Scanned by CamScanner
瓦
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
に
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
し
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
虱
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
一
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
nï
=
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
닉
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
一
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
知
_
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
岁
岱 ベ
ー
邑
智
į%14l
歹 シ 罗
(
ゴ 日
曳
心
= 區 冒
n 到
習 、
習
# 侧
目 罾
。
、
霤
吕 '
-
習
.
目 眉
,
需. ,
智
.
缸
吕 . 回
・
研
雪
月
若
:
身
/
.
習- 智 卫
爰 惡勇
. 月
「
一
》 制
¥ 势-
署ıa 智
智
.
-\
k
.
目
尋
目 層
冒
畫
自
。
尝
岩 专谷
- 署
図
H
巴
召 憂
名 4 ł
n
習+ 召 (
.
7
召4l
n n
褐U+ 售 신V 慰
召 回
-
四 喟
星
-
咽 胃 吕 凸 o
9
月
昌i 習 層妇 層
わ
一
-
身. 剧 層
启
;
勇 習 J 心 手,
售 暮
)
一
、
岧Ų 岧
驷
N
b 弓
慰 勇 段 ì 可+ . 剧 钍 回
一
*
)
個
'
、
曾 、 朻
黜
省 習
倒
(
一
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
ー
门
一
(2 4 4 )
び
ー
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
一
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
尚
山j )
ij
・。 +
E tk
哉
・!:t
・
,
r e s u ltin
in th e fo
g
rm
(2 5 "
,
,
Scanned by CamScanner
\ ı Th e
* °n 1 o
쁘
ew
ı ar f ıta ı
ı u tlq
一
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 )
_
,
,
一
,
(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
=
彗
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 )
恕
印
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
區
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
ぴ
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
一
-
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
一
、
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
一
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
一
'
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
一
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
一
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
kŤ
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
kŤ
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
耳
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
一
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 ,
八
n ekT
一
(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
一
互 二・ 。 /
一
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 '
・
_
人
っ
刀 。 。
認
ー
、
召 一
人 月
)
人 。 エ
。
(
一
、
-
ぶ
多 一
。
ミ 、
.
。
。 、
り
し
コ
エ
(
一一
圧島 侧 ロ
人 り二
ロ ー
ロ
コ
り
多多
ぶ
卜 刊 岡 )
コ ロ ㈹ ( 一
」
刊 們 )
团
日
っ
ー
一
り
ト
ミ ぷ り
(
ー
コ の ニ っ ニ し
泓
し
瓮 の
)
一
し
一
」
り
む
)
闐
试
ー ー
式
亡 团 コ 团 の (
口 り り ー 口 ) ロ
コ
一
瞬
ロ ン 划
仁
ー
一
巴
幼
ニ
一
ロ コ
一
)
ー
リ
어
コ
( )
」
,
国
そ 材兩
一
一
一
の ン
一
。
、
一
の
)
一
。
)
卜 口
刊
そ り
事ミ
個 コ 丁
? 闃 口
侧
召 の
、
囹
一
一
.
十
ー
-
口
刀 口
ミ
一
一
口 人 出与
し
。
ー
っ
ー
っ 臼
ミ
쩝 ン ニ
日 。
ぷ
レ
ミ
し
一
ー
ー
。
。 (
一 ・
一 一
-
っ
\这 艺 り
1
+
口 っ
-过 一
m
\
ー
一 一
确
っ 島
ミ っ
一
刀
ミ っ
一
)
レ
、
、
、
ぐ
ン の
み っ 二 、
巴 の
ミ 一
口 っ ー
一
島
)
囹
の し
コ 阴
哟
の
团 团
レ
リ
エ ー
っ
し
岛 口
っ ー
の 卫 一
口 囹
む
二 閱
三 む し
コ 阴
名 田 一
口 っ ー
の
ー
己
ミ っ り (
刀 )
っ 口 囹
し
島
这
ロ
闐 口
ー
ロ レ
心
ー
の
ー
り
占
的 ー
コ
、
叻
の ー
り ー
丽
づ ロ ロ
ミ っ
圧 叩 一
っ
一
の 日
回
日 )
口 個
一
コ
ミ ー
口
め ー
ー
人
阴
阴
む
の
一
コ
っ
ー
名
ー
琶
多
ー
区
叻
回
쩝
ミ
の り
9
一
ミ
ー 一
口
し
レ
フ
ぶ
钓
相 リ ニ
ミ
口 ー
ミ
の
确
口 の
与
后
ー
っ
臼 三
津
ー
ー
。
の
ぶ
ー
。
三 器
。
し
り
一
口
の
ー
如
も
ー
ニ 閱
認
咛
腎 一 츠
ミ
島
り
(
ー
コ
む
口
巳
月
レ
-
」
り ニ
ロ
쩝
、 。
レ
(
ー
ヒ
の
阴
一
コ
ー
り
团
0
ー
-
っ
昀
쁘
ミ 、
ね
쿄
レ
三 ミ 口
的
、
、
刀
、
っ
一
ー
コ
ー
一
阴
の
名 、
的
り ー
口 囹 ぷ り む
