e hw

,

u

p

2

r r r4 =

1

o w tll ìie llT

Z 8

Scanned by CamScanner

) (t t ç ) s u o ll» n b ttn (U p £ a !sn i ç) p ・

p



« }iio u to tl u o ï ì!s o s tto ? t

d tu o ?

? lï ıp u u

? ?u ? q p u u Y Ju ı s u 3o Ķ ı ? R u l 13 111 o ? t l u ı ! u ¡? p ! S t s rłŝ ? 1 1u 1 1 ? 1 tu t ts s e o } ? l E u o s u a l s l ı ı q i

s u o !ł e n

b ? Jo ł? s n ı ıg

(n l ? s ? tp

s

Su !u m s s e

'

(ľ ç )

tl ľ 8 )

p I? !K

b?

u o tı en

ĵ

憾 1點 関 ı

01

P?1eJ?lU! ? q

四 图ı

0

q

s u lu tq

ļ p ru

?qr

(瓦뇨

J +



\p e

? tu

u t x rtu ? A ł ! 3 \ U O ? o u s l a i? tll

ŝ un



村十

p ? s s a ıd x ?



Ru ţ u ı puL





(E tu (0 1 8 ) u o u tıb p g 1tm ls u o ?

,

?q

sI

IV

=

a

d J J £? ? u !S t

.

U ıq o {U n u g ı

?A \

'

d

c

J u

T ıçq (6 8 ) u o p u n b a B u !K ld trlm

u

pu u

神 甲 ișu !ro

u

IN

\

q ] !ų \\ (8 8 ) p u » (L 8 ) s u o p » n b a

N qo

u o u ?w ! p

? \\

u!ppE p u n

\

l

N

? ltm s ? q ı& l e ll A lO U

Áq (1 8 ) u o p n n b g

t!ldţ ılnł

(gN 文嫘

叫 睥 q s !u 臥 邗 !s p 四 中リ? ı即

J e

u倒 u o s tı

网 印 ド 公 1s r g 呷

ı

uuo

,.

E ł ıı$

ıï O )

ißł? u

撫ou

乂ド 萄 S

j ? q r u ! u o !m





u ?su o )

ĵ

Scanned by CamScanner

8 2

rrla )

we

n In s u

h

3 tl

=

2

l se t fu ı

th e

ìm a ry ,

2

4 rr r p

u

M

=

d r

dT

Fequ

a t io n s

3K p

F

T

be

to

,

r,\đ

(8 ı2 )

ļa T 4

=

r u

is (r ) p (r ) T (r ) a n d F (r ) ,

,

(8 14 )

ą T 【C L

r

vJ ı

)

Į

+ F

(8 16 )

c o n s ta n t

_

(8 ]7 )

ĄJ r r

tw o c o n s ta n ts t w B e s id e s th e tio n o f th e tw fo r th e in te g r a

p

ı v e d fo

so

r

ĵ

d

an

t

c o n s ta n

+

c

n i

ı3 5

a tı o n ı

P

:

Ąa

ı o ıı ・q u

a rl

l

+ 3

U I

=

m

P

_

P

į.2 +

Ń

o

T hı

2

d itio

o m o re c o n

n s, o r

bo

u n

q u ir e d g r a v ity

u e s , a re re v a ı

d a ry

he q u a tio n s W e n o te th a t t l to th e r a d ia tio n e q u a tio n is d im in is h e d b y a fa c to r e q u a m o m e n tu m te rm in th e b id e s th e h E d d in g to n lim itin g flu x W e s h o u ld m e n tio n th a t e s flu x d iv id e d b y t e be h f c e e x e r te d b y th e r a d ia tio n p r e s s u r e th e r e m a y i ta tio n a l fo r c e a n d t e o r v a r g flo w , s u c h a s fr ic tio n p r o p o r tio n a l to i e d in g o r d ń v in g th e m a s s o th e r fo r c e s m p l lin e o r b a n d th a t tio n c a u s e d b y p h o to n s in a p a r tic u a r l v e lo c ity o r a c c e e r a tin u u m (b la c k b o d y ) r a d ia tio n are n o t p a r t o f th e c o n

d iffe

o

r e n tia

l

e

,

,

,

H is to r ic a l N Su n ,

w as

o

p ro p o

se

fa c t th a t

w e ll k n o w n

po in ts in th e

T he

te

,

co n ce

d by L

a n tis o la r

d w ig B ie r m

u

h e th e r

w

p t o f c o rp u

o

the n o v e l id e a m e t w

ith s tr o

d e lo f w

n o te w o r th y th a t

y p o s itiv e

U

v e lo c

n

g

,

l

o fm a ss u n aw

by

i? e o

itie s In d e e d H

a s ta r , a r r iv e

d

at

f th e ir im p lic a tio

,

o r

p a r tic le

in g

s s tr e a m

o u t o

f

,

o

,

ppo

w

,

ho

i

s tio n

so m u c

,

j

w a s r e e c te

w e

m

itie s d e s c r ib in g

,

n

1 9 5 1 to e x p la in th e p a p e r p u b lis h e d in il a lw a y s i a r d s o r a w a y fro m th e S u n , ts ta

hav e

h

s o th a t th e

a lr e a

dy

d

o u tw a r d

s o lu tio n s w o u

e rm a n n

th e s a m

e e

B

o n

qu a

n to th e n e w

flo

ld

w s

e n c o u n te r e

H

su

pap er

o r e v ie w e r s

d b y tw

i ınew th is m o d e l w a s n o t e n t r e y

a n d th e s a m e tr e a tm e n t a n

rre a g tiy e v e o c

a

d ia tio

d th is id e a a n d A fe w y e a r s la te r E u g e n e P a r k e r p u r s u e b e in te re s tin g to n o te th a t h a t h e te r m e d th e s o la r w iııd It m a y

C h a n d ra s e k h a r

on l

in

a c o m e t m o v e s to w

theAstn9ı T/ysical】 Oumatin 1 9 5 8 is a lso

ann

d ir e c tio n

de v e lo p e d th e fir s t m

o f th e e d it o r,

s c u ia r r a

b m itte d b y P a r k e r to

It to o k th . i.. ,

o w e v e r , th e

in

w a rd

"

d to g e t

It is tr u e th a t th e

a p p ly to

' "e

e

u

q u a tit

flo w

s cc

h d i, s tu d y in g th e p r o b le m o f s p { i 19 5 1 b u t tio n s a n d s o lu tio n s n

ly p o s tu la te d

,

e

fł e ctof

m a s s e e c ti(

j

Scanned by CamScanner

虹 ■ M

8

lo

a ss

fr o

ss

s ta r s

m

36 tio n io n e q u a n se rv a t th a t th e ın a s s c o

2

ı

r

d fo

an

id e a l g a s , th e

r an

ニニ 十

i下

+

d e r iv a tiv e

o

=

fo

in th e m o m e n tu m

r

e

q u a tio

n



re s s f th e g a s p

dr

as w r ittc n





d

p g lıs

y be

a

m (8 ı4 )

\



,

山!

P c lr

T dt

(8 15 )

u re a s

w e o

b ta in

11

1?

is

d it th a t is , ttu / r T h is e q u a tio n h a s a s in g u la r y f d o th e g a s h e rm a l s o u n d s p e e u is e q u a l to th e is o t u n

d e fin e d

w

he

n

o w th e fı

v e lo c

ity

,

(8 2 1)

Us =

d s id e o f E q u a tio n (8 0 ) v a n s h e s , u s ? th e le ft h a n p o in t w h e r e u k ts o n th e r ig h t h a n d O th e r e , th e te r m in s q u a r e b r a c e a n d s in c e o b v io u s ly u d itio n s e r v e s to d e te r m in e th e p o in t r c , w h e re s id e m u s t v a n is h a s w e ll T h is c o n h e r ic a l s u r fa c e fi k n o w n a s th e c r itic a l p o in t, w h ic h in o u r c a s e d e n e s a s p u u -

2

S in

s

l

f r a d iu

o

Ex

s Tc

8 I A

e r c is e

b y To ) fin d th e ,

th e

e sc a

pe

o rd e r

s su m

v e lo c

g a in

in g th e te m p e r a tu r e to b e

c ń tic a

ity

S o lu t io

8 3 ln

i

c e a t th e

l r a d iu

s rc

F in d th e

u n

ifo r m in th e flo w

r e la tio n

b e tw

een

' " o n ev

(d e n o te d

th e s o u n d s p e e d a n d

a t Tc

n s to

t h e w in d e u a t io n s q

t h e is o t h e

rm

a

ıc a s e

in s ig h t in to th e p r o p e r tie s o f s te lla r w in d s a v o id in g a t th e s a m e tim e n u m e r ic a l c o m p lic a tio n s w e n o w c o n s id e r th e s im p le s t , fo r m o f th e w in d e q u a tio n s fo r w h ic h th e s o lu tio n s c a n b e r e la tiv e ly e a s ily d e s c r ib e d T h e c o n c lu s io n s i ll w b e q u a lita tiv e l y v a lid fo r m o r e c o m p lic a te d to

so m e

,

c a se s

W a ra ra

a ssu m e a u n

e

d iu

d ia tio

s r o , th u s n

fı ux

ifo r m

te m

p e r a tu r e fo r a n o u t e r r e g io n o f g a n is o th e r m a l s te lt a r w in d I n th is b y E q u a tio n 8 1 ( 7 ) F o r a n id e a lga s

d e s c r ib in

v a n is h e s ,

a

s ta r s ta r tin

c a se

,

g

at

he s tr ic tly , t

,

2 U : S

TZ T =

=



c o n s ta n t

Scanned by CamScanner

8 3

so ı u tı o n

p ¢e

e x

**

ı

to th ı w ı n d

T in ıen11

r

o

o ce s ı « du

Ąn

ņ

Tı tc

U.

ı

r

u ılt ı o n



p u

th ¢

ï

sc t n

=

l

ı n d « u a tk īm ł

w

13

ca le

(8 1 4 { 8 17 )

c «M s ta m

(8 2 2 )

(8 2 3 ) s o lv e

m lw

d fo

r u

(r ) a n d p (r )

w

h e re G M

Tc =

th e

s

Equ a n o u (r

u

p o in t a t w h ic h th e n (8 2 3 ) is in d e p e n d e n

) l iv e n

i io n a an a dd t Th a t

m ıiq u e

v s rc ıl s o

It is

l

a

bo

u n

d a ry

c o n s ta n t

is

ı u tio

co n v e n

Th e r e n ex

r ig

to

d itio

c o n

sa

y p is o n ly

ht ha n d

f th c

o n e

s id e

e

d im

u

(r o ) =

Po W

e

sha

ı ın o

F

uo

o r e

v a lu e

y

o

,



an

s o

f w h ic h E q u a tio

n

w

d

m ay

T h e fu ı ıs o lu tio sho w

M

fo

he

v am

be n

th a t th is s o

q u iv a le n tly

so

ve

d

re q ire s lu tio n 1

h ic h

r w

y

(8 2 5



U

(8 2 3 ) b e c o m

2

U

d

ıC te r m

uo

(8 2 3 ) an

e n s io n le s s v a r ia b ı es

r

X

f E q u a tio n f th e s e t

,

sa

is ts

ie n t to d e fin

o

o th e r e u a ti o n o q

n

(r o ) =

(8 2 4 1

2u

s

es

u e s o f y ; th e v a r io u s c la s s e s T h e fa m ily o f s o lu tio n s is d e te r m in e d b y th e in itia l v a ı h W th e o u te r la y e r o f th e s ta r t t 3 e a m 8 a s s u e i o f s o lu tio n s a r e s h o w n in F g u r e d to th e o c c u r s (o r th e w in d is g e n e r a te d ) is tig h tly b o u n w h e re th e m a s s flo w ,

s ta r, w

fo

<

fc

h ic h

H

m e a n s th a t a t th e w e

en ce

s ta r t th e

b a s e f o o f th is re g io n liesc » u . » in te g r a tio n o f E q u a tio n (8 2 6 ) a t

oo an

d th e re fo

so m e x

fy ı

<

he s

1

re

an

d

u n ity

i e a se s p o s itiv e a n d y n c r d th u s y (x ) is a m u lti 1 n a b e fo re x d o e s th e n x (y ) h a s a m a x im u m a t y ly i l E qu a ı 2 o f F ig u r e 8 3 w h ic h is u n p h y s c a v alu e d fu n c tio n s h o w n in r e g io n f th e fig u r e If o n th e o th e r h a n d x u n p h s ic a l a r e th e s o lu tio n s in r e g io n 4 o y 1 w h ic h m e i\n s m at x i h e n y (x ) h a s a m a x m u re a c h e s u n it y b e f e y do e s, t d d e c r e a s e th e r e a fte r A s s h Q w n tha t th e v e lo c it w ill f e a c h a m a x im u m v a lu e a n y h is to b e p h y s ic a lly possibı by the s o lu tio n s in r e io n 1 o f F ig u r e 8 3 F o r t g h e flo w in g m o s s w h ic h n ta y

罗< 1 T h e d e r iv a tiv

e

d y /d x is th u

s

,

re a c

,

,

x e rt c d o n t d ir e c te d p f e s s u re m u s t b e e d b \n n n y o p de rs o f m a g n itu e be s h o w n to s u r a s s th e in te r s te lla r g a s p r e s s u re y p u iï ı g in F ig u r e 8 3 th a t u tio n s iıp p e ł H e n c e this s o lu tio n is u n h y s ic a l a s w e ll s o ı p h e w in d a s th o s e o r re g io n th e b u s e o f t c o rr e s l o c itie s a t e v e l r l a d o i T h e o n ly g p n to in fin te y v e lo c itie s th e t» v a n is h in g r o t 3 a re i n e ì n i e n c o n flic t w ith th e r e q u r h th a t X a n d y s ta r tin g a t ic h u o is s u c h w r v ja ◆ b f t h e s o lu tio n th e r e fo re is t a

an

in w

,

a rd

,

,

,

,

,

Scanned by CamScanner

ı 38

M

8

Fig u

re

8 3 T he

T he

u n

iq u e

lo

v a lu e s

w

p o in t (f c iL

so

,

u

v ia

n o m i a liz e

b le

Re a c s

)

h

T hu

s o lu tio n

d is o th e r m

a ss

a

ı o s s fr o

l w in d

s ta r s

s o lu tio n s

T he

e m a rk s c ir c ı

th e s o n ic p o in t

is h ig h lig h te d in b o ld

u n ity s im u lta n e o u s ly , w

in d is ttu

s th e w

m

s o ııic : s u ıı

a p p ly in

In te g r a tin g E q u a tio n (8 2 6 ) a n d lu tio n fo r u (r ) a s th e r o o t o f

In y



h ic h

=

4 ln

m e a n s th a t u

b s o n ic b e lo w g th is

4 x

+

co n

3

(r ) p a s s e s th r o u g h

rc a n

d itio

n

,

d

su

w e o

a bo v e

p e r s o n ic

b ta in th e

th e

un

iq u e

(8 2 7 )

,

X

ow p ta b le v e lo c ity a t th e b a s e r o o f th e is o th e r m a l fı re g io n fo r a g iv e n te m p e r a tu r e o f th is r e g io n a n d a g iv e n s te lla r m a s s W ith it, th e 4 rr r p o u o (T M ) T h e r e s u ltin g d e n s ity p r o file m a s s lo s s r a te is o b ta in e d a s Jii _ w

h ic h d e lirze s th e

o n

ly

ac ce

ŝ

an

d

( ) in c r e a s e s

s in c e u r

w

ith

2

r

,

th e

,

d e n s ity d e c r e a s e s

w

ith

r a d ia

l d is ta n c e

o re iï ı

p ly th a n r In th is s im p le e x a m p le th e e n e r g y c o n s e r v a ti d is o n r e q u ir e m e n t (8 1 6 ) w a s d c a r d e d b e in g r e p la c e d b y th e c o n d itio n T r ( ) = c o n s ta n t a n d F = o w a s o b ta in e fr o m E q u a tio n (8 17 ) A lte r n a tiv e ly , w e m a d is b ta in c a r d E q u a tio n (8 1 7 ) a n d o y s te e

,

,

,

Scanned by CamScanner

8 4

th e

h e a t flu

x a s th e s o

lu tio

n

o

M [ģ(u (r )2 oĥ

in d iffe r e n

t ia l fo

rm

,

u

M

a n

f E q u a tio

lo

n

n

(8 16 )

e s tı m a

,

c =c

(r ) ) +

h ic h

w

2

c o n s ta n t

ı3 9

t* ı

ı+ F

m a

y be

w r itte n a s

c o n s ta n

=

t,

as

d F

d

ır

ģÀiı u(

=

2

)

r

U . ..

2

(8 2 9 )

(r ) I

f h fl A t th e b a s e o t e o w d e s c » u o a n d th c te r m in b r a c k e ts is n e g a tiv e T h is m e a n s d e r to m a in ta in a n is o th e r m a l w i th a t in o r n d e n e rg y m u s t b e p u m p e d in to th e h A t w e a s i l n r o n c r e a s e s u in c r e y g flo w a a s e s w h ile s d e c r e a s e s h e n c e th is e sc i t ı l n o o n ı l i o c i m a y n c r e a s e (a n d w iı te r m w l e v e n tu a ı ly b e c o m e p o s itiv e ) T h u s if d a s e x d t n c e F a O e _ p , F + f ( T )d T /d , w h e r e f is s o m e fu n c tio n o f T l i h a c a s e m r s t e n t l o r i i e a s tic u n le s s a d r iv in th e s o g fo r c e o p e r a te s th a t p u s h e s th e k i w d i n r o N o o b n t d e v e r th e le s s d e ta ile d n g y w in u m e r ic a l a n d a n a ı y tic a l s tu d ie s b l d i h r o e m s n w h o w h t i e i t a t s n o t s o fa r fr o m r e a lit p oft y ,

,

,

,

,

,

.

,

,

,

Ex

e r c is e

A p o ly tr o p ic

8 2

w

in d is d e ń n e d b y th e P

w

h e re K

is

a c o n s ta n t

H

K pv

_

a ssu m

p tio

n

,

e n c e

P K p

1

V



(a ) S h o w

th a t th e s o lu tio

th a t o b ta in e d

fo

n

to th e w in d v e lo

is o th e r m

r a n

a

l w in d

,

w

c

ity

e

q u a tio

ith th e is o th e r m

n

h a s th e

al so u n

d

sam e sp e e

d

fo re

rm

a s

p la c e d

by

11s

(b ) S h o w is

th a t fo r y

-

5 /3 ,

o n e o

=

b ta in

s

F

-

c o n s ta n

t, w h ic h m e a n s th a t th e

flo

w

a d ia b a tic

Scanned by CamScanner

ı4 0

M

8



s

p c c tr tıın

lc m p c

r iï tu m

,

W ith k n o TC

bc

m ny

W ie n

w o m ny u e

fr o

Iu w ( ı4 ) 1o

s

s ta r s

m

till e s tim a te

b tı\in

o

Fo

r th c c

ľ fe c tiv

4000 K

s l\y ,

y n

'

o ss ars ı

M

lłu n d T

,

e

th c s o u n d s p e e d U s is k n o w n a n d th e c r itic a ı ra d i

,

c n lc u ln tc

d b y E q u tttio n (8 2 4 ) W d im c n s io n ı tio n y (x iı c s s ıe ı

th u s h łw c th e

e

so

ua

lu tio

u (p

) by F E q u a tio n 8 ( 27 ) S in c e iii = 4 tr r 2 u i s c o n s ta n t it m a y b c e v a lu a te d a t a n y p o in t o F th e Ħo p w To d o so ho w e v e r w c n e e d to k n o w th e d e n s ity a t th a t p o in t In S e c tio n 3 7 w c h a v e e n c o u n te re d th e c o n c e t o F o tic a l U /ı a n d i ep ı p p ts ľ c lu tio n to th c la r r a d iu s th e ıa d iu s o f th e p h o to s p h e r e w h e r e m o s t s tc ı o f th e Ķ tc llu ı ılld ia tio n is e m itte d in to s p a c e T h u s th e r e la tio n , d o n o rm n

liz in g th c

) th c ,

so ı u tio n

n

o

,

,

,

,

,

,

u se

P to nn Ý a

D

Į

-

' "

\

_

ils th c

dcinition o F th c p h o to s p h e r ic r a d iu s R ïilc is g iv o n b E u a tio n 8 2 8 i h f y q ( ) n t e o rm p

d 2

<

s

3 1x )r th c

p e r s o n ic fu n c tio n

,

-

w

ill s u p p ly p (R ) T h e d e n i s ty C r s , w h e r e C is a c o n s ta nt

,

g io n (fo r m o s t o f th e s u b s o n ic r e g io n 2 < , < 4 ) T h c o a c it lc is a p o f te m p e l a tu r e a n d d e n s it y i v e n y, g g e n e r a lly b y a w o l th c fo r m (3 6 3 ) a n d s in c e th Po w c I ı e te m p e r a tu r e is c o n s ta n t a n d k now n b e c o m e s a fu n c tio n o f d e n s it y o n ly W e th u s o b ta in <

su

re

,

K oT

w

h e re

o

p a c ity

a

=

jb

0 fo

"

ıt c

r

5

1

r e le c tıo n s c a tte r in

g , a n d (ı _ 1, b _ ı a w (3 6 5 ) T h e in te r a l in E u g q a tio n (8 3 0 ) m a y b e _

«

[T

,

p (R

)]p (R )R

H

7 /2 fo

permed

to a M c to r o f o ıd e r u n it ) fro m w h ic h p (R ) is d y , e r iv e d ve ı o c ity a t R is g iv e n b y u - u. fo r x _ R /r a n d th u M s c at R

m

o

F

su c

h

s im

p le

r a tio n s : a m a in

e v a lu a tio n s a r e

se

th e K r a m to

e rs

y ie ld

ı

(u p

E x a m p le s s te lla r c o n fig u

r

sho w n

fo

r

m a

T he

g iv e n T

y be

e v a lu a te d

in F ig u r e 8 4 fo

r s e v e ra l

q u e n c e s ta r o

f s o la r m a s s a m u h c m o re m a s s iv e , q u e n c e s ta r, a n d a r e d g ia n t o f s o la r m a s s W e n o te th a t th e a c tu a l m e a s u r e d v a lu e s o f th c s o ı a r w in d , A i . 2 3 × 10 " M 1 r an d T H o y 1 5 × 10 6 K a re n o t v e r y M r fr o m th e c u r v e o f o ib s s l e s o lu tio n s c p o n s id e r in , g th e v e ry w id e ıa iıg e o r v a r ia tio n o f s tc lla i IT \a s s l o s s r a te s T h e s ig n ific a n t r e s u lt is th a t d u r in g its litiıne a s a m a in s e q u e n c e s ta r th e s u n s h o u ld l , o s e a n in s i n ific a n t a m o u n t o f g rn a Į e r ia l p a r tic le s , a ı rı o u n tin g to le s s th a n a th o u s a n d h t o f its m a s s In fa c t th e w in d t11 a s s lo s s r a te d u ıin g th e m a in s e q u e n c e s t a g e is lo w e r th a n th e m te o f l m a s s o « s d u c to c o n v e r s io n o l' ı Tì a s s in to th e ener 2 g y ıa d ia te d a w a y b y th e S u n 6 7 × ı ıo c o 1 ıM o y r ı m a in

se

,

,



,

.

