Sunspot Cycle

Summary of my model. It explains: 1) Long and short sunspot cycles 2) Very low sunspot activity. 3) Why there is a difference between the sunspot numbers South and North of the equator (slightly different speed Southern and Northern polar field) 4) Why there is very low sunspot activity South or North of the equator, while there is sunspot activity in the opposite place! 5) Outburst of magnetic field activity are seen on the theoretical model. Even in declining and low sunspot activity! 6) Why Sunspots ABOVE the equator appear with the PLUS first... and UNDER the equator with the MINUS first....or vice versa 7) How a 3 dimensional model of the sun can be constructed

[B]A Theoretical Calculation of the Sunspot Cycle[/B] With the help of a simple integral, a theoretical sunspot cycle of eleven years can be imitated (copied) as follows: The polar magnetic field of the sun rotates (theoretically) in about 37.2 days; the equatorial field in 25.75 days (the average of the last 75 years: see Long Term Variations of the Torsional Oscillations of the Sun, Solar Physics 170: 373/388, 1997, by Dirk K. Callebaut). At a certain moment, the equatorial field takes over from the polar field. Therefore we can only investigate the relationship between the field of the sun and an independent observer by measuring only each take-over movement. Through this we always compare only two variants: the converging positions of the fields in relation to the shifted point of observation. In fact we are doing nothing more than calculating the winding process of the magnetic field of the sun. At this moment we can calculate the numbers of the fields together with the converging position: Subject: Re: Re: Speed in degrees of the equator field: 360 ¸ 25.75 = 13.9805825 degrees Speed in degrees of the polar field: 360 ¸ 37.19 = 9.6800215 degrees The difference in degrees between the equator and polar field is: 13.9805825 – 9.6800215 = 4.30055848 degrees The polar field is taken over by the equatorial field after the following number of days: 360 ¸ 4.30055848 = 83.710058 days = 1 bit The number of circles traveled by the equatorial field is:

83.710058 ¸ 25.75 = 3.25087545 The number of circles traveled by the polar field is: 83.710058 ¸ 37.19 = 2.25087545 0.25087545 circle forms a bit and will be used as a basic unit in the calculation

First point: 0.25087545

x 360 = degrees

= 91,3 degrees

= A

Put this in relation with an observer who travels the length of the mean of the polar and equatorial field in one day. Total length equator field = 4.370.880 km Mean of Polar field = between 700.000 km and 900.000 km = 800.000 km 4.370.880 + 800.000 = 5.170.880 km mean =2.585.440 km => This is about equal with the speed of an object that travels 360 days around the sun in one year (plus/ minus) => To be corrected when we know the circumference of the polar field more excactly Comparisson speed earth Speed earth = 29,77 km sec 29,77 x sidereal day = 2.565.000 km/day

Conclusion Point B goes in plus minus 360 days around the sun in this case

= 83, 7

days = 83,7 degrees

because days is same as degrees

= B

A - B = end formula When you calculate and subtract both graphics, the result will be the difference

between the magnetic field of the sun and an independent observer. Filling in the previous numbers in the Excel file this results in a sunspot cycle of 54.5 bits. 54.5 x 83.710058 days = 4,562.2 days = 12.49 years. Note: The changes of speed of both the equatorial and polar fields were not taken into account. Sunspot cycle of 9 years We change the hypothetical speed of the polar field into 37.16 days: 360 ¸ 25.75 = 13.9805825 degrees 360 ¸ 37.16 = 9.68783638 degrees Difference = 4.292746117 degrees 360 ¸ 4.292746117 = 83.86240187 days = 1 bit 83.86240187 ¸ 25.75 = 3.2567923 0.2567923 circle = 1 bit When you put these numbers in the Excel file the result is a sunspot cycle of 42 bits. 42 x 83.86240187 = 3,522.2 days = 9.64 years. Important conclusions: 1) Only a small change in the speed of the polar or equatorial field can result in a considerable prolongation or deceleration of the sunspot cycle. 2) From a mathematical point of view there has to exist a very close correlation between the equatorial and polar field. 3) The sunspot cycle together with the polar reversal of the magnetic field of the sun lasts longer when the polar field rotates somewhat slower. A difference of only (!) 0.0807 percent causes the cycle to rise from 9.64 to 12.49 years! Third example: the cycle of 11 years Speed of the polar field: 37.176 days 360 ¸ 37.176 = 9.683666882 degrees 360 ¸ 25.75 = 13.9805825 degrees Difference: 4.296915618 degrees 360 ¸ 4.296915618 = 83.7810262 days = 1 bit 83.7810262 ¸ 25.75 = 3.25363208 circle 0.25363208 circle = 1 bit

When you put these data in the Excel file, the result is a sunspot cycle of 48.0 bits. 48.0 x 83.7810 = 4,021.5 days = 11.01 years. Very low sunspot activity. Equator field: 25.75 Polar field: 37.291 Very long cycle => ALMOST ZERO SUNSPOT ACTIVITY! Further findings: 1. Sunpot Cycle of 11 Years First possibility Polar Field: 37.176 Equatorial Field: 25.75 37.176 : 25.75 = 1.4437 Polar field = 1.4437 times slower then equator field 2. No Sunspots Polar Field: 37.291 Equatorial Field: 25.75 37.291 : 25.75 = 1.4482 Difference between (1) and (2) = 1.4482 - 1.4437 = 0.0045 Polar field = 1.4482 times slower then equator field 3.

Sunpot Cycle of 11 Years

Second possibility Polar Field: 37.4075 Equatorial Field: 25.75 37.4075 : 25.75 = 1.4527 Polar field = 1.4527 times slower then equator field Difference between (2) and (3) = 1.4527 - 1.4482 = 0.0045 Same difference like between (1) and (2)

POSITIVE AND NEGATIVE SUNSPOTS 1. If you take the ABS from the final formula then you find the following A. The Sunspot cycle from 25.75 and 37.176 =

POSITIVE

B. The Sunspot cycle from 25.75 and 37.4075 = NEGATIVE 2. If Sunspots ABOVE the equator appear with the PLUS first... then they appear UNDER the equator with the MINUS first Conclusions from (1) and (2) a. If the Southern Polarity field from the sun has a speed of 37.176 Northern Polarity field has a speed from 37.4075

then the

b. These speeds must change in the OPPOSITE with a new cycle.... because sunspots have then the OPPOSITE value from the previous one 37.176 has to change in 37.4075 37.4075 has to change in 37.176 3 DIMENSIONAL MODEL OF THE SUNSPOT CYCLE I tried to reconstruct a 3 dimensional model of the sunspot cycle Use the constant values of

1.4437 and 1.4527 of the 2 sunspot cycles

Then decrease the speed of the equator under 25.75.

Example 25.5

Results: 1. The Sunspot cycle from 25.75 and 37.176

DECREASES in length

2. The Sunspot cycle from 25.75 and 37.4075 INCREASES in length Then increase the speed of the equator above 25.75.

Example 26.0

Results: The OPOSITE from the previous findings happen! 1. The Sunspot cycle from 25.75 and 37.176

INCREASES in length

2. The Sunspot cycle from 25.75 and 37.4075 DECREASES in length CONCLUSIONS a. The average speed of the equator field rules the sunspot cycle ( fastest speed last 75 years = 25.35 days. Slowest speed = 26.28 days) b. With the values from prof Callebaut is must be possible to recalculate the last

sunpot cycles and possible future sunspot cycles c. There is a mathematical principle in this theory that gives a constant sunspot cycle of 11 years (shorter and longer cycles are also possible) Final conclusion: The used formula's are basic...With more advanced programs it has to be possible to calculate sunspot cycles.