ミ ミ コ ー
口 囹 コ
江
리 一
口 む
日 の ー
の の
ミ コ ー
っ ン 日
日 ー
ぷ ー
ヲ っ
一
ー
츠
闐 口 一
쩝
扭
っ ー
し
っ
口
り り
泓
钓
っ 日 서
闐
一
ら 囹
く
的
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
4ı
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
一
币
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
每
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
!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
铺
跡 滿
Fa
*= t e g *
科
04
ı
m
i
鼬
m
bt
@
ı
锄
*
« i»
2 /'p
卢
* 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
锄
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
郜
» 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
湖
i« a n i n in k
e
拥
C
湖
ħm
Ĥ M p «
栩
*
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
着
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
iì
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
固
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 )
,
5ı
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
巴
sta rs
54
fhËr
-
e
a ' "
f °
こ
ー
く
斗 勇 黒 ご 币
6Li
名 目
口
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
기
司
夢
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
田
券 每 ■
四 四 国团团
厂
-
:
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
氇
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
十
w
h ic h is M g h ly
and u n s ta b le
リ
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
fź
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@
主
24
16
ダ
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
#Á
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
彆
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
7ı
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 )
" ,
阿
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
Aı
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
<
一
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
门
have
口
(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
中
,
학 エ
,
,
,
,
,
、
以
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
く
r a d ia t iv e
in e q u a lity (5 3 4 )
ー
一
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
如
く
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
學
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
$
«
=
口
(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 )
.
鳥
Scanned by CamScanner
5 6
The
s ta n
d a rd
m o
8ı
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
一
K
声)
一
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
乒
っ
李
们
芸
名
钓
っ
三
切
0 =
侧
三
の
团
ニ
づ っ 二 凶
飞
コ
ロ
ミ
7 り
榭
ミ
팀
己
在 ー
ミ コ
ヱ カ コ ヲ 비 비
コ り
己 人 闃
ロ
ぶ
の り
쩝 口
岳
园
呂っ
比
口
っ 已
。 侧
ロ ニ
島 っ
っ
の
。
。
っ
っ
り
凹 。 。 り
弘
每
コ 哟
ニ
り
人 力
日
与
。
ニ
ロ
っ り 囹
ト
っ む 国
阗
卷 =毛
舀
コ
己
。
巴
に っ
田 田
。 每
H
の
っ
\
ぶ
闐 に
钍
摹
)
团 的
。 っ
。
。 り
往 コ っ 。
区
n っ
岛
島
個 っ
り 囹
口
の
の
X
臼 の
っ
国
っ
划 コ ヲ の
ね
し
っ の
白
百
入
り
ロ
ン
の
ミ コ 。
썹
书 钿
っ 。 っ
の
的
鼠
ン
り
岊
む
日月 晒
レ
旧 闐 っ
の
っ 。
む
卫
っ
自
日 の の
国
二 っ
쩝
书
写 昌
の
。 っ
囹
り
ミ
の
刀 0
江
の
召 回
卫
り 侧
쩝 ト
の
回 节
島 っ
召
目
:
U
兆 铲
の
쩝
的
) U
-
q
=
쩝 日
一
日
U
ぷ
划
/
の
=
:
の コ 口 っ m W 们
日
っ 侧 コ
の ン 侧
ぶ 人 個
日
唱
.
(
-
一 )
,
靠
.
巨
鸟 闐 口
ヒ 闲
口
: .
江
词
寓
Ų
的
闐
と
.
の
吕 口
'
」
一
켭 口 く
)
囹
っ
巴 라 西
侧
コ 了 口
업
の
的
囹
コ 回
口 0
り
て
囹
ミ ー の
っ 島
日
口 っ
国
っ
目
后む の 召
日
名
日 っ
。
们
N
团
人 团
ミ
们
们
の
囹
口 っ
江
田
们
与
闐
。 囹
と
ぶ
6
二 っ
口 の ン
の
の
口
む
い
썹
の
く
っ
钿
囡
。
呂旧
丽
名
月
v
侧
口
人
闐
り
闐 口
島
侧
人 口
っ
囹 的
們
村
/
的
口
6
쩝
昀
コ ニ
囹
ぶ 闐
の 闐
后
の
日
回
닳
ぶ
们
钿
8
目 コ
U
们
口 っ
月
国
人
の
り に
。 四
ぐ
阴
.