Scanned by CamScanner

8 4

R

5

a sr

ı o ıs

14 ı

e s t im a t e s

T

1

ı

N

e

gi an

d

wi nd

t

-

一 (



あ ー





W in d fro





30 M

a

m

m a in s e q u e

.

n c e s ta r



10 S o la r w in d

Lo g

Fig u

8 4 E

re

s t im a te

d

m ass

o e d v a lu e s to th e m e a s u r

Ex

e r c is e

ro u

aw

w

to

in d

o r a te o r d e r s

2 o f 30

a

,

l

he n c e o

m

is le a d

n

u s

la r

in d

so

f

m a

w

is b o

in to

u n

u n

n o

o o fd e r

d

A

r

a ss

f its

,

f s o la r

a tin

lsym

Fo r

m a sse s

ia b le

ro g th e p

m e tr y

o

th e r a te

th e

ex am

ss b u t th e m a

p p re c

o te th e

p o in t c o

th th e n if a t E a r io s s tr o m th e s u ,

m a ss

(7 4 1)

in d s N

a lw

is o th e r m

h e r ic a s su m e sp

a ll a to lo s e

d e r e s th n

u

[T (K )]

th a n d e h ig h e r g n itu

r e la tio n

g to

f th e

3

cm

t fr a c tio s ig n iń c a n

a c c o r d in

M ghe r fu tu r e S u

s s r a te s

fo

t h e r a te o f m 8 3 E s tim a te

r r tic le s p e g h ly 7 p a he S u n a y fro m t

lo s e

lo

f th e

a

5

4

lo

S im ila r ly

ex

i n c o n v e rs o

o

p le

o

s s r a te

,

to am o un

b le m

f

m e a s u re

in d

fo f th e

w

r r e s p o n d u rg

d

p a n s io n

f

m a ss

f F ig u r e 8 4

,

is h ig h e r b y

in to

th e tim e

a

fa c to r

d in g th e d g ia n t in c lu th e r e d g ia n t i a ss du r n g

a fe

fm

he A lth o u g h t

m u ltip le

s o lu tio n

Scanned by CamScanner

u tio n a n d th e tr a n s o n ic d so ı p ro p iq u e n e s s o ı th c v ia b le w in t a o m h n u o c m m w id e r h d is ta n c e a re c o e r ly o r th c v e lo c it a rid y v a r ia lio n w it i l b em s fa r fr o m o f l s s o s s a p m b e in le s s r e s tr ic liv c ra n g e o f c o n d itio n s th e g d d t k e l v o e s s o l b o e o i d n t t e a o e t r y e s r t a i s s o lv e d c o m e lla r u t o n e x c a se s a n d so ı pı b d e r e o a n h h t e t l r e i a y u c t s ; y r co e w in d s in g e n e r a l a n d th e s o la r w in d in p a p of c la s s e s ,

th e

u n

,

T he

fo

u

d i ti h fl p le c a s e s th a t w e h a v e a d d r e s s e d h a v e a v o id e d t e r a a o n o w W e h a v e n d th a t e n e r g y m u s t b e c o n tin u a lly s u p p lie d in o r d e r to m a in ta in o r a c c e le r a t e s im

th e w in d o u t o f th e g r a v ita tio n a l p o te n tia l w e ll o

f th e

s ta r

T h is is th e

c ru x o

f th e

p r o b le m

E q u a tio n (8 15 ) s h o w s th a t th e v e lo c ity w o u ld e a s ily in c r e a s e w ith d is ta n c e w e r e th e s e c o n d te ľ m o n th e r ig h t h a n d s id e v a n is h in g ly s m a ll T h is te r m v a n is h e s w h e n th e r a d ia tio n flu x a p p r o a c h e s th e E d d in g to n lim itin g flu x th a t i

s,

,

w

h e n th e

T hu

s, a

it is

w e

ra

lth o

u

d ia tio

n

g h th e

p re s s u re s te

lla r

be c o

m es

do

m

in

,

O in E q u a tio n (5 4 2 ) Ř t y e t fu lly s o lv e d th e o r e tic a ll y

a n t, o r

in d p h e n o m e n o n is n o a s s lo s s is d r iv e n b y th e in c r e a s in g l d o m in a n t r a d ia ti y on in o s ity a p p r o a c h e s th e E d d in g to n lim it T h e im o r ta n c e p w

,

ll r e c o g n iz e d th a t m r e a s th e s te lla 】 lu m

p re s s u o f r a d ia tio ,

p r e s s u r e fo r th e e je c tio n o f m a tte r b y n o v a e w a s fir s t a c k n o w ı e d ge d b y W illia m M c c r e a a s e a r ly a s 19 3 7 in th e c o n te x t o f n o v a o u tb u r s ts w h ic h w e s h a ll e n c o u n te r in C h a te r 1 1 T h e id e a w a s la te r p u r s u e d in a v a s t n u m b e r p o f a n a ly tic a l a n d n u m e r ic a l s tu d ie s o f s te a d y w in d s H o w e v e r it is n o t a lw a y s n e c e s s a r y fo r th e b u lk lu m in o s it y to a p p r o a c h c r itic a l v a lu e a n d th u s d is r u p t h y d r o s ta tic e q u ilib r iu m (s e e S e c tio n 5 5 R d i i ) a a t o n p r e s s u r e is c a p a b le o f a c c e l i e r a t n g m a te r ia l o u t o f th e s te lla r g r a v ita tio n a l p o te n tia l w e ll e v e n fo r a n o v e r a ll s ta te o f h y d r o s ta tic e u ilib r iu m b e c a u s e m a te r ia l a r tic l q e s v a r y w id e ly in th e ir p b i l i ty to a b s o r b r a d ia tio n W h ile th e i t a n e r a c tio n o f a p ? tic le w ith a g r a v ita tio n a l fie ld d e p e n d s s o le ly o n th e a r tic le s m a s s its in te r a ti p c o n w ith a r a d ia tio n fie ld d e p e n d s o n its c o m p o s itio n s tr u c tu r e i s z e a n d d e n s it y , a s w e ll a s o n th e r a d ia tio n w a v e le n g th T h u s if in th e o u t e r la y e r s o f a s t a r th e r e a r e s u c h fe p a r tic le s th a t a i e x c e p t o n a lly a b s o r b e n t a t th e l e a d in g w a v e le d n g th o f th e p h o to n s a s d e te w w n e b y th e te m p e r a tu r e th e n fo r th e s e p a r tic le s th e r a d ia tio n u st p r e s s u r e m ig h t j o v e rc o m e g r a v ity In o th e r w o r d s th e h i h , g o p a c ity r a th e r th a n th e p h o to n flu x W O u ld c a u s e K F /4 7r c G M in E q u a tio n 8 1 5 ( ) to r e a c h o r e x c e e d u n ity T h e f e s u lt w o u ld b e a n o u tw a r d a c c e le r a tio n le a d in g to a m a s s o u tflo w o f s u c h a r tic le s a n d p o th e ıs e n tr a in e d b y th e m B1D y a Lh e u n s tic a r g u m e n t a t a m a s s lo s th e s r a te M d r i v e n b y r a d ia tio n r e s s u fe p m a s s Aåt e je c te d d u r in g a tim e in te r v a l ô t a c a q u ir e s e s c a p e v e lo c ity b y a b s o f b in g n

,

,

,

,

,

'

,

,

,

,

,

,

,

Scanned by CamScanner

8 S

fra c tio

sa

n

y qb

'

b s titu tin g

a fld s u

f th e

o

,

m

o m

E m p ir ı c a ıs o ı u tı o n

e n tu m

c a r r ie

d b y th e

ra

s

ı4 3

d ia tio

(L /c )ó t c

n

o n se

e n tly ,

qu

C

U

2G M

=

.

/R

d

an

,

¢ = ¢/2 '

,

w e m a y w r ite

(¢ ) U

T hu s

tine

m

lo

a ss

r a te

ss

p ir ic a l fo r m ke y th e r a d ia tio n fie ld to m to e m

i w av e s o r a c o u st c c u lt to

p e r tie s o

f s ta r s

h p o in t in t e

n ex t c

p ro

o f o b s e r v a tio

Ex

th e th e r m a

fo

r m

b e tw

a ss

w

E q u a tio an

d

ho

n

a

hav d

e

th e d im e n s io n of L R

to e x

y be

p re s s

À

i

T he

T h e d im

e n s io n

se m ,

a ss

lo

h e re

w

/G

M

an

d th is is th e

tr a n s fe r o f m o m e n t u m

fr o m li t c d a e in v o lv in g tu r b u le n c e s h o c k p le s s c o e f fic ie n t in a r e n th e s e s is d ifri p

v e ry c o m

,

tic a lly , b u t it m a y b e o b ta in

e s c a le o

l tim

lo

s tim

(a ) E ss

r a te

at a

8 S

e r c is e

a ss m

h a p te r

th a t, u s u a tı y, T m

Ex

u se

o re

th e m a s s

een

la e

u

(8 3 1)

s s r a te s c a n

be

,

d fr o

e

m e a s u re

w e c o n s id e r n u m e

th e o b s e r v e d g lo b a ı

m

e sh a

d W

ń c a l s te lla r

m

ll r e t u r n to th is

d e ls in th e lig h t

o

n s

8 4

e r c is e

u st

e n e rg y

la te th e

c a lc u

m

lo

ss

ļ <

A

(8 3 1 ):

s su m

M

Tn

a te

f

th e m a s s

is

s s tim e s c a le

(b ) S h o w

a s ta r

M

lo

a

v e ry

sm a

Tm

,

fen

th a t th e r a te

o

ll fr a c tio

f L

tim e s c a le a n d th e n u

n

o

an

b

d

co m

e rg y su

p a r e it

p p ly

(c ) F in d th e

c le a r tim e s c a le o

f th e

re

w

ith

q u ir e d

r e la tio n

s ta r a n

d

e tr iz e

d

sh o w

u c

t in g th a t th e m a s s lo s s r a e th a t fo r m sho w o ( L R /G M

m ay a in

be para m

se

qu

en ce

s ta r s

M

as

in L

a

,

e v a lu a te c e

Scanned by CamScanner

t io n o f s t a r s

e v o lu

The

d e t a ile d p ic t u

T h is A

n

c

h a p te r d iffe r s fr o

a cc o u n t w

n u m e

ńc al

qu a ū o s tu d iæ

e

n s o

o

d e s fo

iı ıb e

c a lc u

ı a tio

f s ta te

f s te lla r

p r e v io u g iv e n o f th e m

n s

s o n es e v o lu

s o lu tio n s o

re

b y b e in g d e s c r ip tiv e ūo

n

o

f s ta r s

as

it

se t o

p a c ity c o e fric ie n ts a n d n u e v o lu tio n d a te b a c k to th e e a r l y 19 6 0 s ,

em

f e q u a tio n s c le a r r e a c tio n

f th e

o

a

-

,

w

r a th e r th a n a n a

rg e s fr o m (2 5 4 ) w ith e

,

Such

r a te s

a c c u r a te

n u m e r ic a

h e n th e fir s t

r th is ta s k w e r e

ly tic a l fu ll s c a le l

p u te r f s te lla r

co m

d e v e lo p e d T h e fir s t to p r o g r a ]n th e e v o lu tio n o m o o n a n e le c tr o n ic c o m p u te r w e r e B r ia n H a s e lg r o v e a n d H o y le in 19 5 6 T h e y a d o p te d a m e th o d o f d ir e c t n u m e ń c a l in te g r a tio n o f th e e q u a tio n s a n d lia in g to o u te r b o u n d a r y c o n d itio n s A m u c h b e tte r s u ite d n u m e r ic a l r o c e d u r e p fo r th e tw o b o u n d a r y v a lu e n a tu r e o f th e s t ll e a r s tr u c t u r e e u a tio n s (essentidly q a æ la x tıı io n m e tlto d ) w a s s o o n r o o s e d b L i o p p H u s e n y y e y ; it is o fte n r e fe r re d to a s tfıe H e n y e y ıTıe th o d a n d it h a s b e e n a d o p te d b y m o s t s te lla r e v o lu tio n c o d e s to th is ? y A m o n g th e n u m e r o u s c a l l c u a tio n s p e r fo r m e d b y m a n y a s tr o p h y s ic is ts a lıo v e r th e w o r ld s in c e th e e a r l 1 9 6 0 s th e lio n ' s s h a r e b l y e o n g s to Ic k o Ib e n Jr T h e d e ta ile d r e s u lts o f s u c h c o m u t i t a o n s c a n n o t a lw p a y s b e a n tic i a te d o n th e p b a s is fu n d a m e n ta l p r in c i le s a n d s i p m p le in tu itiv e e x p la n a tio n s c a n n o t a lw a y s b e o ffe re d W e m u s t a c c e t th e f a c t th a t b e in p g h ig h ly n o n lin e a r th e e v o ı u tio n e q u a tio n s m a y b e e x e c te d t h o p a v e q u ite c o m l i p c a te d s o lu tio n s A s th e c o m p le te s o lu tio n s o f h t e e v o lu tio n e q u a tio n s r p r o v id e in p a r tic u la r Tı o b s e r v a b le s u r fa c e p r o p e r tie s o f s ta r s w e s h a ll f o c u s in th is c h a p te r Lï ı o r e th a n w e h a v e p re v io u s ly d o n e o n th e c , o m p a r is o n o f th e o r e tic a l re su ı ts w ith o b s e r v a tio n s T h e u ltim a te te s t to th e s te ll a r e v o lu tio n th e o r i y s th e u n d e r s ta n d in o f th e R d ia g r a m in a ll i[s a s e c ts d g ( e g c r ib e d b r ie n i p n C h a te r 1 y p ) W e th u s e x p e c t to lin rl s ta r s in th e H R d ia r g a m w h e re th e o r e tic a l ı ïı o d e ls p r e d ic t th e m to b e M o re o v e r th e b a s ic s ta tis tic a l r i i p n c pı e m e n tio n e d in C h i\ te r 1 p s h o u ld a o n ge r a n e v o lu tio n a r p p ly : th e ı y p h a s e o f a n in d iv id u a ıs ta r th e la r e r th to b e o b s e r v e d in th a t a r ti e n u m b e r o f s ta r s g eu ı p a r p ha se A d e ta ile d c o m p a r is o n b e tw e e n th e o r e tic a ı p r e d ic tio n s a n d o b s e r v a tio n s is th u s p o s s ib le fo r lo n c o r e h y d r o g e n b u r n in g e v o lu tio n a r y p h a s e s s u c h a s g a n d to a le s s e r e x te n t c o r e h e liu m burning Ħ o c e e d in g c o

d e ls

,

,

,

,

,

,

,

,

,

,

,

,

na a

Scanned by CamScanner

9 ı T h e H a ya s h ı zo

to a

dv a n c e

d

fu

n u c le a r

k w ea

lu tio

ev o

e

n a ry

l (fıo

m

s ta

ge s

n e a n

,

d th e p re m

n c u tr in o em

nı n so

is s io

n

q u e n ço p ha eo

hO

ı 4

th c d e n s e , h o t c o ıo # o l

m

c a rb o n

to ir o n th e a m o unt o l e n e l g y rc ı i t v e ly s m e a «o p c r u n it l a l) is ı i u c k ly c o q n su m e d c o f b a b ility o d e te c tin g s ta r s d u r i n s e q u e n tly o r n g th e s e b the p l ic f c v o l i u t o n i a ı h l l n h w t o fo e co m y p a s e s is ı g o w p le tio n o f n u c le a r c o o lin g in r e la tiv e l lo burning w m r o a s l c e b l y w s s o s u rs , s t s u a c o o lin p g s ta r s w h ite d w a F is a g a in ıs b e c o m e r a d tı h in te ı a lly ı g d m o r e d iffic u lt to d e te c t ass o ïı

m a te r ia

f burnt

l is

,

r e la

,

,

,

an

T h e H a ya s h i z o

9 I

n e

a n

d th e p re

m a in

se

qu

pha se

e n ce

C h a p te r 7 d e a lt w ith th e e v o lu tio n o f s ta r s b y fo llo w in g th e a th o f th e s te lla r p th e (lo g T lo g p ) p la n e T h e c e n tr e in p r e s e n t c h a p te r fo c u s in g o n th e s te lla ı fo llo w s e v o lu tio n a r y tr a c k s in th e (lo g T fr lo L ) la n e th e th e o l is ts s u r fa c e g c p In th e (lo g T lo g p ) p la n e w e fo u n d z o n e s o f in s ta b ilit w h ic h H R d ia g r a m y ,

,

'

,

,

,

,

c o n s tr a in e

ha v e

d th e

ev o

(lo g T e ff lo g L ) p la n e h a s its ,

Jo rb id d e n w

ho

zo n e a n

T h e fo r b id d e n

fu lly C

co n v ec

tiv

o n s id e r a

zo n e

n a ry

o w n

'

p a th s o f s ta r s W e s h a ll n o w fo r b id d e n z o n e ' It is k n o w n

sho w

th a t th e

a s th e

ya sh i H a y a s h i,

H

a

y a s h i tr a c k , a fte r C h u s h ir o ity in th e e a r ly 19 6 0 s p o in t o u t a n d s tu d y th is ty p e o f in s ta b iı ' h ti l e v o lu tio n o f a s b o u n d a r y is d e te r m in e d b y th e h y p o t e c a

d its b o

th e ū r s t to

w as

,

lu tio

u n

d a ry

a s th e

H

a

e s ta r

c o n v e c tiv e

f u lly

s ta r o

f

m a ss

M

,

w

h e re

c o n v e c tio n

re a c

he s

ou t

6 w e s h o w e d th a t in a c o n v e c tiv e z o n e lla r p h o to s p h e r e In S e c tio n 6 d e v e n a s lig h t l s e ly a d ia b a tic O n th e o n e h a n th e te m p e r a tu r e g r a d ie n t is v e r y c o h te m p e r a tu r e s w h ic h r e d u c e t e to h ig h h e a t flu x e s u p e r a d ia b a tic ity g iv e s r is e n d r e d u c e s th e i n c he s c o n v e c t o n a d s u b a d ia b a tic ity q u e g ra d ie n t O n th e o th e r h a n if c o n v e c tio n e n s T h e re fo r e r a d ie n t s te e p h e a t flu x ; a s a r e s u lt th e te m p e r a tu r e g l tin g to th e a d ia b a tic N e g e c s v e r y c lo s e i d e n t r e m a in a r e r t u a r i e e g h ll m a s s M p r s s ts t e te m p e c t to th e s te a r h e r e w ith re s p s t o h o p h th e m a s s a n d th ic k n e s s o f t e p in te r io r o f a fu lly d e s c r ip tio n fo r th e s im p le r e v a y t 1 a n d r a d iu s R w e m ay ado p 1) (h d ex n i n f o e c o n v e c tiv e s ta r a s a p o ly tr o p (9 1) " ł p = K p R b y E q u a tio n (5 2 3 ) to M a n d e la te d r i s K (s e e S e c tio n 5 3 ) T h e c o e ffic ie n t (9 2 ) 3 " ıı ' R ıı M " G C .. =

to th e s te

,

,

,

,

,

,

,

,

K

f o u n da y t th e re h h t s o o p p b o u n d a ry in g th is c ro ss x l u f th e e n e r g y

r a d ia ti v e r a d ia t e

w

ill d e p e n d

on

th e

elge n

Scanned by CamScanner

ı4 6

d e n s ity Te m p e in tu

e v o lu

The

9

re a n

d p IE

t io n o

f s ta

rs

s s u ıe a c r o s s

it IĄy d ro s ta tic

ib r lu q u iı

ı n rc c ı u ir c #

(9 3 )

l i2

P







,

d in te g ra tin g fr o m R w h e ıt th e p r e s s u r e is P n b ta in v a n is h e s o r fo r s im p lic iry to in fin ity , w e o

an

c

re

G M

p

d

c tu ı o d pı d e ta ı

a

-

,

to th e

,

le r c lh c p o in t w ı p rc # # tıru

,

ffe c tiv e te m p e ra tu r e o f th c s ta r s a tis ı y in g 1 = ' o p tic a l d e p th o f th e p h o to s p h e r e is o i th c o rd e r o l u n ity (s e c u tio n o l th c r a d ia tiv 3 7 ) th e e x a c t v a lu e d e p e n d in g o n th e ty p e o f s o ı c l h Ř h 1 _ t e s w re e q u a tio n T h u s d e i o r ¢ a c l « p tlı p p , y aver

T h e te m p e r a tu r e 4 Jr R 2 c r Tr T h e S e c tio

n

ged

pow c ru d e

A

th e p h o to s p h e r e

o v er

a

er a

is th e

R

e

,

,

tr a n s fe r a

at

la w

p p ro

fu r th e r

in d e n s ity p R x im a tio n ,

r e la tio n

T a k in g k to b e th e an

d te m p e r a tu

re

p a c ily a t R a n d e x p r e s s in g il a s o f th e fo r m (3 6 3 ) w c h a v e a s il

o

T e lT

d e n s ity

,

,

d te m p e r a tu r e a t R is ro v id e d p fo r w h ic h w e a d o p t th e s iıT ı le s t c a s e o f a n id e a l g a s p a n d n e g lig ib le r a d ia tio n p r e s s u r e E q u a tio n (3 2 8 ) P R - (71 / I ) T I p R « W c th u s a r r iv e a t a s e t o f fo u r e u a tio n s ll i a h t n f q e o r m o f r o d u c ts o f p p o w e i s o f p h y s ic a ı q u a n titie s w h ic h a r e e a s ily s o lv e d w h e n tu r n e d in t li o n e a r lo g a ıith m ic e u a tio n s b y th e

e

q u a tio n

o

am o n

f s ta te

g p re s su

re

,

an

,

,

,

,

,

q

lo g P R

n

lo g P n

-

(n

-

lo g M

2 lo g R

1) lo g M

+

(3

-

lo g p R + lo T g

ro

g Pn

B y e lim in a tin lo R l g og pR g lo g T e æ a n d lo g M in th e f oľm , ,

lo g L

.

a

n

lo g p

)lo g

R +

b lo g T c n +

R

c o n s ta n t

(n + 1) lo g p lt + rr

+

c o n s ta n t

(9 7 ) (9 8 )

(9 9 )

c o n s ta n t

1o )

(9 an

d lo g p te

A lo g

Ą rr +

,

w e

o

B lo g M

b ta in

+

a re la tio n

c o n s ta n t ,

b e tw

ee n

l0 8 L

(9

.

,

ıI)

(9 ]2 )

Scanned by CamScanner

k

9 ı T h * H a y a ıh ııo

n ı a n

d th ı p n

n ıe a ı

m

・n c o

qu

ı4 7

p h ııe e

k fb r e a c h y irs h l tn ıc hc Į ıa c k s in t w e to th a t «»l th c u p M T h e s e tr u c k s p la y 11 s im iliır I o ı M f o c a th s a s v lıIu la n e b u t th e y c t\n n o t b c tu k e n to r e p re s e n t c v o lu ıio n i\r y p ı og p )p r d a re og e d c r iv c (ı r ts h c e a u s e th e a s s u m p tio n s o n w h ic h th e y w e r c o u n te r p a lı s w c s h tl u t io n n r y p a th s a T h e y r e p r e s e n t (1 ç v m p ın ï ť T to c v o ı d i ı n v lı n y c ı t en

lin

a

t es

l: m ıh ic

o g TIT lo g / ) (ı

in d m

e

d

in g ıilm

th e H a

,

,

,

,

.

,

,

no

*

l ľ c n Is a I c u = ( ] ï ıłıu ıų ıw hı th e d is c u s s io n w e a s s u m e (r 7 1» Simplilj iv e " y p o s it u c s m o s tı id e r a n g e o ıv a ı T h c p o w e r b H o w e v e r m n y ils s u m e a w o w mation a tiv e ı y ı 3 ) B e c a u s e p h o to s p h e r ic te m p e r a tu r e s a r e r e ı m F ig u r e 3 o f r l l e (a s s e n d u c e tt ) ffic ie n ts (9 ı2 ) th u s e co e W

«

'

,

.

,

m

l ta in e d b y d y n a ın ic a s ı l th a t th e p o ı y [r o p ic in d e x is c o n s tr a n c lu s io n l I 5 5 II < 3 T h e n r s t c o i n 6 3 ) a n d h e n c e o v e ra ı t o S e c 3 ( < biliry to n h H a yashi ı3 ) is th a t th e s lo p e o f t e E u a tio n s (9 ıI ) a n d (9 m f ro q n w to b e d r a e s, w e fı o w te m p e r a tu r F o r b = 4 a n d / ı - ı5 ty p ic a l o t e e ı s e m p e r t x y to a a c k is e lT e s p o n d in g u e n t ly tr a c k s c o m o s t v e r tic a ılin e C o n s e q n a ı a 0 2 = A o b ta in f M s h iftin g a r g e r v a lu e s o th e r w ith ı e s a r e c lo s e to e a c h o s s a m l l r a t e s t d ifte r e n h e n c e fo r s g n [A ], a n d s g n tB ] = l e ft T h is is b e c a u s e h e t t o s a l w a s y W o 1e lin e x h ig h e r M r a is e s it ( e w h ile ı) r A < O a l w e r s th e lin e o M h r e i h g A > O a e ftw a r d ) W e t r e in c r e a s e s ı th e e ffe c tiv e te m p e r a u i d a g ra m R H h e t i n t h a re c a ll t l th e s lo p e fo r n > 2 T h u s , fo r e x a m p e e c h a n g e s s ig n l o h s t e t h a p t t e o fu r th e r n 1 5)a n d = h e r e o f a to m ic h y d r o g e n (n i l n e d fo r a p h o to s p i c l n t n e f i r d e r y w ill b e lla r s o f c o n v e c tiv e s te 2 5 ) A c c u r a te c a lc u la tio n n n e ( d o r h l r a g l u c e y one o f m o iv e n M c h a n g e s s lo p e , r e s p o n d in g to a g a s h i tr a c k c o r H a h e t t h a y t h w m o d e ls s o th e r ig h t a t la r g e L lo w L a n d s h iftin g to t f a t l e h e t t l o h t i l be n d in g s g y iz e a f H a y a s h i tr a c k s w e c h a r a c te r s ig n ific a n c e o h e d t n a t s d r e n In o r d e r to u o v e r th e e n tir e s ta r in g y e d b y a v e ra g i n a b t o l e u 】 s ta r b y a u n iq u e v a f lly c o n v e c tiv e s ta r , o nen t fo r a u a d ia b a tic e x p e a r e v a h e g t S im ila r ly ý. D e n o te s io n s d ia tiv e z o n e s , th e n in s o m e re g h e s ta r h a s r a f t I = w e o b v io u s ly h a v e Ý i i d e x n fo r s u c h e r a g e p o ly tr o p c n e s p o n d in g a v rr o c h e T y < ya , a n d h e n c e 】 < \ d ia b a tic p o ly tr o p ic in d e x to d e n o te th e a In a d d itio

n

,

w e re c a

,

,

,

,

,

,

,

,

,

,



,

tis fie s n

>

th a t d e fin e s th e

H

s ta r s s a

w

h e re

/? a

is ta k e n

l a r is e fr o m o r n < n a c an o n y > i tr a c k T h e r e fo r e Ý ' N o w c o n s id e r a s ta r b id d e n le a n d h e n c e fo r b a t s n u i s u p e ra d ia b a tic it h s i h c y w d a s a b o v e by a c a n b e d e s c r ib e n fig u r a tio n o f m a s s M a n d lu m in o s ity L w h o s e c o its e fre c tiv e te m p e r a tu r e c h a n g e H o w w o u ld e h r e s t o h l p p o y tr o p e o v e r la id b y a p o t e c o n s tr u c t h is q u e s tio n w e h a v e o r a n sw e r t m ? w ith th e n x d e i n polyopic d e n c e o f th e c o n s ta n ts (o n t o f th e d e p e n E q u a tio n s 9 7 i n g acco u n k t a o 1 9 ) ( 14 b t in th e f u n c tio n in d e x in o f d e r to o a the ri h t h o ly tr o p ic h e t n p o d id e s) an s g d lo g T c fF /d n > 0 lis h e d th e r e s u lt is lo g T i s acco m p k s t a s i u d o rr(n ) W h e n th is te /ı£

a

ya sh

,

,

,

'

,

,

,

,

,

,

,

,

,

Scanned by CamScanner

Th*

9

48

c

o n s e q u e n tly

H

aıy

T he

by

a ra

r o le o

p id

fo r b

Th e

lH

o

o n ı u tı

aw

f s t ın

i tr a c k s

f a il

d in g

b id d e a n d fo r

u n s ta h le

g

t tu ı ・d p ı d ıt ・ı

a

-

o n o r re s p id d e n z o n e c

aya sh

lla p s e

c o

o

<

to n

n To n e

H

\ ı

n

lie s 1o

tlı[ r ig /ıt o

ľ th e

lu s tr a tc d h y th c p tc is h e s t iı

o f s u c h a c o lla p s e T h c in it it\tio n d in C h a p te r 12 A t l b c d is c u s s e iı tu r c r is e s it m pe n ı a n d its te

l c lo u t ase o u s w

s

p ro c e s b e in g a g a la c tic R a th e r th a n de n se s t a s it c o iĽ n t b u d a n d th c b o u n d a r y la y e r firit th e m a te r ia l is tr a n s p a s h ie ld e r is n o w i o r t e i n a u e T he w h ic h w ilıb e c o m e a e v e n tu a lly b e c o m e s o p q e o b je c t n ib ı a d is c e r defines s 3 e 9 a n d te m p e r a tu r e s o l fro m w h ic h r a d ia tio n e s c a p o ı kg m 1o o f a bo u t 1 o i s i t e s n d e n is in m o le c u la r s ta r T h is o c c u r s a t d itio n s h y d r o g e su c h c o n r d e u n i K e lv n d c o n tr a c tio n a fe w h u n d r e d d e g r e e s a l fo r c e a n r a v it a tio n r e s is t th e g t o d l o c o t s c a le (o f th e o r d e r (H z ) fo r m T h e g a s is o n ì ic a l tim e n th e d y n a f r e e fa ll o l i d a a r l s a l i t a y le is c o n s i? r a b ly lo n g e r p ro c e e d s E s s e n th is tim e s c a 7 )) w e n o te th a t 5 2 i n o t ( a E u 1 f T h e r is in g g a s o q / in g s o m u c h lo w e r d e n s itie s b e s r t a s r e t u a f m th a n th a t ty p ic a l o d is s o c ia tio n o f th e h y d ro g e n o u g h fo r a lly h ig h e n t u n e v e s e m b o c e te m p e r a tu r e a to m s a n d ĥ n a lly i n o f th e h y d r o g e n l e th e n fo r io n iz a t o m o le c u le s to ta k e p a c b s o rb a v a s t a m o u n t o f A ll th e s e p r o c e s s e s a fo r io n iz a tio n o f th e h e liu m a to m s d in c o n tr a c tio n T h e n e r g y r e le a s e li d b y th e g r a v ita tio n a l e e n e r g y w h ic h is s u p p e h in th e s a m e w a y a s f m fu r th e r in c r e a s e m u c i n o w p r e v e n te d r o s t r e u r a e t m e s a p g l th o u g h e n e r g y is c o n tin u a l y ta n t, a ı a te r r e m a in s c o n s th e te m p e r a tu f e o f b o ilin g w l c o n tin u e s th r o u g h o u t th e s e s ta g e s it b o ilin g T h u s fr e e fa ı s u p p lie d to it to k æ p t m p e r a tu re m o s t c o m p le te th e g a s e h liu m is a ı W n e n io n iz a tio n o f h y d r o g e n a n d e i e f r a v ita tio n a l e n e rg y T h e r e c o m e s a t m in c r e a s e s a g a in d u e to th e r e le a s e o g t ll n d a s ta e o f ffic ie n t p re s s u re to o p p o s e th e g r a v ita tio n a l p u a w h e n it g e n e r a te s s u r n a s te lla

,

.

,

,

,

,

,

,

h y d r o s ta tic a

e

q u ilib ń u m

p r o to s ta r A ro u g h

is

e s ta

b lis h e d T h e g a s e o

u s co n

de n

sa

tio n h a s n o

w

be c o m

e

b ta in e d b y a s s u m in g d in c o lla p s e to th e p r o to s te lla r r a d iu s R p l th a t a ll th e g r a v ita tio n a l e n e r8 y r e e a s e la r 2 i ń n ity u G M /R p s w a s a b s o r b e d in d is s o c ia tio n o f m o le c u p r a c tic a lly fr o m n tio n w a s h y d r o g e n a n d io n iz a tio n o f h y d r o g e n a n d h e liu m , a lth o u g h in r e a lity a fr a c i b y x H th e d is s o c ia tio n p o te n tia ıo f H 2 (4 5 e v ) B y e m itte d a s r a d ia tio n D e n o t n g n t tia l o f h y d r o g e n (1 3 6 e v ) a n d b y X H c th e to ta l io n iz a tio X H th e io n iz a tio n p o e n 7 9 v = 2 4 6 e v + 54 4 e v ) w e h a v e p o te n tia l o f h e liu m ( e e s tim a te o

f p r o to s te lla r

c

h a r a c te ń s tic s

m ay

be

o

,

,

,

an

d ta k in g Y

H

1

X

an

d

a

Ři

R

R

ģw

ps

o

,

e o

b ta in 50

0 2X M

(9 15) o

Scanned by CamScanner

hi 9 ı T h e H a ya s

T he p

U s in g

tio n o x im a

d t h e p re

a n

b e in g in h y d r o s ta tic

s ar r o to

a pp r

zo n e

e

(9 15 ) w ith X

q u ilib r iu 0 7

H

m

m

ı4 9

pha re

e n ce

qu

a v e ra

an

,

g e In te m

a

ıte m p e r a tu

re

b ta in

w e o

,

a ı n se

ps

ta r is d h e n c e th e p r o to s o f r a d ia tio n is h in d e r e d a n ı f w o h e t 3 3 ) ha se Įn F ig u r e H a y a s h i e v o lu tio n a r y p h e s ta r tin g p o in t o f th e i t i s h s T v e c tiv e ,

,

se e

(

fu lly

con

t re ffe c tiv e te m p e r a u an t e t s n o 2 c

de c re a s in g th e

ro u

,

an c e n t re

g h ly

d th e

ly a t ń r s t fa r lu m in o the s te lla r s lo w

,

o v es aw a

s ta r m

m

a in

the r e m a in s o

ev o

f th e

internal

a s th e

y fr o

th e

m

u s m a sse s

io

d e c r e a s in g

s

ilib r iu fr o m th e r m a l e q d e r s e its tr e n s ity to r e v

m

H

,

an

a

lu tio

c lo u

pha se

n a ry

d

o u t o

a re

an

p e r a tu r e

te m

k to

d its lu

in

m

o s ity

to c o n tin u e s

w a fd

M g he r

r is e

ffe c tiv

e

,

e

c a u se s

to w a r d

o b ta in e d l o g L ) d ia w T l o f r e ( g a ls a f e d in g tim e in te r v o rr e s p o n ,

T he

c

h a r d to

w e re

f w h ic h th e y

d ily

i s ity T h s b u t g a in in g in in te n e v o lu tio n d s ta r t h s in g T h e

in th e

i ns c a lc u la t o

s te a

y a s h i tr a c

h e r o to s te h ro u g h o u t t p e s c a le t

i r e le v a n t t m

se qu e n c e

,

d iu

u

t rs o f v a r c e d by s a p a th s a a lu tio n a r y fro m d e ta ile d e v o

th e

ra

In tim e

R

as

,

its

lla r

s ta

d e te c t fo

rm e

he g e s is t

n o t o n

r e la tiv e

ly a u s e

d T h e te s s

ly s h o r t

th e y a r e

a s s iv e a m

m

o n

g

ite s

b a b le s 1a r d is c s P r o te ı 7 c if c u m s b d y e d 10 y r u n e s o f u p to i m e sc a ı t n o t e d to d is s ip a ,

kn o w

n as

T la

T hey

u r i s ta r s

o f p la n e t fo r m a tio n

,

w

h ic h

o a f e s u fı

im a te are e st

fin a lly s h ift to e s c a le a f y tim n m a in ill th e e v o w a f d th e ce w c tio n to n a t e r u n o C e s q O n ly o n th e m a in e ro u s e n u m eco m b s r a t s l the n u c le il ar o n e an d w

lu tio

3

×

7

1o y r

sc a l e s s h r in

co n

k

i tr a c tin g p r o

s ig n

ific

an

tly

r to

: th u s

ig n itio n

n h y d fo g e

fo

f a

9M

o

s ta r

th e

,

in

t to c o n tr a s

th e

conaction p h a s e

10

o ı

y r it

ta k e s o n ly

Scanned by CamScanner

上 4 4

4 2

Lo g

F ig u

9 ł E v o lu tio

\

4 0

1

L 3 6

3 8

(Ą ïr)

k i p a th s in th e 14 R d itrg ľ a m fo r s ta r s o f d iĦe r e n t iı ı itiN m a s s r m a r k e d ) d u r in g th e p re m a in tie u e n c e q p h a s e T h e s h a d e o r s e g m e iıts is in d iæ tiw o f d tim e s \ n t in e a c h p h iu ie r a n g in ro m le s s th a n 1o 3 g ı o ' y r (k \ y i (lig h t) to m o r e th a n ı a s g iv e n in T a b le 9 I (a d a p te d ł T o m I lb e n J r (19 6 5 ), A s ttu p /ıy ò J 14 1) re

n a ry

,

,

Scanned by CamScanner

两部叫目

ł e缸



Fı gu

9 2 Je t

re

c lo u d

o

f ga s

a n

o

f ga s

,

o n e

f ly lo haı

d d u s t th a t h id e s th e

n

g

,

s ta r





r s t in

g

s ta r

bu

(p h o to g r a p h b y J M

o rse

(S T S c L)

e

by

je c te d

a

yo

u n

o u

g ,

w

t

o

f

a

d a rk

ith N A S A

s

H u b b le S p a c e T e le s c o p e )

T he

9 2

A ll s ta rs

un

in g T h e

m

d u r in g th e c a p tu r e o n

j

m

a in

p fo

c a rb o n

in

qu

se

e n ce

pha

se

se

,

,

qu

se

a

e h y d ro g e n b u m c h a r a c te r iz e d b y c o r q u e n c e p h a se n th e s iz e d i o r ta n t is o to p e s a r e s y d u c t is h e liu m b u t o th e r m p r e s u ltin g fr o m p r o to n n h a s e a s w e ll s u c h a s n itr o g e

m a in

d e r g o th e a o r

m

p le i in th e

en ce

n u c

,

,

s te

lla f

c o re

,

an

d th e

r a re r

3

is o to p e s H e r s e o f th is lo

an

d

ı3

c

,

g p h a se s ta tic a n d

In th e c o u re o u ts id e th e c o pr o d u c e d in c o o le r r e g io n s h h y d ro ń u r a tio n to a c h ie v e b o t th e re is a m p le tim e fo r th e s te lla r c o n g ha se s i ' c tu r e a n d e v o lu t o n a r y p fo rg e t its fo r m e r s tr u d th e r m a l e u ilib ń u m n a q ı i h e s ta r tin g p o in t o f s te lla r e v o u t o n T h u s th e m a in s e q u e n c e m a y b e r e g a r d e d a s t to o d p a r tly d a r e le s s w e ll u n e r s fo r tu n a te l s o fo r th e e a r lie r s ta g e s o f e v o lu tio n y tr ic te d b y th e s h o r t d b y o b s e r v a tio n s is r e s p e r h a p s b e c a u s e th e g u id a n c e p r o v id e ,

n

'

,

,

d ? o g e n burning c o r e is tr a n s p o r te t d in th e h y r8 y g e n e r a e 0 3 M o ) th e m a in m a s s s ta r s (M o w I ı o u tw a r d b y r a d ia tio n o r b y c o n v e c tio n n ly c o n v e c tiv e (e x c e p t r s b e in g fu ı m ean s o f tio n th e s e s ta e n e r g y tr a n s fe r is c o n v e c in S e c tio n 6 6 In th e a n tic ip a te d s w e hav e th e p h o to s p h e r e o f c o u r s e ) a a s h i tr a c k m e e ts th e io n w h e r e th e H a y H R d ia i n th e r e g d n f u r o h a e t m r a e g y d s m a lle r o u te r c o n v e c t iv e m a in s h a v e s m a lle r a n e qu e n c e M o r e m a s s iv e s ta r s d o v e r o n ly a b o u t tiv e z o n e e x te n s zo n e h e co n v ec t s ; in th e S l e m a x f e r p o u n T he

n u c le a r e n e

,

,

,

,

,

Scanned by CamScanner

龟秀晨昏毛飞 告甚 召 g

島君 国

名 制日日自 言 島1





口 の









.



c

.



o













. め

. 崮 じ

曾 弓



ぶ 驾 二



云售 乞 丐 )

唧 中

0



っ 网





崖訾 每 秀甚 口



叵 若罗 黜

葛 多 甚苫械



君 目





1笆





显岁



ä 掣胃

閱 口



己 的





の リ



钿 °







与 り



日 瞬 卫 間 巷智 畜 口









ぶ 己 阴





力 六

っ ぶ 島 リ ぷ

岱 り

彐 口

、 。 、 、

二 と









ご 石

. 芸

.



バ ー 歹一

量甘







ー ド

必 響 菊霆ー



っ 。











三 军













人 二

g



三 军





日 っ







树 り 加





密 加

っ 磷

て ぶ





买 ミ

メ ロ

勇合

四 く



っ 菡

く コ

之 妫





己 謗





目 葛





了 く



七 乙









卢 穆







的 っ

舅 邕







む ぶ





























寥 ぽ多 置 碧 趕ミ 暑。

宕 虽 卫勇





勇 =趴 旨





ろ だ

U 〉 3



8

言ゼ 多 屋 霆 図 名 島 差 習

















り ぶ



呂丽









.















鳥 ど り ミ 分コ



试 杉













、 、 、 。



り ぶ



罗 コレ









く 杉 8















ロ ン ロ り

、 。 、

















。 む ン



と ミ 。



1

っ り





/



詛 事













、 。













義 。 り 卑 舅 ン 口 萑 ー 钍 ミっ 。 ミ っ 三 ミ 芒







基直

ー墓差









器 召 口

暑芽 金 豸 ぶ

む ン



召 U 習 ミ 訾 ぶ





















目 四 四 万 西











曾 徨 令 仨岩 零 と 卫 e ミ 口 勺 と 零 口島 に 乌





吓 匈军









后ヱ )













岛 的



老っ







.