们
っ
の
0
口 っ
나
レ
ミ
曳
摹
ペ
龟
の
的
ー
っ 口 囹
の り 口 の
回 っ
皂
三
名
の 二
の
人 囹
日ミ
W
ロ の
j
쩝
毛ミ
白
龟 寸
这
书
レ
の
6
m .
囹
レ
l
뇨
し
人
W
ト
ニ
ģ:
・
们
U e
弓
门 口
U 口 侧
W
ニ
团
侧
ロ
フ 的
四
子
っ
0
四
侧 コ
口
四
ね
っ
多
り
寸
阴
コ
し
っ
・
宇
の
的
の
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
,
一
口
,
,
罾
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
一
ll s e e la te r )
-
口
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 ' " " ^
仁
喟
n
气
, 一
a ss
m
an
ow n s
山 ゲ
マ
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)
口
=
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
(É
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 )
一
八
(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
一
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
爪
p o s itiv e coefficients C
4 /3
<
,
sgn
十b
td p c /p c ]
sg n
=
o m
竺
(6 7 )
.
孔
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
虹
(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 ,
,
く
m d
r a d ia
,
o
dnı
一
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
(Ó
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
中
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
m»
*
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
躑
a
e ın ıw
p P
$m
a ¢e
置in t
八 \ tM
e
a ı
lı4 ın
r ır m ¢
u
蹦
邮 個
c ı》 冒
p n eM
T ht e
¢
m n a ıp e w ı
\
¢ııe
»
m
k
む
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
聞
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
十
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
ー
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
一
,
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
一
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
뇨
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
一
三p T
一
K
o
pT
,
口马
弘
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
一
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
一
=
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
rı
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
伍
c e sse s
亡
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
ノ
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 , 、
飞
,
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
一
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
、
一
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
一
,
一
厢 一
一
,
博
,
ge
m a
y
a ls o
b e in fe iT e d fr o
ー
n ı th e
イ
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
龆
,
。 。
,
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 =
恳
P
=
,
(7 17 ) i
pT
內
(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。
一
(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
,
MÎ
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
,
エ
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 )
ー
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
以
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
기
砣
,
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
一
飞
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
び
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
卅
吕 づ
吕
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
園
o m
a w
い
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 .
ー
パ
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
新
O
=
如
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
,
?
計
a
u
Y d 1
n ııL
itr e p o r
山
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 +
一
\p e
? tu
u t x rtu ? A ł ! 3 \ U O ? o u s l a i? tll
ŝ un
十
村十
p ? s s a ıd x ?
。
Ru ţ u ı puL
押
,
(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
陜
떻
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
山
re s s f th e g a s p
dr
as w r ittc n
ず
り
d
p g lıs
y be
a
m (8 ı4 )
\
丁
,
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 =
=
弘
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
Aï
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
,
三
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
三
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
)ı
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
冗
(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
目
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 (
レ
あ ー
苍
舊
W in d fro
一
零
30 M
a
m
m a in s e q u e
.
n c e s ta r
一
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
划
瓦
。
,
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
弩
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
。
氓
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
巴
찧
口 の
・
。
一
一
.
显
c
.
り
o
三
レ
罚
ロ
人
三
. め
. 崮 じ
曾 弓
。
ぶ 驾 二
阴
云售 乞 丐 )
唧 中
0
ミ
っ 网
罗
巴
崖訾 每 秀甚 口
习
叵 若罗 黜
葛 多 甚苫械
し
君 目
コ
夥
1笆
仍
鹰
显岁
マ
ä 掣胃
閱 口
て
己 的
目
若
の リ
初
钿 °
阴
心
口
与 り
叫
日 瞬 卫 間 巷智 畜 口
。
だ
り
の
ぶ 己 阴
人
으
力 六
っ ぶ 島 リ ぷ
岱 り
彐 口
、 。 、 、
二 と
り
な
り
、
ご 石
. 芸
.
弓
バ ー 歹一
量甘
目
っ
り
ー ド
必 響 菊霆ー
り
っ 。
ご
く
目
っ
ニ
三 军
杉
圈
巴
写
囂
目
人 二
g
地
三 军
っ
目
日 っ
田
く
貨
树 り 加
心
加
密 加
っ 磷
て ぶ
划
ぷ
买 ミ
メ ロ
勇合
四 く
的
っ 菡
く コ
之 妫
し
っ
己 謗
に
ヨ
目 葛
り
ピ
了 く
己
七 乙
ヨ
标
节
図
卢 穆
り
出
リ
的 っ
舅 邕
二
旨
り
む ぶ
ず
ぶ
二
钿
り
ぷ
礴
ズ
り
し
ぶ
り
筠
쬡
寥 ぽ多 置 碧 趕ミ 暑。
宕 虽 卫勇
え
」
勇 =趴 旨
。
。
ろ だ
U 〉 3
口
8
言ゼ 多 屋 霆 図 名 島 差 習
丽
し
っ
。
宕
。
葛
ひ
り ぶ
鹄
呂丽
口
咨
っ
。
.