心 ぢ ト 喘 島

c

イ心 目 。

昏势

呂 업彭 w

Ø



岁 & 习

壁 名











。 リ

后l

に 口



























隹鑫

豸 唇 區 罗

冒 正 丽

丽 a





贸 占

男 乃

8 召 回 a

对 目









岱 人



く 魯 む

Scanned by CamScanner

9 2

T he

a in

m

se

qu

e n ce

15 3

p ha se

he p p in g t ilı n v e c tiv e c o r e h d r o e n b u r n in g p ro d u c ts w o f th e g y b o u n d a ry r e t ı ot th e to th e s u r fa c e o f th e s ta r w h e r e th e y c a n b e o b s e r v e d in th e ir w a y e k a he tï r e a d in g to t a p p in g c o n v e c tin g z o n e s ı T h is e c t o f c o n s e c u tiv e o v e r ı u 111 c tł e sp re n c e f p r o c e s s e d m a te r ia l to th e s u r fa c e e n a b le s u s to in fe r th e o c c u r e up o d g ť ttı d e te c tio n in b u r n in g p r o c e s s e s in th e s h ie ld e d s te lla r c o r e s T h u s th e u c le a r n f n t o th a t a r e d iffe r e ti v o lv e d s ta r s o f h e a v y e le m e n ts a n d is o to p ic r a o s tr a o f e c e sp ll a s g u id e to th e u n g s ta r s c o n s titu te s a n o th e r c r u c ia l te s t a s w e o se o f y o h t ì ì r fro th a t A lth o u g h th e re is a m p le o b s e r v a tio n a l e v id e n c e e v o lu tio n o f s te lla r f o y th e te lla r in te r io r s lid a te s th e th e o r y o f n u c le a r e n e r g y g e n e r a tio n in s c tly v a e i r d in te s t th e v e r y d e v o te d to te s tin g it d ir e c tly E x p e ń m e n ts a im in g to ff o r ts a r e e t a d s c f ib e d in g re k in g p la c e in th e c o r e o f th e S u n w ill b e e b u r n in g p r o c e s s ta n e o 山 g hy e e rrv

lly b e c o m e fo r m e r ly c o

e v e n tu a

ill

w

lo p e

,

c o n v e c tiv e

,

,

its in

bo

ne r

u n

d a ry

o v e r la

,

,

,

,

,

,

,

,

O

f th e

ne o

io u s c th e p r e v e se q u e n c

m a in s e

an

,

o

d th e A

g o fr o m a lth o u g h th e m a ss,

w

r a te s o

s ta r s

h a d th e y

lo f

n

'

w

se

ass a

se m

lo

m ass

pace o in d s lo w ,

c o n s e rv e

is

m

a s

TX

'"

s

do

w n c o m

To

a ss

h ic h

A

s w e

ha v

in

e se e n

r ex am

she

d

p le

.

h e qu en ce p a s a o r e in te n s e A s se

w

ith in

c r e a s in

a c o n s id e r a

a ss

Re m o v e s m

A

g

s w e

lt

re s u s te

b le fr a c tio

,

lla r o

n

f

f th e s e h th e e v o lu tio n a f y r a te o p a r e d w it d e fin e a p a r a m e te r illu s tr a te th is e fre c t w e

by

lo g (r M 06

ss

discernible e ffe c t o n th e

i m a in p le tio n o f ts th e w in d b e c o m e s m id ly n d e c re a s e s r a p

a s s iv e s ta r s , w

m

lo

g

fo

co m

m

d th e ir

a ss

to h a v e n o

life s p a

en ce

f

n

lu d in g th e m a in t a ll e v o lu tio n a r y s ta g e s , in c w er e O n th e lo w id e r a n

/,

n

lu tio

s o s lo w

a s s iv e s ta r s ,

qu

ev o

s s v a r y o v e r a v e ry

is

r a te

a s s a t th e

s m

m a s s to m

m a in

f s te lla r

in S e c tio

s sho w n

b y th e

m a ss

a

r , s ta r s

th e e v o lu tio n

th e ir

a tu r e s o

th e m a s s lo s s

f th e s u

lo

lie n t fe

h a p te

qu e n c e

la r m a s s s te ı

1/1o o o

sa

s

/r M

s o

)

=

lo

g

d e te r m in e d b y th e tim e s c a le s a r e e v o lu tio n a r y t a h t 7 r t W ċ h a v e s e e n in C h a p e h ig h e r p o w e r ) l to th e s q u a r e (o r a r o p o r tio n a l e r s p e v i y s te lla r m a s s , a s th e y a r e n d c e th e s o la r iń n g th e m to r e p r o u te d b y r e q u b a r i l a c e o f th e m a s s S o la r m o d e ls a r n d e n tly k n o w n S u n , w h ic h is in d e p e e o f th e t a n e g s e r ra d iu s a n d lu m in o s ity a t th e p lib r a tio n is u s e d h e E a r th T h is c a e age o ft h t f o s t e a i fro m g e o lo g ic a lly b a s e d e s t m id e r a n g e o f m a s s e s s o v er a w e o f s ta r s h a e c n p se q u e fo r c o m u tin 0 1M o 5 g th e m a in p in itia l m a s s r a n g e h w ith in t e s r t a f s T h e m a in s e u e n c e life tim e s o th e m a in s e q u e n c e in q r k e d o n to

M 5 25 M F ig u r e 9 5

o a re ,

9 2 lis te d in T a b le

d

a fe

m a

d in g s te lla r m o n lc e is n o t c

n th e c o r r e s p o

g w ith 2: lu m n o f t a b le 9

a lo n

an

a sse s s ta n

T he

v a lu e s o

f ce

a re

lis te d

l e m t; fo r r e la tiv e ly a ig

,

it

in th e th ir d c o se q u e n c e a ge s : a t a n o f m a in e la r g e s p h t t e o n d e c re a s e M W e f th e u n iv e r s e s w ith in c r e a s in g d b y fa r th e a g e o ex cee h e t y e th e lo w u en c th e r m a l tim e s c a le e r e n d o f th e m a in s e q te r th a n th e m e sho r o c e b by c o n t d , th e y r a s t , a t th e u p p e r e n 0 1 th e S u n

y

'

Scanned by CamScanner

54

9

The

evo

ı u t io

o

n

a

a in

qu e n

e 9 2 M Ta b ı

life tim M

a ss

(M

o

m

a in

s te

9 5 T he se

lla r

qu

e :n c e

c lu s tte r a

a in

m

se

in th e H

ge s

qu

0 1

6

0 5

7

× ×

a

2 8

10 12 10

2 8

"

o ı l x i0

ı2 5

4

×

10 9

4 1

15

2

×

10 9

4 0

3 0

2

×

10

8

3 6

5 0

7

×

10 7

3 1

9 0

2

10

7

2 8

10

7

2 6

10

6

2 3

l

25

6

en ce

life s p a n fo r

R d ia g r a m

a c c o r d in

ce

T in t e (y r )

)

15

re

se

g to th e

re

es

10

F ig u

e d p ic t u d e t a iı

f s ta rs

× × ×

s ta r s o

f dirent

(s e e F ig u r e 9 3 )

,

m a in

sequ e n c e

'

w

h ic h

tu m o

m a s s e s m a rk e m a

y be

u se

d

a lo n

g th e

d to d e te f m in e

ff p o in ť

lly a la r g e g r o u p o f s ta r s b o r n i H R d ia g r a m f h l l a t th e s a m e tim e m o r e o r le s s T h e a g e o t e c u s te r w iĮ s h o w o n ts tt s ta r s w ith in th e c lu s te r a s th e u p p e r e n d o f th e m a in s e q u e n c e Orthetumopoił ife tim e s s h o r te r th a n th e c lu s te r s ī e s p o n d in g to m a in s e q u e n c e ı w ith m a s s e s c o ı i t b r a n c b In a g e w o u ld h a v e a lr e a d y le ft th e m a in s e q u e n c e to w a r d th e r e d g a n ld h a v e c o n s u m e d th e h y d r o g e n s u p p ly o f th e ir c o r e s o th e r w o r d s s u c h s ta r s w o u w h ite th e c o r e s c o n tr a c tin g to w a r d th e n e x t burning s ta g e (o r to w a r d b e c o m in g s a ge d w a r fs ) C le a r ly s ta r s w ith m a in s e q u e n c e life tim e s lo n g e r th a n th e c lu s te r de o i h R d ia g r a m w e a r e th u s p r o v i w ill s tilıd w e ll o n t e m a n s e q u e n c e o f th e H d l (a c lo c k ) fo r m e a s u ń n g th e a g e o f s ta r c lu s te r s a s illu s tra te w ith a r e lia b le to o C

o n s id e r n o w

a s te

lla r

c lu s te r , w

h ic h is

,

e s s e n tia

,

,

,

,

'

,

,

,

'

,

,

Scanned by CamScanner

9 )

$o ı »

.

N o te : T h c

rv a o hse

lio n s

m a in B e q u e n c e o

h a Ħ th c

i * te lla r

m e [t* u r e d a p p itre n t

y

t tlm

弓弓 ı

c lu * ı e r« w r v e» n o to n

h r ig h tn e

ly iı # a tim e in s tr u m

ent

but

d e fin e d b y ï× ł ualion ( ï I), in # le a d o f « c ı a e h t i a g n itu d e lo (4 » tr a n # la te s i , n to a u n ifm ?n g ?r ć [z ) rrı v aı c h in suc h a di g a r a m w jjh th h e d e te r m in a tio n o f th g t s e l e b c a lib f u e d o n e e * h ifī ena a n d he n c e o f th e d i » ta n c e ta th e c ı c n c e is th e m a in s c q lı tı a te n A s th e o st o u ı ow e r m ı p p a M r e io n o f th e H g R d i r i d h o a n c e r a u r r m e t c o I l t t o i a n y c lu s te r , g p g e s m a in l the m y o n th e m a in w qu e n c e am ı h t i i d h i t r m t u # n t e a e o n s m e th o d o f (w h ic h , in r e a ı dis la n e c it% i» c o m lic a te d b s p y u c H fa c to r s a s m e ł ic ity a ïł Į e r s te lla 】 a b s o w tio n C h a te r ı a n d in 2 ) i* c a lle d p /?u tijı «e u q e n c e jh E n g

ım in o s ity a « the u l s h ill o f m e rtic a

o r d in a te

S in c e ,

o 11 th e

# «,

lo g a r iıh

m

ic

,

,

,

S ta r s

f a lım

o

p a r ta k c in th e o f d iffe r e n t m

a sse s

m a in s e

q u e n c e p ha s e bu t s u bse u e n t e v o q In w h a t k ) llo w s w e s h a ll d is tin u is h g be tw e e n s ta r s w h o s e m a in s e q u e n c e life spa n e x c ee d s th e p r e s e n t a e o f th e u n i g a te s t e s tim a te v e rs e (a c c o r d in g to ı s - ] 4 × 10 ıo r d y ) a n s ta r s th a t c o u ı d ha v e e v o lv e d o fr th e m a in s e q u e n c e w e r e th e y b o rn e a rı y e n o u g h S te lla r m o d e ls yie ld th e u p p e r m a s s lim it fo r s ta r s th a t a r e s till o n th e m a in s e u e n c e (e v e n if q d a s th e u n iv e r s e ) a t 0 7 M the y a re a s o ı D u e to th e ir ]o w s u r fa c e t o e m p e r a tu r e a n d th u s r e d d is h c o ı o u r th e s e s ta r s a r e aı so kn o w n a s r ed d w a ŕ c s S ta r s o f m m s M > 0 7 M o m a y b e d iv id e d in tu m in to tw o s u b g r o u s a c c o r d in p g to th e ir m a s s th o s e w ith in itia l m a s s e s b e lo w 9 10 M o a n d th e r e s t w ith th e fo r m e r e n d in g th e ir liv e s a s w h ite d w a r fs (a fte r s h e d d in a c o n s id e r a b le fr a c tio n o f th e in itia l g m ass) a n d th e la tte r u n d e r g o in g su pe rn ov a e x p lo s io n s T h e fo r m e r fa ll in to to w m a s s s ta r s (0 7 M 5 2 M O ) a n d in te r m e d ia te ı?ı a s s s ta r s (2 5 M 9 lO M o ), a n d th e la tte r (> IO M ) a r e k n o w n a s m a s Ýiv e s ta r s T h e d i i i o s t n c t o n b e tw e e n lo w m a s s a n d in te r m e d ia te m a s s s ta r s is b a s e d o n th e w a y o f h e liu m ig n itio n in th e c o r e lu tio n d ifk

rs

fo

r s ta r s

,

a sse s

,

,

,

,

th a t is , w h e th e r o r n

W

e no w

,

o t

it o

c c u rs u n

f s o la r

m ean

fr e e p a th

fro

co n

d itio n

s

th e c o u r s e o f s te lla r e v o ı u tio n to a d d r e s s

m

n e u tr in o s

9 3 S in c e th e

d e r d e g e n e r a te

m a k e a s h o r t d ig r e s s io n

th e c r u c ia l is s u e o

,

o

f p h o to

S o la

r n e u

in

s ta r s

ns

t r in

o s

is b a r e ly 1 c m

,

s te

lla r

c o re s , w

h e re

n u c le a r

d W e in fe r th e o c c u rr e n c e b r e a c tio n s ta k e p la c e , c a n n o t b e d ir e c tly o s e r v e of n u c ı e a r r e a c tio n s fr o m th e fa c t th a t s ta r s s h in e a n d th a t th e ir lu m in o s itie s a re w e ll u tio n b a s e d o n n u c le a r e n e p re d ic te d b y th e th e o r y o f s te lla r e v o ı rg y ge n e ra tio n

How

,

an

d

a ls o

fr o

m

th e v a r ie ty o

f

s u r fa c e a

bu n ?

n ces an

d is o to p ic

f th e th e o ry w o u ld b e p o s s ib le b y d e v is in g g n e u tr in o s th a t a r e e x \ lie d in n u c le a r r e a c tio n s F o r th e m th e P a th e x c e d f i e s s te lla r d im e n s io n s b y a b o u t te n o r d e r s o m a g n tu d e B u ever

ca t p u r in

,

a

d ir e c t te s t

o

,

ra

tio s

m ean s m e an

t

if

o

f

fr e e

m a tte r

Scanned by CamScanner



豇 艮

嗫苕 嚅











盪 歹 氧

腎 \ 為

Ą



腎 与

\ 与

ー き 霭





営 茎孚 声 w

ぎ ー驻孚



ー氧 ぼ





ー 叫

貧君 复腎 $ ぎ

腎腎争

腎2



為 伯

8

骨 氧

-

豸 势 芦署







. 岫

\ 一



差腎 罗





萍 氧



ー寺

势ヘ 秀

)



者 霄



古 営 堑 墓 罗 背 范 骨瓯 習蓄 力 歪 蠡 営 ı ¥ ぎ 需

驰 朝

営 ー \

魅 學

绉 w





背 녘

湯 看礁 心ぎ ー 費歹









兰叁

ぎ腎

4

澹 年

曼 歹 暴 君 著冶 戛









霪 友矿



寡腎 警 笋 営 鼕 ヨ 督営 香 腎 蝨 腎 静 挙毳 吝習 岔 滔 っ 理 守ぎ焉 丞 蚕 覆 落罾受 藿 丞営 歹 歹 長 薯 腎 営 蓼窘哥 霄 兹 腎署 ー夢 霄 腎 譬 理



量星署 斟

鼋着

巴 w





- 自 勾

牙ぢぎ 腎芽 吕 置 守 露目 曇 (









腎 汲 腎蜜 礴汲含 售露 氧

邕腎

資乐





習 研



黒 各魯 落 腎

腎 習 碼

势昏 君 貧良 ミ

勾 帝 君













会 魯 玺 彩

差鑫

塁孚 璽

杯 葛



零 ぎ

+

$

君麥 涎

背 势 氧蓄

玲飞

q



盛 誓 瓜 夏 葛 秀 媚

営杂 鑫

词 矛

-

ー劣

ビ◆ \



巻零







缸 耄淊



\





\

咱 )

孑 番 敦





耄云

飞 飞



尘 歹

塾 置

◆气 ヘ

◆ 零





篷文

-

& *

\



歹 玲

내 & 孑 口

奄 奄 i





嗦每 亀

转 甑 番

ぎ き 诎要



ぎ零杂 韋护ぎ

Scanned by CamScanner

9 3

o fo

rgo

n

So ı ap

15 7

n e u t r in o ı

,

V

37

+

Cl

弘 e

+

37

A

,,

o h a v in g a h a lf life o f 3 5 d a y s E v e n tu a lly , ir th c c h ı he w ib r iu m is a c h ie v e d b e tw e e n t b r a s u fric ie n tly lo n g tiıľ ıe , e q u iı o se d t x e p 37 c is i o to p e s r itr tr u c tio n o f a r g o n T h e e q u ilib r iu m a b u n d a n c e o f A : » a n d de s n i o t d tıc s h o ld prtt d e r iv e th e flu x o f h ig h ly e n e r g e tic n e u tr in o s A s th e th re 1 o d e s be u ll 8 B n e u tr in o s ; o n ly a s m a r e a c tio n is 0 8 M e y th e s e a r e m o s tly o f th e nt 7 e n e rg y B e T o g r a s p h o w fo r m id a b le th is e x p e r im e t fr o m I/6 ) m a y r e s u ı ( n i o 0 0 to n s ra c t h t it in v o lv e d a h u g e ta n k c o n ta in in g a b o u t 6 u ld m e n tio n t a o h s e s w de e p l i d in th e a b a n d o n e d 15 0 0 m l a n o r d in a r y c le a n in g f u d ) p a c e d i ( l f u 1 c 4 h d o lc ź 9 6 (T h e e x p e r im e n t a i d m in e in S o u th D a k o tĄ s h o w n in F g u r e l o k e g d by H o n ìe s ta id b a c k g r o u n d n o is e c a u s e d e e p u n d e r g r o u n d in o r d e r to a v o d t e c u d con o re to b e f a r g o n a to m s w a s n o m d l i e s ) T h e e q u ilib r iu m a b u n a n c e o c t r a M c ra y p N v e r th e le s s 2 × 10 3 oc c h lo ń n e a to m s in th e ta n k ! e n s a m o n g th e e t w f e iha n a G e ig e r c o u n te r t d a n d by m e a n s o f a o n a to m s c o u ld b e e x tr a c e r a e i v t g c a i o d th e r a 3 lo w e r th a n b e in g a b o u t a fa c to r o f 2 to f r r e d n e u tr in o flu x e i n h e T d c o u n te d w ha t ha s be e n r a n g e c o n s titu te d e ls fo r th e s a m e e n e r g y o m l r a o s b d y r e d ic te

hic h

sttı sequcntly d e c a y s

,

N

,

,

?

,

o

d c a le i n a lw a y s o n a g r a n s t e d fu r th e r in v e s tig a t o m o r l e z z p u i n p ts T h e p e f s is t g p T h u s o th e r e x p e r im e n i f n e u tr in o d e te c t o n l t o i u c iff d h y e ? d by t n d a s de m a n II in th e m id 1 9 8 0 s a h e K a m io k a n d e t d : 8 w e ll f o o s i o n h e B n e u tr a im in g a t t d s till o p e r a tin g b o u t te n y e a r s la te r a n K a m io k a n d e a r e S u h e t p r iı c o n ta in in g s su c c e s so 4 0 m h ig h 4 0 m in d ia m e te r a n d t an k i b f a o t i g s s T h e la tte r c o n s h e e x p e r im e n t b t h a lf is u s e d fo r t o f w h ic h a o u t r e 3 a w r e u o f v e fy p 50 0 0 0 m i la c e d in th e h ie ld in g it T h e ta n k s p n d in g a n d s u o T 】 f 1 J l 5 h a ts e lf w ith th e o th e r 0 0 m Its w a lls a r e o r e th a n 10 a d e p th o f m t a n a J a i n p K a m io k a M o z u m i m in e l i lie r tu b e s p h o to m u t p h t d e te c to r s i l i e v i t g s n e s 0 0 0 v e ry u n t n e d w ith s o m e 1 1 io n u s e d a s m a lle r a m o e a r lie r v e r s h T e s ( n t o h i le p o c a p a b le o f d e te c tin g s n g i ba se d o n e x pe ń m e n t s r e s u lts ) T h e e t a r u c c a s l w hat e s o f w a te r a n d y ie ld e d s o m e io n s n o e le c tr o n s c a tte r in g r e a c t n ,

,

'

,

,

,

l

,

,

,

,

hic h p r o d u c e e le c tr o n s a te r (b u t is le s s th a n th e

m o v in

g

ith

w

a sp e e

d th a t

he spe e s u rp a s s e s t

d

o

f lig h t in

d ia te e n e rg y S u c h e le c tr o n s r a cu u m ) a v i n t h i l w spe e d o f g ro d u c e d b le s a s h o c k w a v e p h a t re s e m t t f c f e kn o w n a s C /ıe r e n k o v r a d ia tio n a n e s o n th e i h its th e d e te c to r i s ra d ia t o n h T d e b y a n a irc r a ft m o v in a t s u p e r s o n ic s p e c e it h g to 7 M e v a n d e n n t is c lo s e e i m r e o f th is e x p ta n k w a ll T h s e th r e s h o ld e n e rg y T h e n u m b e r o f e v e n ts 8 e u tr in o s o ng B n m a i c is o n l s t e d e te c te d b y th e y e n s itiv e to th e m o r e e n e r g h n e u tr in o flu x k no w s t e e n f o i l Pe r d a y is le s s th a n 2 0 In p r in c ip e in e e x p e r im e n L T h is D a v is s c h lo r b d e y t ı 1e u h i c t e n o s th e flu x th a t s h o u ld b e d e w

,

,

'

Scanned by CamScanner

ı5 8

9 w as

fo

u n

th e

so

la r

'

The

evo

ı u t io

d to b e h ig h e r th a n th c n u

p r o b le m a r k a b le a c h ie v e m

n e u tr in o s

d ir e c tio

d

f th e

n s o ,

w a s th a t th e

la r

s c a tte r e

fo

a re

T h e d is a d v so

a n ta

n e u tr in o s a r e

A

m

s

ge

o

th e th r e s h o ld

h ic h h a s o n

m e r ly

C

So

lla b o

b e tw

ra

e e n

o u

lly d e te c te d ,

w

re

h ic h Fu r th e

v

e n e rg y

ie t) A g io

tio n

19 9 0

r co m

p lic a te d

io k a n d e

am

d o in d e e d h ic h

co m e

p e r im e n ts is to h a v e fr o m th e S u n T h e b ex

o

il in th e d ir e c tio

re c o

c

h lo r in

d th e

e an

f th e

n o

Su

n

se rv e d

i

s c a tte r n g

in th e

C he re n ko

w a te r

e s ta b

s ky

in s ig n iń c a n t b r a n c h

o

,

7'

+

G

a

7'

+

e

G

e

,

b e in g o

o n ly 0 2 3 M e y to p r o d u c e r a d io f 1 1 4 d a y s a n d d e c a s b a c k to a lli u m y g

m e r ic a n

c o

n o

fR

u s s ia

in

an

u n

an

f th e K

t a c c u r a te ly th e p o s itio n o f th e

th is r e a c tio n w e r e so o n

a u c a s u s re

c o

d e t a ile d p ic t u

v e x e ri p m e n ts f th e p h p c a in T h e b u ı k of th e lo w e n e r g y o n e s p r o d u c e d b y th e fu s io n o f tw o p r o t ons it tu r n s o u t s u c h n e u tr in o s c a n in te r a c t w ith l l i a u g m a r a th e r

h a 1F life

a

en to

f b o th th e

u

ba se d

a

rs

x a c tu a

e le c tr o n s , w

d to tr a c e

u n

y te s te d

in to d e u te r iu

w

f s ta

n c u tr in o

T he re m lis h e d th a t th e d e te c te d n e u tr in o s

o

n

,

lla b o

an

d e rg ro

d

r a tio n

in

an

u n

d 6 0 to

d e rg ro

u n

d G A LLEX

d la b o r a to r y in G u se

d SA G E

o n e n am e

a n o th e r n a m e

u n

d 2006 S A G E

d e s ig n e d

f

ra n

a c tiv e

a

S a sso

,

d

Tw

g e rm

o ex a

R

a n iu m

p e r im

u s s ia n

,

e n ts

ifo r

tio n in th e

ex c av a

p r im a r ily E u r o p e a n Ita ly B o th o e r p a te d

llic g a lliu m (m o r e th a n th e am o u n t p r o d u c e d w o r ld w id e in a e a r ! G A L L ); E X u s e d h a lf th is a y m o u n t in a n a q u e o u s s o lu tio n S im ila r to th e m e th o d u s e d in th e c h lo i r n e e x e r im e t n p th e w a y o f d e te c tin g th e n e u tr in o s w a s to c o lle c t a n d c o u n t th e r a d i o i a t c v e a to m s in th e ta r g e t M o r e th a n h a lf th e n e u tr in o s d e te c te d in th e se e x i p e r m e n ts c a m e fr o m th e p + p r e a c tio n p r o v id in g fo r th e fir s t i t m e u n am hi u o u s c o n fir m a tio n g o f h y d r o e n fu s io n g a t th e c e n tr e o f th e S u n T he c o m p a r is o n w ith th e o r e tic a l r e d ic tio n s w a s s i n ific a n tl i p g y m p r o v e d T h e e x e r im e n ta l r e s u lts n o w p c a i m e w th in 6 5 % o f th e s o Į a r m o d e l p r e d ic tio n s a n d th e d is c r epan c y d im in is h e d a s m o r e d a ta a c c u m u la te d a n d m o r e r e fin e d e ff e c ts w e r e in l c u d e d in th e s e m o d e ls (s u c h a s d ifr u s io n im p r o v e d m e th o d s o f d e a lin i w t h c o n v e c tio n b g e tte r o p a c itie s ) T h is w a s th e s itu a ti , o n c lo s e to th e tu m o f th e m ille n n iu m h a d b e e n o b s e r v e d in fi s o la r n e u tr in o s v e d if n s o

m

e ta

,

,

,

,

re r e n t e x

p e r im e n ts w ith th e e x p e c te d e n e r g ie s a n d flu x e s M o r e o v e r it w fir m e d th a t th e ir s o u r a s u n e q u iv o c a ll c o n y c e w a s th e S u n W e m i h t s f a g l e l o f th e n e u tf in o d e te ti y c a im th a t th e m a in g o a l c o n e x e ri m e n ts p th e v a lid a ti o n o f th e th e o th e n u c le a r e n in e th r y concerning a t p o w e r s th g e Su n an d t s a r s h a d b e e n a tta in e d B u t th e d is c r e p a n c y b e tw e e n d e te c te d a n d p r e d ic te d n e u tr in f o lu x e s e v e n if a t th e o n s e t o f th e D s m a lle r th a n , a v is e x e r i m ent w as p , s till n a th u s c o n tin u e d g g in g T h e q u e s t fo r a s o lu tio n T h e s o lu tio n to th e s o la r n e u tr i n o p ro b l em an d n e w w ith it s tr o n h fo r i s c s w p y a s s o o n to b g in d ic a tio n e fo u n d , p r o v id e d by n ew ex e p e r im e n ts e v e n n lo r k in d n a m e d S N O (fo S r u d bu r y N e u tr in o o b s e r v a to r t y ) w a s d e s ig n e d to d e te c ro u

g h ly b u t ,

n o t

q u ite

,

th e e x e c te d p

,

,

'

'

,

,

,

,

,

Scanned by CamScanner

ey

(a ) Figu r e

9 6 T he

B ro o k h a v e n N o f E rn e s t

H

o m e s ta

a tio n a

O r la n d o L

so la r n e u tr in o s

(b ) ke

l L a bo

a w re n c e

in

e

r a to r y

)

m

B

ex

an

e r k e le

pe ń m

en t

(a ) (p h o to g r a p h b y

d th e S N O d e te c to r (b ) (p h o

y N

a tio n a

th r o u g h th e ir in te r a c tio

n

l L a bo

w

r a to r y

c o u r te s y

o

f th e

to g r a p h b y c o u r te s y

)

n u c le

ith d e u te ń u m

i

d

an

e le c tr o n s

T he sphe ń c a l di i g a in o n C h e r e n k o v r a a t o n 0 0 m b e lo w g r o u n d in th e C r e ig h to n f e 9 6 w a s p la c e d 2 0 h 10 0 0 to n s o f s a lt h e a v y w a te r M in e lo c a te d in O n ta r io , C a n a d a a n d fille d w it s h ie ld a n d b y a lm o s t 1 0 0 0 0 It w a s s u r r o u n d e d b y c le a n w a te r th a t s e r v e d a s it n s itiv ity d v a n ta g e o f th is e x p e r im e n t w a s s s e pho to m u ltip lie r tu b e s T h e s p e c ia l a h h c o m m o n e le c tr o n n e u tń n o t e r e a r e to d iffe r e n t k in d s o f n e u ? in o s a s b e s id e s t e s th e m u o n a n d th e ta u th e r k in d s o f le p to n tw o m o r e t i t e d w ith tw o o a c o s s a e s yp th e d iffe r e n t a n s itio n s b e tw e e n In 2 0 0 1 2 0 0 2 it r o v id e d th e fir s t e v id e n c e o r tr p th e s o lu tio n o f th e e d th e w a y to kin d s (n e u tr in o o s c illa tio n s ) w h ic h n o t o n ly p a v a s s a n d p la c e d e u tr in o s h a v e m i a te d th a t n d c i n s o la r n e u t i o l s bu t a r n o p r o b le m i e n ts w e r e h ile th e e a r lie r e x \ r m V e r y b r ie fly w c o n s tr a i n ts o n its m a g n itu d e h c le a r t is r e le a s e d in t e n u th e k in d th a s e n s itiv n ly e to e le c tr o n n e u tr in o s o e d to o th e r n e u tr in o s d e c a y n o t th e s e a fra c tio re a c tio n s i n h a c o f th e P P d e te c tio n w h ic h e x p la in s h u s e s c a pe d ty p e s b s an d t r o t c t e d e e fo r e r e a c h in g th e itio n s to b e p o s s ib le F o f th e s e tr a n s o flu x i the a n t r u e n p p a r e n t d e fic ie n c y in th e th a i in M a y o f s o o n a fte r in 2 0 0 6 a n d d t e a i n m T h e S N O e x e ń m e n t w a s te r d e rg r o u n d la b o r a to r y in p am e u n a t th e s d 200 7 h e c n a n o th e r e x e r im e n t w a s la u p

pre s e n t in s a lt h e a v y w de te c to r s h o w n in F ig u

ba se d

a te r t

a

,

,

,

,

,

,

,

,

,

,

,

,

,

Scanned by CamScanner

N

P r iz e Fo th e K a m

p r iz e

o

y

F

a

N

p th e

o

n o

D

an

r

ic

2002 ,

r

p io

am

an

,

H is

D

av

co

ith th e

f th e S u n

,

an

d

en

ex

e n t e ar n e

ith M

w

p e r im

e n

d R

a

K

a s a to s h i

ym

o n

d D

o s h ib a

,

a v is th e

w

ho

N

o

w o rke

d

d G ia c c o

r

ye a rs r o n

n

ld

o

i fo

h a v in g le d to th e d is c o

a t th e tim e

,

m a k in

gy

an

d

a s tr o n o m

t o f th e p e r s is te n t a n d

w o rd s :

g h im th e

o

v e ry o

r

'

I

am

d th e p ıo p e r tie s

o

am aze

on

y th e

u n re ı en

tin g

d th a t fla s h e s

f n e u tr in

o s c an

n ex t

ld e s t e v e r

o

e

ye a r

,

an

re c

d

ffo r t d e v o

f lig h t in

b e lin k e d in

su c

th e

f c o s m ic X ip ie n t

th e s o la r n e u tr in o e x p e r im e n t, J o h n B a h c a ll,

c o s m o lo

be ı

ts , a n d w ith R ic c a r d o G ia c c o n i Th e

to a s tr o p h y s ic s , D a v is a n d K o s h ib a fo

id p ľ iz e fo r

w

s h a re

p e r im

c o n tr ib u tio n s

lla b o r a to

h ie v e m

x

io k a n d e

g

a v is w a s a lm o s t 8 8

p e r iın e n ts

re o

h ic h h e

n e e r in

ke E

o m e s ta

n e u tr in o s , a n

e x tr a o r d in a r y a c ex

w

d Su pe r K

d fo

o sm

b e l P r iz e

p e r a tu

te m

Fc

d th e D

n e u tr in o

w a

io k a lr d e

s o Iu c e s

a w a rd e u

p h y s ic s fo

r

w a s a w a rde

d e te c tio ra

T h e 3 0 ye£uS ı o 11 g H

te

o

su m m e d

te d to th e

a m

h

a

w as

in

e

,

th e

b e a u tifu l

y

Scanned by CamScanner

d

c ï 11 lh c o r

dircnl

(S e c tio

c o n te x t

ith in it b y H

w

c

l

2 4)

n

(M

an

e

M

aR

c

e

c

p h \ ıı

t

a n

r e tt « h a w e «l 15

y c a r * la te r a lth o u g h ın a c o m , p le te ly g # ta r lo n n a tio n b y r a v it i g at o naı c o lla p s e )

r c it w a # H [ u «ly in

d th c te m e r a l p u rc b y

h a v e I'ľ o

w e

,

E q u a tio

m

(2 2 4 )

n

'

P h e r e Ą is th e p r e s s u

w

y

d

r e a t th e c o r e ' s

"

P d v

S u b s titu tin g

r e la tio n

(9 1 8 ) a n d V c

g iv e n c o r e m a s s th e p r e s s u r e 八 一 O at ìd iu s fr o m R

Ps

v a lu e

u m

m ax

a

/3

ow

M

3T

fo

n

id e a ıis o th e r m

r an

T M

(9 ]7 )

n

,

d a r y in c r e a s e s

lıc

c

lgas,

w e o

w

b ta in

ith th e

c o re

(9 2 0 )



T.

a

(9 18 )

c

in to E q u a tio

th e c o r e b o u

o cG

,

Ī

=

.

o

-

d a ry N p d v

at

,

a m a x im

u n

4 7r R

=

:

or a

bo

Ž

=

\a

P.V , +

°

t

Ąc e G M

gT Ł

c

lıc

r.

lla s e u n d e r ld 0 A c o r e o f r a d iu s R . < R o w o u c o p g d p s /d R . = d i s R . > R . Th e external p r e s s u r e F o r a c o r e o f r a u o w n g r a v ity , w ith o u t a n y T h u s th e m a x im a l p r e s s u r e b e s m a lle r th a n P s m a x )r e s s u r e a t its b o u n d a r y w o u ld f c tio n o f th e c o r e m a s s is n d a ry a s a u n t c a n b e a tta in e d a t th e c o r e b o u am e

d by

s e ttin

.

ps

h is p r e s s u e x e r te

re

,

d b y th e

ñ g lir a tio

n w o u

e x e r te

pe

ld b e p o

=

c o n s ta n t

h

ith in th e c o re a ttc r w th e ı e s tim a te

,

th e g a s w

d by

e n v e lo

m

M c) ax (

To

s s ib le

,

H

(9 2 2 ) b a la n c e th e p re s s u r e P e . th e c o r e to b e a nìa y a ssu m e

m u st e

fo r im c o n d itio n s ta b ility h e t e c en

1S

G M

P$

m ax

(M c )

=

nt c o n s ta

M

ır

. õr

8

r

R

2

is o th e i? n a l c o

re

(9 2 3 )

4

w

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

Scanned by CamScanner

9 S

I6 7

H e lı u m

bu

pn ı n l

ı n th ı

c o re

u m in o s ity t m r e ı a tio n Ib ľ C e p h e id s d e r iv e d fr o T h e p e r io d ı Figu r e 9 8 9 6 8 ), A s tr o p lty s J 15 1) d e a n d G A T a m m a n n (ı fro m A S a n a g

o

m

b s e r v a tio

n s

(

It tu rn s n o s ity o

u re

f

a

o u t th a t a w e

C e p h e id

9 8 T he

ı l d e fin e d

s ta r

L

w

e e n th e

d its p u ls a tio n p e r io d P c e p h , fro m o b s e rv a tio n s o f C e p h e id s

rg e s r a te lu m in o s itie s

,

is ts b e tw

c c p l, a n

c o r r e la tio n e m e

d is ta n c e s fo r w h ic h a c c u Im a g in e n o s e s ta b lis h e d

c o rr e ı a tio n e x

can

b e d e r iv e d ,

an

(a v e r a g e ) lu m i in F ig

a s sho w n w

ith

d th u

w e

L

s

c

e

ll k n ph

o w n

(P c e p h )

l t r of th a t a p u ls a tin g s ta r is d e te c te d in a d is ta n t c u s e ta r h c h a r a c te r is t ic o f C e p h e id s If t e s ith e r io d P

a p d is ta n t g a la x y w o bs its s p e c tr a l c h a r a c te ń s tic s ) its a p p a r e n t l d o n o s b a e id s h a C e ep ( d e n tifie d a s a s ı h ic h b s e d to d e r iv e its d is ta n c e d w bń g h m e s s Io b . A n d its p u ls a tio n p e r io d c a n e u l te r o r g a la x y w ith in w h ic h it r e s id e s s a ls o th e d is ta n c e to th e c u s s ta rs o r a

,

,

,

e p h e id s c o n s titu te w o s t a c c u r a te a n

d

re

ha t

a re c a

lia b le

lle d in

a n d a r e th e y s ta n d a rd c a n d le s T h e p e r io d lu m in o s ity r e la tio n s h ip w a s id s in th e n e a r b y a n L e a v itt fo r th e C e p h e

a s tr o n o m

g th e m r ie tta S w

am o n

d in 1 9 12 b y H e n d (o r S M C ), a n d th e s e s ta r s im m e d ia te ly a x y c a lle d th e S m a ll M a g e lla n ic C lo u lu m in o s ity re la tio n h a d a lr e a d y v e r y th e p e r io d se to fa m e A y e a r a fte r th e d is c o h e r fa m o u s a s tro n o lT ie r s to d e te r m in e d is ta n c e s en u s e d b y H e r tz s p r u n g a n d o t a x ie s ga ı

r st d s c o v e r e

,

,

N o te

W ith in

o u r ow n

G

a la x

y th e

r e la tiv e

b r ig h tn e s s

o

f

s ta r s

in

a

g iv e n

v o

lu

m e

is

t g a la x y , h o w

e v e r l a ľ e a ll rs o f a d is ta n d b y th e ir d ifre r e n t d is ta n c e s S ta l i s e th e d is ta n c e to a g a a x y s fa r la r g e r y d is ta n t fr o m a n o b s e i v e r o n E a r th , b e c a u i e u a l to th e r a tio o f f a p p a r e n t b r ig h tn e s s e s s q s s iz e C o n s e q u e n tı y th e r a tio o l s e s a r e fa r m o r e r e lia b le fo r H e n c e s ta tis tic a l a n a y # u m in o iń s e s fo r th e s e s ta r s M a g e lla n ic C lo u d s n th e n e a i b y g a la x ie s s u c h a s th e

e ry a fte c te

Scanned by CamScanner

D

its h ig h te m e r a tu r e s e n s itiv it h e liu m b u r n in o c c u r s in a c o n v p y, g e c tiv e c o r e (a s d o e s h d y r o g e n burning b y m e a n s o f th e C N O c y c le ) T h is is th e in n e r p a r t o f th e la r g e r h e liu m c o r e w h ic h r o w s a s a r e s lt f h u d o r o g e y g n burning in th e s h e ll s u r r o u n d i n g it S o lo n g a s th e in n e r c o r e is c o n v e c tiv e , its c o m o s itio p n is c o n s ta n tl m ix e d a n d t u r n s g r a d u a ll y y fr o m h e liu m to c a r b o n a n d o x yge n a lth o u g h h e liu m burning, w h ic h v a r ie s w ith te m p e r a tu r e a s T 4 o , is c o n fin e d to its v e r y c e n tr e W h e n th e in n e r c o n v e c tiv e c o r e b e c o m e s d e le te d o f h e li p um a n d he n c e burning w ith in it s u b s id e s c o n v e c tio n is q u e n c h e d a s w e 1ı T h e s ta r c o n s is t s o f a c a r b o n o x y g e n c o re s u r r d o u d n b e , y a h e liu m la y e r re m n a n t o f th e o r ig in a l h e liu m c o r e w h ic h , in tu m i s s e p a r a te d fr o m , th e h y d r o g e n r ic h e n v e lo p e b y th e h y d r o g e n burning s h e ll H e liu m burning c o n tin u e s in a s h e ı1 a t th e C 0 c o r e b o u n d a r E l v i o u t o n a r y p a th s in th e H y R d ia g r a m u p to h e liu m burning n a s h e ll a r e tr a c e d in F ig u r e 9 9 fo r s ta r f s o d iffe r e n t m a s s e s a n d th e c h a r a c te r is tic tim e in te r v a ls a r e lis te d in T a b le 9 4 A c o m p a r is o n b e tw e e n th e o r y a n d o b s e r v a tio n s is m a d e p o s s ib le b y v a r y in g th e s h a d e o f th e a th s m p F ig u r e 9 9 in p r o p o r tio n to th e l e n g th o f tim e s p e n t a n d h e n c e to th e n u m b e r o f s ta r s e x p e c te d to b e o b s e r v d e in e a c h p h a s e A m o n g c o r e h e liu m burning s ta r s th o s e o b s e r v e d m e p r e d o m in a n tly th e lo w m a s s o n e s p o p u la ū n g th e h o r iz o n ta l bra n c h u e to

,

,

,

,

,

9 6

The

.

T he

c arbo n

o x

yge n

rm

a

lpu ı se s '

c o r e s e v o lu

a n

d th e

asym

p t o t ic g ia

tio n a r c o u rse a n d y

its e rgy so u rc e s , th e c o r e a r e s u lt , th e e n v e lo p e e x p a n d s a n d c o o ls , a n d c o n v e c tio it A s th e in n e r b o u n d a r y o f th e c o n v e c tiv e e n v e lo e p b o u n d a r y o f th e n o w e x ti n g u is h e d h y dro g e n m a in ly h e liu m a n d n itr o e g n , is o n c e m o r e d re d g e d u p an to th e

h e liu

m

'

c o re s

D

ev o

id

o

fen

n

c o n se

t b ra

qu

n c

h

ila r e n c e s a r e s in ı

d h e a ts u p a s bo u t a in tĺ ? o u g

c o n tr a c ts a n

n s e ts

in

o v e r la

ps

a

g th e

u te r e a r lie f o

te ria l p ro c e sse d m a e ix e d in to th e e n v e lo p

burning s h e ll

,

,

d

m

Scanned by CamScanner

Lo g

9 9 E

re

a r ke

vo

lu tio

n a fy

d ) u p tjo th e

s ta

in th e H

p a th s ge

o

f h e liu

m

(Ħ )

R d ia g r a 】n fo r

burning n

a she

s ta r s o

ll T h e

l 4r t ◆ f dÀ iff e r e n t in itia l e

sha de o

f th e

se

gm

mm aa sc sc pe sç

e n ts

is

5

re » m le s s th a n 10 y r (lig h t) to m o h p h a s e r a n g in g o e o h e s in d ic a te d b y n u m b e r s 4 T h e d iffe r e n t p a s 9 l b e T a i n n Op y f (d a r k ) a s g iv e h ic k s h e ll 5 h y d ro g e n burning in t t r a c tio n ; 3 n o l c l r a e Ł m a in s e q u e n c e 2 3 , o v iu m burning 8 9 e n v e lo p e 10 c o re h e ı b ra n c h ; 7 t i m d r e 7 g l n a m m H in g 6 , eł A s lıu p lłv s 5 ) A n n R e v A s tn m 7 6 9 ) ] J ( r n a io n (a ? p te d fr o m I Ib e

"

f th e tim

e s pe n

t in

eac

,

,

,

,

,

,

.