ロ
り
ぶ
乒
己
口
勺
鳥 ど り ミ 分コ
多
试 杉
り
。
ぶ
移
っ
っ
、 、 、 。
葛
り ぶ
ひ
罗 コレ
弓
召
藍
く
く 杉 8
っ
り
二
」
っ
二
丁
ロ ン ロ り
、 。 、
、
ど
り
£
。
ン
り
幼
。 む ン
切
と ミ 。
飞
1
っ り
図
り
/
差
詛 事
佛
習
侧
っ
の
り
、 。
宝
万
役
事
、
哄
義 。 り 卑 舅 ン 口 萑 ー 钍 ミっ 。 ミ っ 三 ミ 芒
る
、
哄
基直
ー墓差
、
与
ノ
的
器 召 口
暑芽 金 豸 ぶ
む ン
划
召 U 習 ミ 訾 ぶ
佐
て
哟
函
に
名
り
ユ
ち
ミ
目 四 四 万 西
亀
多
层
豆
て
曾 徨 令 仨岩 零 と 卫 e ミ 口 勺 と 零 口島 に 乌
乡
目
吓 匈军
口
乡
レ
ト
后ヱ )
り
丽
エ
三
に
し
岛 的
。
老っ
く
ミ
ン
.
的
曾
心 ぢ ト 喘 島
c
イ心 目 。
昏势
呂 업彭 w
Ø
コ
岁 & 习
壁 名
。
函
阴
寥
イ
。 リ
后l
に 口
ロ
台
一
邕
」
的
て
ミ
写
与
阴
っ
。
隹鑫
豸 唇 區 罗
冒 正 丽
丽 a
多
万
贸 占
男 乃
8 召 回 a
对 目
っ
了
ひ
口
岱 人
卫
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
旨
豇 艮
嗫苕 嚅
肾
氧
淤
菌
良
盪 歹 氧
腎 \ 為
Ą
歹
腎 与
\ 与
ー き 霭
腎
腎
営 茎孚 声 w
ぎ ー驻孚
霈
ー氧 ぼ
腎
腎
ー 叫
貧君 复腎 $ ぎ
腎腎争
腎2
与
為 伯
8
骨 氧
-
豸 势 芦署
廖
守
自
. 岫
\ 一
飞
差腎 罗
氧
は
萍 氧
く
ー寺
势ヘ 秀
)
営
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
爱
秽
背 녘
湯 看礁 心ぎ ー 費歹
隽
代
蠡
尹
兰叁
ぎ腎
4
澹 年
曼 歹 暴 君 著冶 戛
零
时
玲
噜
霪 友矿
镌
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
够
量星署 斟
鼋着
巴 w
呜
鳥
- 自 勾
牙ぢぎ 腎芽 吕 置 守 露目 曇 (
气
勺
看
ー
腎 汲 腎蜜 礴汲含 售露 氧
邕腎
資乐
署
腎
習 研
移
黒 各魯 落 腎
腎 習 碼
势昏 君 貧良 ミ
勾 帝 君
卢
零
咎
甘
呐
弔
会 魯 玺 彩
差鑫
塁孚 璽
杯 葛
芽
零 ぎ
+
$
君麥 涎
背 势 氧蓄
玲飞
q
霄
盛 誓 瓜 夏 葛 秀 媚
営杂 鑫
词 矛
-
ー劣
ビ◆ \
蔓
巻零
哖
售
专
缸 耄淊
参
\
奴
诌
\
咱 )
孑 番 敦
香
戛
耄云
飞 飞
豢
尘 歹
塾 置
◆气 ヘ
◆ 零
铀
哥
篷文
-
& *
\
驻
歹 玲
내 & 孑 口
奄 奄 i
斗
然
嗦每 亀
转 甑 番
ぎ き 诎要
窘
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@
괍
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
万
一
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
一
ņ
一
im it to th e ı
一
一 一 一 一 一
)
(
(9 3 o )
y"
f th e fo
¡ n it ia l c o
re m a s s
一
˜
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
e«
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
イ
园
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
云
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
一
(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
く
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
鳞
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
飞
ı8 3
s ta r »
ん
中 っ
コ 三
田
号
く
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
一
. ıo
m
m
dı w
* m
lp ı ı o ıu 〒
广
ı8 7
ı
呷
T
中
丁
lo R o
미
ı
10 y r
O \R .
\
L o g jh
)
\会
中
ヨ
3 0
日日
心
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
仁
)
.
飞
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