,

io r T h e its d e e p in te r

h e liu m

th e c o r e in te f r u p te d b y o w ith C b r a n c h p o p u la te d b y s ta r s

Iıa s b e e

n

' tru m s ta r s s p e c

in th e

a rs l m e n ts a p p e g n a tu r e o f th e s e e e i k in g p la c e n ł s to th e p r o c e s s e s ta

burning e p is o d e

c o re s ,

,

w er e

ffe c tiv

e te m

p e r a tu

he re s a t t

bo

u n

d a ry

o

is

ca

lle d th e

,

g a in b e a n n g e x p a n d in g s ta r a

T h is p a ıt o f th e u s tm ı p ıu ıic g ia n t

b r b id d e n f th e H a y a s h i

zo n e

Scanned by CamScanner

T he

9

17 0

ic t u d e t a ile d p

a

fs o f s ta u t io n ev o ı

re

1 o e yr o t yr

0 25

0 20

0 15

2

ěĝ@



ķ

Į

0 10

j

r l

ı ,

0 05

!ı T im

F ig u

re

v o lu tio n

9 1o E

o

f th e in te r io r

h e D q u e n c e to th e A G B p a s D v e c tiv e z o n e s (iĮ d a p te d fr o m se

N

o te th e o c c a s io n a

H

e n c e s ta r s

th e a

fo

bo v

C

l c h a n g e s in tim

(1 0 6 y e a rs )

s tr u c tu r e

in d ic a te

P r ia ln ik

an

83

82

d G

o

f

6M

a

n u c le a r

o m

o

de l

burning

S h a v iv (1 9 8 0 ) A ,

a n

s ta r

d

fr o

sha

s tr o n

A

th e

m a in

o n e s

con

m

de d

s tn o p h y s

8 8)

e e sc a ı

in th is p h a s e o f e v o lu tio n (k n o w n a s A G B s ta r s ) a r e e v e n b ig g e r th a n th e y a r e n o w b e c o m in g s u p e rg ia ııts C o o lin g o f th e la y e r s re d g ia n ts

rm e r

C 0

e th e

a rk a r e a s

e

81

80

O

;e ig n ite la te r

on

g u is h e s th e h y d r o g e n burning s h e ll t e m p o r a r ily ; it w ill e n v e lo p e e x p a n s io n w ill c o m e to a h a lt C o n tr a c tio n o f th e

c o r e e x tin ,

a fte r

c o r e r a is e s th e d e n s ity u p to th e p o in t w h e n e le c tr o n s b e c o m e d e g e n e r a te a n d s in c e d e g e n e r a te m a tte r is a n e ffic ie n t h e a t c o n d u c to r th e c o r e b e c o m e s is o th e r m a l A n illu s tr a tio n o f th e internal e v o lu tio n o f a 6 M s ta r fr o m th e m a in s e u e n c e u to ,

,

th e o n s e t o

f th e

z o n e s, c o n v ec

a re

m a rk e

tiv e

d T he

n o te w o r th y

T h e re

1

N

a r e th r e e o u ts ta n

u c le a r

d in g

c h a r a c te r is tic s

fo

r

A G B

s ta r s

burning ta k e s

p la c e in tw o s h e lls a th e r m a ll u n s ta b le c o n ń g u y lo n g s e r ie s o f tlie n ?ta l p u ls e s T h e lu m in o s it is u n i y q u e ly d e t e r m in e d b y th e c o r e m a s s in d e e n d im ttı th e to ta l m a s s o f th yot p e s ta r A s tr o n g s te lla r w i n d d e v e lo p s a s a r e s u lt o f th e h i h r a d i ti in th e e n v e lo e th e a o n p re s su r e g p s t a r th u s l o s in g a s ig n ific a n t f r r a tio n

2

o p q p to tic g ia n t p h a s e is g iv e n in F ig u r e 9 1 0 c h a n g in g burning z o n e s a n d b o u n d a r ie s b e tw e e n r e g io n s o f d iffe r e n t c o m p o s itio n r e m a r k a b ly d iffe r e n t e v o l u tio n a r y tim e s c a le s a r e p a r tic u la r ly

as y m

le a d in g to

a

,

3

,

ac

tio n o f its m a s s

Scanned by CamScanner

9 6

w

e sh a

ll n

T he

a d d re

o w

rm

a

ıp u ı se s

h

ss e ac

c

a n

d th e

y

y m p t o t ic ia g

n

t b ra

n c

ı7 ı

h

h a i a c te r i

s t ic in 11 1 o r e d t e a il T h e t ls w o b u r n in g s h e ı y d u r in g th e a s m y p to tic ia n t g h a s e p a r e s e p a r a te d b e x te r n a l s h e ll a t y a h e liu m th e b o tt ay o m o f th e h d r o g e n r ic h e n v e lo e y i h bu rn s t s u n c r e i a s n n e p g th e h e liu m ı hyd ro g a y e r 's m a s s T h e in te l r h n l l a s e o n to p th e b u 】7 1 s h e liu m th u s e a tin C o c o re , g in to th e h e liu m l a y e r a n d b u ild in In p r in c ip le a s te a d g u p th e c o c o re y s ta te c o u ld b e a c h ie v e d w ith th e tw o b u r n in g n c in g o u tw a r d a t th e s a m e r a te H lro n ts a d v a o w e v e r th e r e a t d iffė r e n c e s b e tw e e n g n u c le a r b u r n in g p r o c e s s e s d o n o t a llo w th e tw o s u c H a s te a d o p y s ta te to d e v e ı h a p p e n s , th e tw o s h e lls d o n o t t i s A su ppl e n e r g y c o n c o m ita n tl y y b u t in tu r n r o c e s s a n d th e m a s s o f th e h e liu in a c y c lic p la y e r s e p a r a tin g th e m c h a n g e s m

s u p p ly th a t he er T

e n e rg

,

,

,

,

,

,

,

,

,

,

d ic a lly

Ū p e r io

D w

u r in

h ile th e s

g ro w te m

in

p e f a tu r e

re s e m

o st o

m

n e r sh e

m a ss

burning n lo w

g in

at

f th e ll is

W ith

its b

a se she m

m a s s s ta r s a t th e

th e n u c le a r e n e r g y g e

y c le

'

e x tin c t

n o

th is th in

iu b le s th e h e ı

c

s

du

r a tio n

h y d r o g e n is burnt in th e external s h e ll lt th e h e liu m la e r s e a r a tin th e s h e lls y g p ,

A

s a re su

e n e rg y s u

p p ly , th is la y e r

be c o

su

m

e s

ll is th e r m

c o n tr a c ts a n

d h e a ts

u

p

u n

til th e

ffic ie n tly h ig h fo r h e liu m to ig n ite H e liu m a lly u n s ta b le a s e x la in e d in S e c tio n 6 2 it p ,

fla s h th a t ta k e s p la c e in th e e le c tr o n d e e n e r a te c o r e s o f g tip o f th e g ia n t b r a n c h A t th e p e a k o f th e s h o r t liv e d fla s h n e ra

tio n r a te

re a c

h e s 10 8 L

o

T he

e n e rg y

is

a

b s o r b e d b y th e

h h d ro g e n g la y e r s w h ic h e x p a n d a n d c o o l A s th e s e la y e r s c o n ta in t e y n s u in g burning s h e ll th e r a te o f h y d r o g e n burning q u ic k ly d e c lin e s D u ń n g a n e li s h e ll h m u h e h t e th e h e liu m burning fr o n t a d v a n c e s th r o u g s h o r t p e r io d o f tim e e x tin c t in to c a r b o n a n d o x y g e n u n til it c a tc h e s u p w ith th e n o w u m in g h e liu m o v e r ly in

,

,

,

,

,

d ro g e n

she

ll

i

f

h h e liu m burning s h e ll le a d to a c h a n o T h e h ig h te m p e r a tu r e s a tta in e d in t e b y tr a c e s o f h e a v y o f th e s e n e u tr o n s n e u tr o n s C a p tu r e e a c ū o n s th a t p r o d u c e s i to p e s th e c r e a tio n o f tr a n s ir o n s o t in th e s h e ll le a d s to e m e n t s th a t a r e p r e s e n tio n 4 8 b v th e s p r o c e s s e x p la in e d in S e c i n ite fr o n t c a u s e s th e h y d r o g e n to r e g burning l i u m h e t h o h e f t i o T h e p r o x im ty h ll is s ta b le h y ? o g e n burning in a s e t e m p e r a tu r e o t i t i i v t s n e y D u e to its le s s e r s ib ń u m A t th e s a m e tim e th e r m a l e q u il a d ju s t in to i t s d n d e y n a T h e te m p e r a tu r e te m p e r a tu r e n o w e la tiv e ly lo w u lt o f th e r h e d a s a re s c n e u s le b e g in s um q burning i in ity T h u s a n e w c y c l l a n d its v c h e s burning r e \ a ilin g in th e h y d r o g e n a 5 /ıe ll l a s h , is l k n o w n a ls o a s u ls e c y c e , l a m r p h e h e e v o lu tio n th r o u g h o u t a t th e d r e d g e u p o f l n o te w o r th y is p a r tic u la r y 1 1 9 i u re i e r b o u n d a ry o f o w n s c h e m a tic a lly in F g b y th e m o v in g n n e n v e lo p e e i v t c e v co n c e s s e d m a te f ia l in to th e ,

,

d r e d s to th o u s a n d s w e e n hu n v a fy b e t d s i o r he pe b o n o x y g e n c o re c a u se t e se c a n n o t b e o b s e r v e d b e th o f th e c a r e g ro w h t i s l e c lt o f e a c h c y e a r s T h e la s tin g r e s u A G B s ta r w ith a c o r e s ity o f a n l u m in o e h t t f h e liu m w th a t th e o n s e t o tio n s s h o w e ll p a s v o lu tio n a r y c a lc u la i s now r a t s th a t th e i s M o 5 M o r e c a ll n g c >

(

Scanned by CamScanner

b

F ig u

re

(n o t in s ta

9 ıI S k e tc h s c a le

ge s b

h e liu

an

) H y?

d

W

c

o

o

f th e p r o g r e s s

g e n is

n en

in

,

burning s h e ll s

th e e n v e lo

pe

c arbo n

yge n

o x

burning

d d re d g e d

an

is q u ite

s ta

ge

c

a c c u r a te

n at

19 7 1 W L

/L

lla r

s te

n o te th a t

3 2

-

o

fo

e

f th e

ly

re

×

10 M

s ta g e s a a n

d d

o

ge n

s u r fa c e

an

/M

o

m

,

w

h ile h e liu

S ta g e

a

'

is

m

in w

burning d u ń n g ard

burning p r o d u c ts

d h e liu m

is th e

p r e s e n te d b y th e fo llo

6

×

10 4

(

w

sa m e

in g

0 5

ń r s t p o in te d in o s ity is o f th e o r d e r

m a ss, a s w a s

th is lu

4

th e r m a l p u ls e c y c le th r o u g h it s d iffe r e n t s ta g e s

as a

,

b e y o n d th e ix e d in to

a re m ex ce

p t th a t th e

th e e x p e n s e o f th e e n v e lo p e

-

r e g a r d le s s o

a

th e o u te r c o n v e c tiv e z o n e e x te n d s

,

p to th e

u

ha s g ro w

c o re

f

burning d u r in g

b o u n d a ry , h y ?

'

m

o

(s e e S e c tio n 5 5 ) T h u

tio n

(9 2 6 )

,

o ut o

r e la

by B

o

h d a n P a c z y ń s k i in

f th e E d d in g to

s s ta r s o

f th e

sam

lu

n

m

in o s ity

e c o re m a ss

th e s a m e h e ig h t o n th e a s y m p to tic g ia n t b r a n c h in th e H R d ia g r a m r e g a r d le s s o f th e ir e n v e lo e m a s s S ta r s r e a h th c p e a s y m p to tic g ia n t b r a n c h a t d iffe r e n t p o in ts , d e p e n d in g o n th e m a s s o f th e c o r e a t th e e n d o f th e c e n tra l h e liu m burning s ta g e T h e y c lim b u th e b r a n h c , a s th e c o r e c o n tin u e s to p gro w d u r in g th e th e r m a l p u ls e s s ta e A t th e s a m e tim e th e g are

u n

d

at

,

e n v e lo

n o t o n

ly

a t th e e x

pen

se o

f

c o re

th ,

bu t

m a in

pe o f

m

a ss

d e c re a s e s

,

ly b e c a u s e m a s s lo s s a t th e s u r fa c e H e n c e th e p o in t a t w h ic h a s ta r le a v e s th e a s y m p to tic g ia n t b r a n c h is d e te r m in e d b y th e m a s s o f th e e n v e lo e t p a th e e n d o f c o r e h e liu m burning a iıd b y th e in te n s ity o f th e s te lla r w in d T h i s b r in g s u s to th e h i t r d c h a r a c te ń s tic of A G B g ro w

s ta r s

T he

o u te r la

y e r s o f g ia n t a n d s u p e r g ia n t s ta r s a r e s u f fic ie n tl c o o l fo r a to m s to y c o a le s c e in to m o le c u le s a n d m o le c u le s in to ti n y d u s t a r tic le s It is th e s e p a r tic le s p th a t a r e a c c e le r a te d b y th e ra d ia tio n p re s s u re th a t d r iv e s th e s te lla r w in d (s e e S e c tio n 8 5 ) H O W e v e th e n a tu re o f su c H p a r tic le s a n d t h in te r a c tio n s in v o lv e d a r e e x tr e m e ly d iffic u lt to c l a c u la te a n d th e r e s u ltin g m a s s lo s s r a te d iffic u lt to a s s e s s A t th is p o in t th e s te lla r e v o lu tio n th e o r y h a s t o r e ly o n o b s e r v a tio n s in ,

Scanned by CamScanner

9 7

The

su

p

ı n d

e rw

d th・ ı p ın

a n

ta r y n e b u ı a phm e

e

ı7 3

its p u r s u it o f th e chan g in g s tr u c tu r e o f or s ta r s o b s e r v a t io n s o f r e d r n d s u p e g ia n ts r e v e a l th a t th e a s t s e s ta ıs l an i o se m a ss 9 g t r a te s r a n in a 4 g g fr o m 1o M o p e r y e a r M a s s lo s s is e n e o r a ll g to 1 y classificd n t o tw o t e s o f in d » w yp o n tin u e d e r to c

A

s te

lla r

in d th a t m

y b e d e s c r ib e d b y a n e m p ir ic a l fo r m u la d u e to D ie te r R e im e r s lin k in g th e s te lla r m a s s r a «liu s a n d \ u m in o s it y b y a r e la tio n o f th e fo r n i (8 3 1 ) th c c o n s ta n t b e i n g d e te r m in d f e ro m o b s e r v a tio n s o v e r a w id e r a n g e o f s te lla r p a r a m e te

1

w

a

,

,

,

rs

L

r y p ic a l w in d

is ū c

M

L

,

e ffic ie n c y in

A

2

su

pe

rw

r a te s a r e o

d R

an

m

in d ,

v

a lu

f th e

e s

e n tu m

o m

e s s e n tia

lly

o

R

o rd e r o

im p ly ¢ tr a n s fe r

,

a s tr o n

ge r

M

M

o

6

f 10

-

w

M

o

yr 1 in E q u a tio

ı

o

The

pe

su

rw

in d

a n

n

in d le a d in g to o u n d in g th e ,

d th e p ı a n e ta r y

w

,

e s h e lıs u rT s te lla r e je c ta in a n o b s e r v a b ı

9 7

'

yr

n e

(9 2 7 ) h ic h fo

r c

h a r a c te r

(8 3 1) th a t is ,

a c o n c e n tr a ce n

,

a

h ig h

tio n o f th e

tr a l s ta r

bu ı a pha

se

p e r w in d is im p o s e d b y tw o d iffe r e n t a n d in d e p e n d e n t d h ll fo r m e d b y th e b s e r v a tio n s : fir s t, th e M g h d e n s ity w ith in th e o b s e r v e s e s lo w w in d w o u ld h a v e g iv e n r is e to m o r e d ifFu s e s h e lls ) a n d s te l A r e je c ta (a s b n ch l ti e p a u c ity o f v e r y b ń g h t s ta r s o n th e a s y m p to tic g ia n t r a s e c o n d ly , th e r e a v lla r s a m p le s H R d ia g r a m s o f s ta tis tic a lly s ig n iń c a n t s te h th e s e c o n d o b s e r v a tio n is n o t s tr a ig t d T h e in fe r e n c e o f a s tr o n g w in d b a s e o n b o f i e r m s o f s im p le a r g u m e n ts T h e n u m e r fo n Ą a r d b u t it c a n b e u n d e r s to o d n t R d ia g r a ]n is c h in th e H th e a s y m p to ū c g ia n t b r a n s e x p e c te d to r e s id e o n d b le s h e ll burning e v o lu tio n a r y i e s p e n t b y s ta r s in th e o u p o r tio n a l to th e t m b ta in e d b y c o n s id e ń n g o n ly th e h is tim e s p a n m a y b e o a s e A n u p p e r lim it to t h y d r o g e n in to c a r b o n a n d o x y i ll A G B s ta r s tu m e v o u tio n o f th e c o r e E s s e n t a y t l e m a te r ia l If Q is th e a m o u n n se o f e n v e o p \ r e s a t th e e x p e 0 o c " C i n r w o g , g 1kg r o u g h ly 5 × 10 e r u n it m a s s , c e ss 1 e e x is te n c e

o

f th e

su

,

,

,

c le a r e n e r g y r e le a s e

rm a

l e q u ilib r iu

im p lie s

m

M

e

)m

L is th e lu m in





c

e o s ity a v e r a g

E q u a tio n (9 2 6 )* w

e o

M

.

d

l ııc ıı Y o v e r a 【n til

"

b ta in u

p

,

p

d in th e p r o

ıH

c

0 5M

=

7 2

×

10

7

yr d t

(9 2 9 )

o

T Scanned by CamScanner

A t th e b e g in

rıin

g

o

oıutıon

The

9

74

f th e

f

o

ia rıt p h ? ic p ta t g

asym

M

o an

d M

c e n M . in te g r a tin g b e tw e h? i c g ia n t p t o t m d u r a tio n o f th e a s y p

E

v o

an

lu tio

n a fy

a ss o

M

th e s ta r

f

.

M

-

r¢

e

一 c a fe

th e

ha s

M

ppe

r



ņ



im it to th e ı



一 一 一 一 一

)

(

(9 3 o )

y"

f th e fo

¡ n it ia l c o

re m a s s



˜

rm

一 一

(9 3 1 )

bM O osü +

c

c

e

o

o

M

m it« s

一 in a rı u w e o b ta

ch

m e

m

th e ts b e tw e e n tio n e x i s th a t a r e la

w a tio n s s h o c a lc u ı

d th e in itia l m

ı

« t ıı pı

« d

d・

,

"

lly , a fu n c t io n o f th e in itia l i k w h e re a a n d b i l s te lla r m a s s e s s n o w n th e ib u tio n o f in it a h e fo r e if th e d is tr fo r a n y g iv e n d t e u s te lla r m a s s T e r m ia n t b r a n c h c a n b e c o p th e a s y m p to tic g B n u m b e r o f s ta r s o n G s ta r s e x c e e d s b r ofA h e x p e c te d n u m e i t turns o u t t e A s s t r f a s o i l t n o d is c r e p a n c y b e in g a s po p u a r s w ith th e f o b s e r v e d A G B s ta b y fa r th e a c tu a l n u m b e r o d b y s o m e p r o c e s s fr o m a r e p r e v e n te e a n s th a t s ta r s la r g e a s a fa c to r o f 10 T h is m h ile lo s in g m a s s a t th e tic g ia n t b r a n c h , w o n th e a s y m p to c o m p le tin g th e ir sojourn th e s u p e r w in d w h ic h i s T h is p r o c e s s d b y R e im e r s s fo r m u la m o d e r a te r a te d ic ta te i a l p o s s ib le e h a s g r o w n to its m a x m m a s s b e fo r e th e c o r l c o n s u m e s th e e n v e o p e t o r e h o c t e l l g r o w b y o n ly t a ow u s t b e s o in te n s e a s o s iz e In fa c t m a s s lo s s m ld b e m e n tio n e d th a t in tir e e n v e lo p e is e je c te d It s h o u h a b o u t 0 1 M o w h ile t e e n a r e c o n s ta n ts

a d d itio n to th e

b s e r v a tio

o

so m e

th e

A G B

h ig h

m

n s o

in d ir e c t in d ic a tio

f

h ic h

s ta r s w

lo

s s r a te

is

e n ce TAG B

is ,

e s s e n tia

th e h y p o th e s is o

n s

j

e e c t m a s s a t r a te s o

th o s e b e lie v e

s ta r s a ss

H

d to d e s c e n d fr o

a s s o c ia te

d

w

ith

a

fa

su

f th e

o

p e r w in d is rd e r o f 1 0

r e la tiv e ı y lo

m

ila r to th a t o f R R L y r a e s ta r s a n d C e p h e id s th a t w e h a v e e s ta r s k n o w n a s M ir a s , o r lo n g p e r io d v a ń a b le s p u ls a te rde r o f a y e a r

s im

o

4

ass

M

ńrm

o

p ro

,

n c o u n w

yr

ed

by

1

In

一 一

=

鲁 国

g e n ito r s

e n v e lo

in s ta b ility in th e

p u ls a tio n

T he s e

m

w

co n



pe

e a r lie r

te r e d

ith p e r io d s

o

f th e

q u e n c e o f th e s u p e r w in d s ta r s o f in itia l m a s s in th e r a n g e 1 M o « M < 9 M o s h e d th e ir e n v e lo p e s a n d a r e le ft w ith C 0 c o r e s o f m a s s b e tw e e n 0 6 M o a n d 1 1M o a M g h e r fin a l c o r e m a s s c o tT e s o n d in t l p g o a h ig h e r in itia l to ta m a s s T h e s e c o r e s w ill s u b s e u e n tl q y d e v e lo p in to w h ite d w a r fs S in c e a s w e s h a ll s e e s h o r tly lo w m a s s s ta r s a r e f ar m w e A

s a c o n se

,

,

,

o re n u m

,

p e c t m o s t w h ite d w a rfs to h a v e b y o b s e r v a tio n s T h u s w h ite d w ex

c o n s id e r a b ly s m a

b e fo r e

m a s se s n e a r

m e

in

0 6M

a r fs o r ig in a tin

lle r th a n th e C h a n d ra se k h ar

d e g e n e r a te , th e s e s ta r s

da n ger

e ro u s

o

g fr o m

th a n m a s s iv e o n e s ,

T h is

c o n c lu s io n

A G B

c r itic a l m a s s a n ,

s ta r s

is

hav e

d he n c e

,

ve

ńĤ ed

m a sse s

a lth o u

gh

o f a c a ta s tr o h i d to p c e n o u e m e n t (c o n tr a r y ń e s ) B u t th e d y o u n d e rg o a sh o r t e i e p s o d e o f p a r tic u la r b ń 1tia n c fa d in g in to c o o lin g , in e r t w h ite d w a r f s

s o m e e a r ly th e o

˜ 。

no

-

左 。 。 、 、



Scanned by CamScanner

9 7

m

Tı ıe

m

a n pı

th ・

p ha

b ıłh

« ır y m

17 S m

qtı m1tł ndetıh y a n lH M k g in m p h a s e n n e T he c s s s p h e r ic a ı s h e ll A n x »r e o r ı nebu ı n fo n n c d h y th c \ Ctidmtcri«ı W he n f th is ı ı ï ìe w lıi n g fm ın th c s u lw r w im l is rc ı n ııv c ı y ekle pm o tr p e e nv e ı k Ę s fin a lly c e a s e & th e « ) rc fn x x 】fn } m lh c in ın ı e n n l a m a s s iw l s ta r s a l th e c n d

cn re s o

o

f th e

a sym

e x k in n e r w

s lig h tly a n

c

d

a s n tĘ s u lt Th c s m a

ı ıc n

ı o pe

w

R h is

n ・n ıc ıM t n ıc l s re ïï ı

c iłu s e s

id B C h w e n lh c s ta r a n d ıls e w m s u h n « ı u e n ıı y A s th e r l s ta r c o n t r a c t th e e fr e c trv e te m p e m tu rc r is e s c o n s id m b ly w h e n iır e n c h e cen a a s in 9 0 00 K th e r a d ia te d p h o to n s b e c o m e e n e r g e tic e n o u g h ıo io n iz e th e ıım m

d ıe ł a

d

an

»

fn

k

nua

r

* Za ræ b ı

ıt ga ņ

th e m

c au se

s ib le s re s p o n ı »

a \n

tn c t s e p a r a tr m

d i«

*

it

a l g h

m a n

a

R is * o r ic a l

D

n o te

e s p ite

t h e fır s t p ı a n e ta r y C h a r le

y

5 Jle a in

Ąm

s e

la te r

D

e* « y ı aı pı

a r q u ie r



ı ie r h e

,

H

O

d

e rg c ł le

o

« r ıı "

,

u n

th o u

d

a

f so

e c e n tly

m e o an

r e so m

d a

m ttx

o

o

b je c

d e te c te d

f th e

ts

g h t th e

p la n ne

H «»w

f th e s e

p la n e ta r y

e

ev er

ne

bu ı a

o

sec o n

d

b u la e

b u la e

fe r in g

h in g to d o

e ta r y n e

e t

U

ra n u s

to

be

w w

b u la

w e re n e

ever an

n e

m

ıth th e

ith

w

b u lo

y be du

Ħo

ĺth p la n e ts

w

e rs c

o

th a t

a fte r a

o

f

u s m a te

ne

e v e n tu a

bń ght

o

f

c e n tr a

ń a ı(g a s

ń a l it

ı ly

ly d is c

ne w

lly it h a s n

a te

s

h ic h

w

lo ı

w e

R in g N c o

e

d

ith

w

A

w as

bo

u t

b u la b y

in e d th c

nam e

b u la e in th e 17 8 0 s H e c a u

c lu s te r s

p re s e n

R u T ıo u

t Th e

he h a d

lv e d

e to th e m

b je c

he lw ho

a v e ry

n ic a

f

o

e t fo

do

g to

ll N e b u

fa d in g p ı an

to a

ific a tio n

u n re s o

d q u ite ir o

m a

H

c la s s

h

su c

be u n rb ł

D

w a s th e n

n o th in

b u la e h a v e

nc

pa ń so

c o m

in h is

b le th e p la n

p la n e ta r y

l s ta r R

ıp e s

o r

S ir F re d e r ic k W illia m

w a s

re s e m

th m

l fo

m

a a ı ïa

raw

to

n am

in 17 6 4 T h e

\W

tb r th e s e

n e b u la

an

It

th e

b u la

e s s ie r

M

s

n e

ith th e d i

w

b e l o ııııd tlıe m

C

ı tM ı

h a n i s m

sa m e

cd a f th is k in d is c a lı )u r c e n g s u m ) u n d in g a p o in ı M A n e x a m p le is g iv e n in e lo n g a te d

In m p s ) A s h in i n g a s a b r ig h t c ir c u la r n

p p e a r tw is te d

(th c

res e e n c c

9 12

F igin e

b

b y fı u o

re s c e n t

p p e a rs

a

s h in e

to

ce o

o r su

o v e re

b je c ts

a

l s ta r th u

s

o

d

A lth o u

fe w

ye

e m a n a te s

p la n e ts

a rs

ith

w

g g e s te d th a t th e p e c t

gh

he be c a 】 m Ee

d u s t ) a s s o c ia te d

f g ıa n

se

o

u

a

lia r

ib itıï ıg th e

S o p la n e ta r y

nc

bu

a e

ll

Scanned by CamScanner





dc ı deı

o

3 0 0 0 0 K th e

g

e

m

Th

b e ıw

Fm

n s

o t* c

th e s u

pc rm

fto n

ı l*ł e

ed

n

een

w w w

beco

re

rı ı e en e

b y fı uo

ń ses

f

o

ı l e n v e lo p e n e ï rm th e s ta r a n d its

s h in e

ı1 $

b« pı

at

p

W ne n

Ķ te ı a t iw ly

-

ew we

massivt

a

T h is

s a n t c o n tra e ¢

c on s

id e r a b ly w

k\

ca u se s

y S u b s e q u e n ¢ı

m

it r e a c h e s

n m

ia

t ic e n o u g h to ro n iz e th e a lo ï n s

w

re s c e n c e

(th e

ı a m p s ) A s h in in g n e b u la a s a b r ig h t c irc u ı ar ń n g su n

o r es c e n t

łıe

w

n id

e sm a

e c tiw e te m

ra

d

p p n ie b

« »

w ww

*

it a p p e a r s b ı¢ı a h o u g h m a n y a p p e a r tw is te d a lı

p*HW l

a \n ı &

th e

n

br Ru ı

s tb le o tı is r e s p

o

.

d ia re d p h o to d c a u s e th e m to

ıla a n n eb ı

dbe

tio n

a s ・ te s u ı :

p ıın

im ) u n d e d þy g ia m p h a s e g in e q \ i m he ın e l a fio r ï n 《 ıb y th e c je c le d m ? r ia l T

«

ca

te s u ı tin

th e c o ¢e

d

tł ıe

h e e n d o f t? tı

ı f ıh is s h e ł

ta a d is tiï ıđ s e ł o r ıl Ĥ a r c ı đı

in d m

» w

o rı e ss

1 1

s lig h tł y an

W

-

s a

p

»

fin a lı y

m

u

f s łÆ

ıa d s lıe ł

p ı* t

a

The

e o re s o

t hc e

T

o r e lo n

g a te d

sm

f th is k in d is

o

d in g

o u n

A

ham

rn e c

sa m e

ex am

n

ı ed ı

ca

p o in t s a \ e is g iv e n pı

* ce

a

m

F iga ï e 9 ıı H is to r ic a ıııo te T ħe fim d is cx n

e «

in e D

Am

) ıa «

ty ı tı

a ıq u ie r

It w

n

fo

a to

be l=

er

H

an

a s ch e

】fo

hat o e m rin e e d ı O

e

« ai

o o ea m

n

R

f so m

so m

d

e o

b u la

b le

th o u

o

f th e

g h t th e m

p la n e ta r y

n e

d im

e r fe r in

a h in

g to d o

ts

b u la

w

g w

n e

d

b u la

m

b u lo

d q u ite ir o a

ith th e flo

w

ith p la n e ts

a

o

f

he lw ho n o

he ha d

n e w

c lu s te r s

ń a l (g a s

h ic h

w

e

d

r

b u ia b y

R iftg N

lı y

co

p re s e n c e

o

fe w

o r su

o

ı

a

th u s

d u s t) a s s o

e m a n a te s

t

p la n

c ia te

e se

he be c a m

d

w

e

i? a ıa r

e ts o r b itin

So pı an

nam

t

u

y ea rs

g g e s te d th a t th e

f g ia n

bo

lth o u g h

b je c ts

o

w as

b ec au

7 a

f

w

A

in e d th e

ı y d i s c o

cenu a

lly it h a s n

ń a l it

w

f n e bu ı 】 th e 1 a c iı

u s m a te

m a te

b u la

e

o us

e v e n tu a

bń g hl

to th e

do

b b trlt N

b je c t Th e fa m

itb

ıiı ıg to ï ï o tł

fa d in g p la n e t fo llo

a \ e fy

n ic a

y be d u e

o

lv e d

u n re s o

ith

n to a

ific a tio

r a n u s th a t

w

ne

h

e rs c

b ııla e h a v e

th e D u m

w as

su c

H

s c la s s

be

io

e w e re

an

b u la e

in M

ne

p a r is o

co m

se c o n

p la n e t U

th e

H O W e w

f 曲ic s G

? te c te d

e \e r

in ı7 6 4 T 13e

b je c

r th e s e o

a

a n e ta r y pı

n am e

S ir F re d e ń c k W illia m

e ta r y n e

e c e n tı y

sı ar a n

y haw

u n

p la n

e s s ie r

as

res e m

o tlıe r s

d

M

s

n e

th e

th e d is c o \ r r y

w r th

b e ım d

e s p ite

p la n e ta r y

d b y C h a r le

a te r n iı

li a

D

e ta t y n e

g th e buı ae

l! fte r a ¡

Scanned by CamScanner

Scanned by CamScanner

W

9 8

ı3 S k e tc h Figu re 9

o

n

it e

f a p la iıe ta r y

W h it e d w

9 8

th e M

a r fs

n e

b u la

ı7 7 ıı?

a iıd

its

e

e

f

n o « ın a «

n u c le u s

t h e fın a ıs t a t e o f

(P N N ) n o n m a s s iv e

s ta r s

d e s c e n d fr o m f c e te m p e r a tu r e p a c t s ta r s o f h ig h s u r a w e ha v e se e n C O e le c m o n Ą e g e n e r a te c o r e s A s w h ic h d e v e lo p s r t a s B G A a l p u ls e s e u n d e r g o in g th e r m t lla r w in d w h iı m a s s b y a s tr o n g s e e l s o s t r a s e th e s d h e lin m in th in s h e u s T h e e n o f h yd ro ge n a n d burning alternate h e t b d y c a u se l e o c c u rs a t a d is s ip a tio n o f th e e n tir e e n v e o p h t a b o u t b y th e u b o r l s s g o ofm ass hase d u r in g th e h y d r o g e n burning p l u ls e If it o c c u r s a h m e r t f a p o e h ra n d o m p a s v e s tig e o f f h y d r o g e n r ic h m a te r ia l a i h n c o a t in g o t h a i t w f t l e b th e s ta r w ill e k s la c e a t th e i h e liu m burning w h c h ta e p d u r itı s r g u c c i o t f I th e lo s t e n v e lo p e l of ill b e c o m p o s e d p r e d o m in a n t y t e r e n v e lo p e w u o h e t bo tto m o f a h e liu m l a y e e f th e p u ls e c y c ı m a ll fr a c ū o n o ta k e s u p o n ly a s h e liu m S in c e h e liu m burning ith a h e lin m r a th e r to tic g ia n t s ta g e w i d n g th e a s y m p n e r t a s f a i l o i b t y p ro b a a lle r is p r o p o r tio n a lly s m tha n a h y d r o g e n r ic h e n v e lo p e lı burning c o m e s to a n e n d a s w e l o s s n u c le a r s s a f m d o s o o n a fte r th e e n h a s e th e fin a l s ta g e o f la n e ta r y n e b u la p d i e v l p t h r o D u ń n g th e in te r v e n in g s

M

o st w

h ite d w

a r fs

co m

,

,

,

,

,

,

,

,

,

,

,

th e

de ge n

e r a te c o r e o

f th e fo

rm

er

A G B

s ta r , w

ith

T he p la n e ta r y n e b u la n u c le u s ld th e r e fo r e e x \ t it d w a r f W e s h o u bec o m e s a w h e the r e m n a n t th in e n v e lo p e l n t o n e s h o w in g h y d r o g e n a : a pre v a e w a r f s p e c tr d t e i h to e n c o u n te r tw o t f w yp e s o d o b s e r v a tio n s c o n fir m h d r o g e n In d e e lin e s a n d a r a r e r t e w ith n o e v id e n c e o f y n lin e s in th e ir yp e n o hy? o ge d w a r fs h a v i t e h w f this e x e % o p c ta tio n a b o u t 2 5 sp e c tr a in a n iu T o w in itia l m a s s m a s s s ta r s w l o i s f s A n o th e r s o u r c e o f w h ite d w a r e r a t u re s to m h h ig h e n o u g h te p o t fe a c t ra n g e o 7 a rs d o n s e s h e T iu m c o r e s 5 M 5 1M o i n tly m a s s iv e h e ı w s u ffic e ign ite d o n o t g ro h e t e y h e liu m s im p ly b e c a u s n d lo s e m o s t o f in to r e d g ia n ts a ĺ o llo th e y tu m e s a h w in g th e m a in s e q u e n c e p ,

,

,

,

,

,

Scanned by CamScanner

ı h y «lm 吕c n b lır n in g (o «1n l r y hoı ı ro w g y th c iı c n v c lo p c s h c tï iyntptotı ı b c tır n in g p h n s o m i ı l u h e 8mu 1c c o ı o 4 M o o r le s s s k ip p in g tı h ceu m o even l r » t a # ı 111\# o l w o w cl ts e th e s e t tr n c b tılu l»h ł p h a s e a n Lì th c p lıin e ł y is tr ib \ıti ı c c L ı th u l m t H «ı m ı ll m o n \in ly o l h c u o s c d n \ı m a s s w h iĺ c d w a r ı c o m 中 h T k s i a c e m ı i u t w n s w ho p p e iık Io d Ir o ın o h s e r v o tio n s s o f w h ite d uv a l ls d e r iv e » N o ı~ 0 ó rv c m a g c m tı s to 0 11 ł M ( f b e lo n g c o ıT o s p o n tı w h ic h m o s t w h ite d w a ı s d 0 4 M tc c o n ı ir m in lh b u n d b c tw c c il 0 2 /þfo n n g u T h e s e c o n d a ry s m a lle r p e a k is ł dwarl u r c e s o r w h ite p re d ic tio n o f tw o d is tin c t s o th e y ľ tlu ia tc Î T h is q u e s tio i n rl e v o lv e n s th e y n m s t s n c e H o w d o w h ite dwił h i i h t w t e d n e t r w ı ı r l s [a c 2 T h e s tr u c tu re o s ile s g w a s c o n s id e r e d b y M e s te l in 19 5 is c h a r a c te r iz e d b y tw o b a s ic p r o p e l tie s tc s lc c u ı c tı w h iı

,

'

,

.

'

,

'

,

,

,

,

'

,

'

,

'

,

,

.

.

.

.

,

.

.

'

,

,

'



d m T h e internal pı ìessule is s u p p lie d p r e o T h e internal e n e ig y s o u r c e re s p o n s ib le d by s u r fa c e is th e th e r m a l e n e r g y s to r e

1

2

de ge n

a

If it h a d

so u rc e s

S e c tio n 6 2 )

,

d is r u p t th e

N

g r a v ita tio en e a ls o

to

gg y

o

,

n a

l

en e

an

,

d

as a

w

rg y A t th e

f th e d e g e n

n

s o m e th in

h ite d w

e le c tr o s ra

s o u rc e o

f

rn

g

f

(fo r

e r a te e le c tr o n s

r e le a s e o

m

s a n to tim e

th e e le c tr o s ta tic p o te n tia le n e rg

first o r d e th e

ne

h ite d w

ca

a t th c

p itc ity

o

l

n u c le a r e n c t gy

n o n s ta

b le

(a s

e ith e r s to

h a p p e n e d to

e

a r fs

it d o c s

c o o ls ,

how

,

w

e v e r , th e

h ic h

se e n

in

p it

or

t¢ o c

p

c o n tıa c [ s lig h tly , r e le a s in

g

h ig h e r d e n s ity

in te r n a l

2 /3

R u d e rm

dM

a lv in

f g r a v ita tio n a l e n e r g y

co m

p e n s a te s fo

is th e th e r m

a

l e il e rg y

o

lo n g

s ta n

f th e io

S e c tio

se e

e s te l a n

y M

(ic e n e rg y T h u s th e y v in d ic a te d th e w

ld h a v

c ı n iltc d

(a s th e h e a t

th e io n s

e ) T h e s ta r h a s g lig ib ı in g w o u ld h a v e b e e n u

w o u

tc e le c tr o n s n ı

s ta r

In fa c t

o te

g a s is u c le a r b u

e le c tr o n

e r a te

in a n tı y by de gc n c lb ľ th e ra d ia tio n

d in g

n s, as

r

r a is e s th e

n s

3 3 .

a n s ho w e

tm

s o ln c

d 3 5) and

d (in ı9 6 7 )山a t

,

th e r is e in d e g e n e r a c y a n d

assu m

if th e

w

p tio

n

h ite d w

th a t th e e n e r8 y a r F w e re r ig id

Scanned by CamScanner

W h it e d w

9 8

14 S k e tc h Fig u r e 9

f th e

o

co n

a r fs

t h e fı n a l s ta te o f

fig u r a tio

n o

fa

lin g

co o

n o n m

ve a ssı

h ite d w

w

79 ı

s ta r s

a rf

ed m a y be a s su m ń e r a tu r e d r o p s a s w e ll a n d r a d ia tiv e e q u ilib u m m la y e r th e te p b a fs it T h e c o n fig u f a tio n e h te m p e r a tu r e g r a d ie n t d e te r m in in g th e lu m in o s y w ith t e o th e d in S e c tio n 9 1 : th e r e to i i ty to th a t o f a fu lly c o n v e c tiv e s ta r d s c u s s e f il a ı i rr s u te r in g in a th in r a d ia tiv e o v a iı i w a s d e te rm in e d b y th e c o n d it o n s p r e i t s o i n y lu m to a n fr o m a d e g e n e r a te s ta te ii s p h e r e ) O b v io u s ly th e tr a n s t o n t h o o h e t p la y e r ( h a r p tr a n s itio n s h a ll a s s 1ım e a s r a d u a l, b u t, fo r s im p lic ity w e i s t e t a s g s a id e a l g h id e a l g a s o u te r a te c o r e a n d t e d a r y b e tw e e n th e d e g e n e r b n u o e c f a r u s a c ro s s a ıv a lu e s d itio n s a r e s u c h th a t e q u a h r e th e p h y s ic a l c o n e i t w n h o t e d s a i e f p ¡ a ye r d e n t th e r a d iu s te g a s p r e s s u r e L e a n d fo r th e d e g e n e r a e r u s e s r s l a id a e h p g tu r e is re s u lt fo r t e F o r r < r b th e te m p e r a i n F ig u r e 9 14 h n w o s s a b r e d a ry b o f th is b o u n i o n s ta n t th e lu m in o s ity s c l e Tc F o r r > rb u l a v t a r n e h c e t d e q u a l to c o n s ta n t a n la y e r r e d u c e tio n s fo r th e o u te r h s tr u c tu r e e q u a T e M in a d d itio n m (r > r b )

,

,

,

,

,

,

,

l

,

,

,

th e re fo f e

,

to

G M

dp



q u a tio n

E T h e fir s t is d e f iv e d fr o m F fro m E q u a tio n (5 3 ) w ith e d e p e n d e n c e o n te m p e r a tu r K

S u b s titu tin g E q u a tio b y E q u a tio o f th e fo r m

n

(9 3 3 )

,

n

=

4 ic



(5 1) w ith

m

M

=

,

an

d th e

se c o n

d is d e r iv e d

e a po w s h a ll a s s u m o p a c ity w e h e t r F o = 3 65) o a c ity la w ( it th e K r a m e r s p a n d d e n s y,

er

la w

,

7 /2

K op T

_

q u a tio n

i a r e la tio n w e o b ta n 16 n a r

戸 瓦引 万

L

E (9 3 4 ) in to

ľ

(9 3 2 )

a c

b e tw

PT

,

9 32) d iv id in g E q u a tio n ( (9 3 3 ) a n d e r a tu r e e e n th e

M T čG 二 T

3Ko

(9 3 4 )

9 /2

p re s s u r

15 /2

dT

e an

d th e te m p

(9 3 5 )

L

Scanned by CamScanner

u t io evo ı

The

9 8o

In te g

T h is

fr o ln th e r a tin g

n r e la tio

,

w

h ic h

ce s u r fa

,

o

n

w h e re

p

T

=

d e t a ile d p ic t u

a

f s ta r s

o , in

=

,

w e

hav

e

h

!

(9 36 ) be

n ìa y

s f th e id e a l g a

o

o s p h e re

fr in g e (a tm

o u te r

d to th e a pphe

ns it b y n le a e de n s y h t o t i n te m p e r a tu R e v e rt g i;ttv a n d th e e de n s y h t n e e d b e tw o b ta in e

is

w a rd

re

e

qu

a

) o f s ta rs

s w e

th e r m a

b e in g

)em

n e g li

in

tio n o f s ta te a r e lą ti ,

on

H

re

e nce

th e

d e p le tio

id e a l g a s o n b o th s id e s o f r n s titu te a n b th e io n s c o e c i n S ld s d o w n to r b r e s s u r e E q u a tio n (3 2 7 n o r t c l e w h ic h h o p l e a d e ) h e r e th e i is th e p o in t w 4 a r e th e s a m e T h is le a d s t it fo llo w s th a t ı1b 3 3 ) i n o ( t , a o E qu tr o n p r e s s u r e n e r a te e le c a n d th e d e g e m p e r a tu r e a t r b s ity a n d te l tio n b e tw e e n d e n a s e c o n d re a ,

,

,

,

C le a r l)\ w o u

ld

w e m u st

r e su

(9 3 8 )

,

w e

lt in

hav e

o

i t t p r e v e n t a ju m p n e m p e r a u r e w h ic h E lim in a tin g p b e tw e e n E q u a tio n s (9 3 7 ) a n d

o r d e r to

T c in

=

u x in fin ite h e a t fı

an

fin a lly

Ą

,

b ta in

6 Ąx

L

a c

G K

r3

5 172 4 x o plıe u

w

h ic h

r e la te s

th e Iu m

in

o s ity e m

itte d

a

In s e r tin g th e v a lu e s o f c o n s ta n ts in E q u a tio n W M t e w a r f c o m p o s itio n (s a y h a lf c a r b o n a n d h a lf o x y g e n ), w

h ite d w

p e r a tu r e o f th e (9 3 9 ) fo r a ty p ic a l

t th e s u r fa c e to th e c o r e te m

a rf

,

w e

hav e

Or

' EXercise 9 3 (a ) S h o w a w

hite d w

a rf o

fm

a ss

(b ) S h o w th a t th e la y e r (e ) C a lc u la te th fr o m L

]

=

10

"

"

(5)

o7

"

(9 4 o

.

th a t th e te m

M

'

an

d

p e r a tu re p r o file th r o u g h o r a diu s R i s g iv e n b y

s th ic k n e s s

t

e r e la tiv e ce h a n mn r e g in 2 L a, to L = 10 4 L 2 o

=

R

rb

th ic k n e s s , L

«

u

of t th e o u te r la y e r

R

I / t 2 Fo r

(n e g le c tin g th e

.

a

s m a ll c

?

o

han

in o s ity p in lu m g e in R )

Scanned by CamScanner

n

9 8

A

hav

s w e

th e r m a

b e in g

l

W h it e d w a lr e a

e

e n e rgy

dy

f th e io

o

the n n a ı s ta te

m e n tio n e n s

H

ence

d e p le tio

r a te

o

f

f

e n e rg

y

e m

a s s iv e

n o n m

d th e e n e rg y s o in th e is o th e r m a l c o re ,

u rc e

o

f

s

a

ta

arf

h ite d w

w

la y e r ' s

o u te r

ı8 ı

rs

c o n

is th e

tr ib u tio n

3 冗

U th e

o

(th e

g lig ib le )

n e

a p fs

I

M Tc

=

2 H

is s io

L

n

m u st e

n

0

(9 4 3 )



q u a l th e

r a te

o

0

a l e n e rg y

f th e r m



中 卅

h ic h

w

e a n s th a t

m

th e

f c h a n g e o f th e lu m in o s it (o r e u iv a le n tl th e c o o lin g y y q s s h a r p ly w ith d e c r e a s in ı t T h u s th e e v o u tio n a r y p a c e g e m p e r a tu r e f l ar s o w s d o w n g r a d u a ll y a n d a w h ite d w a r f o f lo w m a s s e v o lv e s r a te o

,

,

r a te o

f

) de c re a se h ite d w

a w

o

fm

L ' ) to

a

a m

a s s iv e o n e

to c o o l fr o m

M

a ss

,

ly th a n

m o r e s lo w

te m p e r a tu

re

e s tim

a te th e tim e

it w

o u

ld ta k e

a w

h ite d w

in itia l te m p e r a tu r e (a n d c o r r e s p o n d in g lu in o s ity L ), w e in te g r a te E q u a tio n (9 4 4 )

an

(lu m

Tc

To

m

in

a rf

Ç

o s ity

(

,

/L ' « T /L a n d th e tim e r e q u ir e d fo r b y E q u a tio n (9 3 9 ) r a tu r e ) o r l to a te m p e r a tu r e Ą (fr o m a m u c h h ig h e r te m p e a w h ite d w a ]f to c o o i iv e n b y i m u c h h ig h e r lu m in o s ty ) s g d e c lin e to a lu m in o s ity L (fr o m a If

Tc

»

,

th e n

,

5 /7

Tco o l

Fo r

1M th e

p le

ex am

o w

In

,

h ite d w

ı u m in

re a

o

a

bo u t 2

u f to Ł

s ity d o w

lity

,

n

×

2 5

10 9 y r

h ite d w

A t first th e ,

eatca

pac

( )

ld b e

For

4

w he n a w

d

w o u

d f o p to 1 0 L o to 0 1 L o fr o m

,

sa

s

(9 4 7 )

yr

lu m in o s ity o f a h q u ir e d fo r t e 1 0 7 y r w o u ld b in g l p a r is o n o n y it ic a l la n e ta r y n e b u la lu m in o s y

re

co m

,

y th e ty p

p

,

h s v e ry a rf r e a c e

f fo llo w th e c o o lin g r a te n o lo n g e

a ppro a c h e s a n

10

*

6

,

i o s itie s ) lo w te m p e r a tu r e s (lu m n i b e c a u s e th e l t io n (9 4 4 ) T h is s

,

a th e s im p le r e

l ic e lliz e s in to a p e r io d ic a tt a s c r y s ta n i o g e h t ity , d d itio n a l se s u n e s d u e to th e a th e n s u f p a s i o n in c r e a s r e i t t ca ac y p

c o ïT e sp o n

ity fa lls

ra

d in g h e a

p id ly

w

ith

p

tu r e te m p e r a

,

fo llo w in g

a

T

3

la w

T h is

m e an s

th a t

Scanned by CamScanner



jg

A

s 9 ı

w M

Ř* a h Ęa a N \

th e \h ì p in N m

ı i «ıi a ?l \

»qigtLT

M

æ s iw

w LXĄhiæ đ waï q i

l Ĥ

\H \u tŲ

Nw

w

lłu * « \h a \\ M

lmmlçLW$lN

d m ĥ n m \ l0 \it w \ų 4 7 h o l d \w ĘË ŁW t f ı 4 1 \ T h t n u tn b e r \u s N\ttw W 10 m ll l* M h ų \ Q F t i æR i N m s ı h tw \\ in I W hxair a s Ĥ ï n c tĥ w \J th e ir \utniwwity s \ Ę i i ıi & ı ħ) th is e lliix t tĘ w s u t '

.

? \ cong i

lo n g

u i{ * iŅ

n

tl* È

'

t

,

§- w ith

wit

4

L

Ų \5

n Ļ d tĘ s th c lų điu s ł ? a n d hŅ ? n ĥ ų ţ ih @ đi t m is \ n\ial a I = \ w \s ta m (s m *i¥ h u li\w .

W Ł

4 h ın +

ıh e e i h Ę n w w e s i n g

(o n s Æ

t

W 40

ith thıı itıc a tlv w ith umim»ł ity ţ a n 1 n im m t ı r e ıS ItĶ Ę R = R{Ałï he e m lu tio n o f w h itç d w w fs oť d iūť tt ? a is s Ęs c o r ı Ę s p o n d s m & s tr i in th t ¢ Ļ r t li w w w i s h p ł s o w n ln n 彆 & nķ uæ 9 ı P a r t o f this m ip s h ıx tld im le h 11111\ h e a y il y M » P U l a th a n \twx p a it l ıt ? t o F tl« m p id l y a s i n g t w rli \ n t w l i 彆 t t e dwaı rı ï m 【 n e a t lo tw w u a r n R *r huninositis th m & t h i h a n e s T h e s e u »n l i g ť u s «» ts u rų c o n ı in n e d þ o b s e r ţ a ù io n s UnlfĐttunatĘl HOwc\r A Ř w łtitc dwt rĥ a \h \ gt\»w s till ï ininr w

ıh e o Ę te ın p s ra ?

.

ı

d m p s d \le m th e bm ci war

ra p id c o o

9 T lıe

e \Đ lu tic lı n o

te r is tic

s

fm

ł \s

hng

The

ū v Ę s tĉ m

In th e

ţ n d th e y w

e v o lu t i on o

(A to

>

fm

ill tu n

ats s lw

\

inMpmLtĥ iı lb・in \ is ib\i

s ta r s

IO ı u d h a s tl ı t Ř) » e n ı\ ť l\ ll\nvit lı

i

Scanned by CamScanner

'

9 9

Th ・ w

u t ï ın

o

fm * v e



ı8 3

s ta r »



中 っ

コ 三







中 9 ı6 W h ite d w

¢W

ı【a 加

I Th

Sw

A

M

m

ee n ey

eı e c tr o n s

e

burning 2

a r f»

s ta

in th e }4 R d ia g F a m

( 19 7 6 ) A ,

in th e ir

ge s , w

r tm

do

c o re s

h e n th e

L in e s

& A

n

fc o

hy s

s tn w

n o t

o

be c

c o r e c o n s is ts o

,

n s ta n t r a

s

(m

ass

)a r e

m

a rk e

d

fin

a

49)

o m e

f if o

d iu

de ge

n e r a te

u n

til th e

l

C

n

9

u tio n lo s s p la y ti a n im p o r ta n t f o le a lo n g th e e n tir e c o u r s e o f e v o ı h e s ta r s f t e s i h o i t l d t e a m h l h i r e a n s e q u e n c e p a s e (s n c e t e m a s s o s s In c u n g l u n c e r tıa in , th is is a ls o th e r e a s o n fo r th e p o o r e r u n d e r s ta n d in g o f s s tiı ł

M

a li#

th e ir e v o lu tio n

T he

evo

ba c k

an

lu tio

d fo

)

)

u m in o s ity 3 T he ı

o n th e m a in s e

,

w

quen

h ic h is ce

,

n a r y tra c r th

b e tw

a lr e a d y

c lo s e

to

th e E d d in g to n

c r itic a l lim it

f internal c h a n g e s h o ń z o n ta l, s h iftin g

f e m a in s a lm o s t c o n s ta n t, in s p ite o

k in th e H

lo

een

w

an

R d ia g r a m is th e r e fo

d u r in g

e

,

re

ffe c tiv e te m p e r a tu r e s S u c h tr a n id o f n u c le a r burning in th e c o r e a n d r a p h h il t e e th e c o r e c o n tr a c ts a n d h e a ts u p w

d h ig h

p is o d e s d u r in g in te r v e n in g p h a s e s w h e n e n v e lo p e e x p a n d s s itio n s a r e s lo w

C

e

,

w e r fu l s te lla r w in d s a s to re s u lt g 30 M o h a v e so p o L th a n m a in s e q u e n c e tim e s c a le s M Q / m a s } o 8 8 tim e s c a le s M /ı1l s h o r te r to w a r d th a t o f a o lu tio n a r y p a th s c o n v e rg e COnieqmtly th e ir m a in s e q u e n c e e v f th e h e liu m c o r e a t th e e n d o f th e m a in 30 M o s ta r īn particuï a th e e x te n t o v o lu tio n a r y s ta g e s T h e i d h e n c e s o a r e th e e n s u n g e e q u e n c e p h a s e iti s im ila n a n h a s e le a d s to c o n fig u d in th e m a in s e q u e n c e p t e m e m a s ß Jo s s th a t o c c u r s u r g r e n v e lo p e s (X R s 0 1) o r liu m , w ith h y d ro g e n p o o a tio n s c o m p o s e d m a in ly o f h e f h y d r o g e n a n d lo s in g m a s s Ju m in o u s , d e p le te d o o h y d ro g e n a t a ll S u c h s ta r s T hey hav e k n o w n a s W o lj R a y e ıs ta r s e r v e d , b e in g a h ig h r a te a r e in d e e d o b s a n d a re c o n s id e re d a s th e d 10 M

S ta rs

o

a s s e x c e e d in

f [n itia ] m

,

,

Ja tiv e ly lo

w

s a v e ra g e m a s s e ,

b e tw

ee n

5

an

30 M a s s iv e th a n f Eita rs in itia lly m o re n l d i to th e ir N o Rayet s ta r s d is tin g u is h e d a c c o r n g o n d to e s c o r re s p )u n d a n c e 吕 ín th e s e q u e n c e o f ty p E c o re s o

,

o

o

,

T h e re

iu e

d iffe r e n t ty p e s

o

f

p o s itio n E le m e n t li ff f i p ro g r e s s io n n p e e n g o o

s u r fa c e c o m

a

Scanned by CamScanner

Scanned by CamScanner

9 9

Th・

ew

ı u tı o n

f

o

m iM

co

9 ı8 C

lla p s e R

An n

ev

o m

p

o s itio n

BUrning s h e lls A s tr o

n

A

s tr o

p r o file s in th e in

a re m

a rke

d

1

e

8M

n er

(a d a p te d fr o

m

o

o

Fi\

re

m ass

9 ı9 S c h e m

lo

ss

A

o o s le

o

s ta r

p r io

y & T A

r to

w

supernova

e av er

(19 8 6 )

burning

burning

0

bu

Si

burning

rn in

g

a tic s tr u c tu r e o

a

ge

o

in p a n e l (b ) o f th e fig u r e In a lĮ m a s s iv e s ta r s h e liu ,

r ıc n

e n ve ı o pe

burning

e

C

r e c e n t im

25M

a

s E w

m

H

f

p

H

ı8 5

Ī

"

Fig u r e

m aa *ı v ı s ta r s

fm

f

a

sup er no va p r o g e n ito r s ta r

j

a s s e e c tio n

burning in

m

by

a

ty p ic a l W

o

lf R

a

y e t s ta r is

th e c o r e is s u c c e e d e d b y c a r b o n

sh o w n

burning

i iń l t p e r a tu r e is s o h ig h a s to c a u s e s g n c a n e n e r g y o s s e s d u e to n e u tr in o e m is s io n T h u s th e n u c le a r e n e r g y s o u r c e h a s to c o m p e n s a te fo r th e s e lo s s e s a s w e ll a s s u p p ly th e h ig h lu m in o s ity r a d ia te d a t th e s u r fa c e A s fu s io n e n e f g y p e r u n it m a s s o f b u r n t m a te r ia l th a n l o f he a v y e le m e n ts r e le a s e s fir e s s fu s io n o f li h t e le m e n ts (s e e C h a p te r 4 ) n u c le a r fu e ls a r e v e r y r a p id ly c o n s u m e d g i il c o re m a d e o f A ll th e m a jo r burning s ta g e s p a s s in r a p id s u c c e s s io n u n t a n n n e r ll f d iffe r e n t c o m p o ir o n g f o u e le m e n ts is fo r m e d S u r r o u n d in g th is c o f e a r e s h e s o p a n d fin a lly th e e n v e lo p e w h ic h b o n h e liu m s itio n s s ilic o n o x y g e n n e o n c a r itio n a n d c o n ta in s m o s t o f th e r i in a l c o m p o s fo r M < 3 0 M t in s m o s t o f th e o g o o re a f th e ir o n c o r e w ill le a d th e s ta r to w a r d n tf a c tio n o s te lla r m a s s T h e in e v ita b le c o f a m a s s iv e s ta r a n d its s c h e m a tic io n T h e s tr u c tu r e o c o lla s e i n a s tłp e ï rz o v a e x p lo s p F ig u r e s 9 1 8 a n d ta e a r e s h o w n in f o g e n ito r s g c o n fi p h i i u t e t r a n o supernova n g ib e d in th e n e x t c h a p te r 9 19 T h fi l t e s o f e v o lu tio n w ill b e d e s c r e a n a s g

A t th is s ta g e th e

c o r e te m

,

,

,

,

,

,

,

,

,

,

Scanned by CamScanner

a

F ig u

re

T h ic k

9 2 0 E v o lu tio n se

gm

p o in ts fr o

m

a ry

e n ts o

f th e lin

th e A

GB

a re

e

tr a c k s o

an

d 25M

m o s ta r

o

d e ls in th e H

R

H

burning e v o lu tio n a r y p h a s e s T h e I Ib e n J r (1 9 8 5 ) Q J R OF p ir ic a lly (fr o m

em

T h e H R d ia g r a

9 ı0

e

o

n u c le a r

d e n o te lo n g

d e te r m in e d

5M

o

re

M m o«

'

26)

So c

W

f 1M

e d p ic t u d e t a iı

ha ve

co m e

to

th e

en

d

th e o r e tic a l c o u n te rp a r t, th e

o

f

d is c u

o ur

(lo g T

E p iı o gu

m

s s io n

on

H

lo g L ) d ia g r a m th u s e n d o f C h a p te r 1 T h e

fr ,

th a t w e s e t o u t to a c c o m p lis h a t th e

th e ,

e v o lu tio n

e

le n c e

o

f

m a in

s e q u e n c e s ta rs th e m ,

,

re m

ar

an

d its

k p le ū n g th e ta s l c c e s s o f th e s te l a r

a rC

H

d ıe

c

com

su

i tic s p u z z lin g c h a r a c te r s it e x p la in s th e p r e ų a a b le

th e o r y in e x p la in in g th e m a n y d iffe r e n t, o fte n f o s ta r s , a s e x h ib ite d b is y th e H R d ia r a m k

g a in

d ia g r a ]n

R

,

rs q u e n c e tu m o ff p o in t in s ta r c lu s te th e r e d g ia n t th e s u e i p rg a n t, a n d th e h o r iz o n ta l b r a n c h e s th e n eb p la n e ta r y u la a n d th e w h ite d w a r f r e g io n s th e he g a p b e tw e e n th e m a in s e q u e n c e a n d t i b t a n h r a n c g and m an y o th e r s u b tle r p r o e r tie s o f i d is p s ta r s T o c o n c lu d e th s c u s s lo n w e s h o w tw o m o r e figures I i n F ig u r e 9 2 o f ll c ks n u e v o lu tio n a r y tr a th e H R d ia r a m a r e g iv e n fo r g da a lo w m a s s s ta r a n in te r m e d ia te m a s s s ta r a n m a s s iv e s ta r

ye

ar

æ F īh e ] th e

se

,

,

,

,

,

,

in g o f o

H

Scanned by CamScanner

f

L



. ıo

m

m

dı w

* m

lp ı ı o ıu 〒

广

ı8 7

ı



T





lo R o



ı

10 y r

O \R .

\

L o g jh

)

\会





3 0

日日



區 旨

Logj,ı ) 가따

飞目

기 四国 10 * y

r

ıo

o ı

yr

印 。 ー

ぴ L o g (n

Fig u

re

9 2 ıE

c lu s te r r e s u lt

th e ir m a s s

lin e s are n o

vo

in

m a r k th e

n a r y c a lc u la tio n s

lu tio

lv in g H

a n ev o

d is tr ib u tio

is

n

m a in

se

yea rs T he H

H R d ia g r a m re d

e r tz s p r u n

sho w n

g

e n c e s lo

m a in s e

qu en

sh o w n a

pe s

W ,

p is

t fo u r a g e s T

a re

lin e s

w

h ile th e

o fc o

he

n u m

ta m

a

h y p o th e tic a l

be r

o

f s ta r s

an

d

t r a d iu s T h e d o tte d

(a ) th e lo w ,

v e r y m a s s iv e o n e s

a s s iv e s ta r s a

in g

rm

n s ta n

10 7 y e a r s

e n o te th a t a t

th e m a in s e q u e n c e o f m

ga

f d iffe r e n t ın a s s e s fo

T h e d a s h e d lin e s

ha v e

uch

m a s s s ta r s

a lr e a d y

e a r lie r

e

po c

le ft it

co

10 8 y e a r s (b ) r e s e m b lin g th e H y a d e s c lu s te r l u la te d tr a c k to w a r d n ? a s t th e c o n tin u o u s y p o p l w m a s s s ta r s le a v e o c h s (c a n d d ) w h e n o

ıt r e c le a r ly s e e n a t a e

,

p



h 10 5

c o n s p ic u o u s a t

in F ig u ľ e I 5 B y

g ia n t b r a n c h is

r s ta r s o

R d ia g r a m

.y a】 .B itr a 】

qu

fo

t y e t s e ttle d o n th e m a in s e q u e n c e

th e o p e n tr ia n g le s s h o w

th e



)

.



ce

v F i u re 9 2 1 p r e s e n ts th e e v o ı l e v o lu tio n th e o r y , g g th e s te l a r b a s e d o n evolution?y c a lc u la tio n s in g H R d ia r a m o f a h y p o th e tic a l s ta r c lu s te r , g D is r e g tu d in g th e n u m b e r f d iffe r e n t m a s s e s o f a la r e n u m b e r o f s ta r m o d e ls o g i h b le fr o m th o s e o f a c tu a l h a r d ly d is tin g u s a o f s ta rs th e v a r io u s u la tio n s a f e o p p , h o w n in C h a p te r 1 iffe r e n t a g e s a s s R d ia g r a m s o f s te lla ı c lu s te r s o f d

F in a lly ,



,

c r o w n in

,

卜尋 Scanned by CamScanner

Ķ

ı ı*

9

it is ? C h\

m

7 0

re

The

lu t io n

¢h

elaboıae D e ta ile d

n e lo g e

in s p

ec tio n

.

f s ta

o

M

Th e ï e

d

rs

a

c le a r

d e ta ile d ic p tu

re

th Į u r th e

ro u h g s k e tc a a e s till fu z z y s p o ts . e s p e c i a lı

h

tr a c

y w be te

be ı

o * i N

n o iN

B ı«r ir d o Un de f[ an d

wt a b f e

a

g re a t

fo

Iło p e ıh tï ıiit t t

d e a l a bo

u t s tiu s

n o r l0 0

d i5 1tıI ł

in p a r tic u \ iu

t ßt

ed

d

,:

ttnľe

W e U n de r s ta ī 1d

Scanned by CamScanner

More Documents from "Tanushree Bezbaruah"