Click on images for a larger view.

Some may be aware I have been trying to track down if we are experiencing any change to the differential rotation rates of the Sun. If angular momentum changes can be tied to solar differential rotation rates, we might have a solid causation. Solar differential rotation can be measured in different ways but basically, different parts of the Sun rotate at different speeds, keeping in mind the Sun is not a solid object. The equator rotation rate is around 27 days, with the poles at around 34 days, as seen from earth. But there is a lot more to consider, if we look at the solar equator there is another speed difference showing the possible rotation speed of the Sun. Recently I heard back from Dr. Rachel Howe from NOAO who specializes in this area, and the results were quite amazing.

Her hot off the press paper here:

http://users.beagle.com.au/geoffsharp/howe2009.pdf

The graphic above is a Doppler image from GONG which shows the regular patterns of the changing rotation speed of the Sun with the yellow sections being the fastest. The image is taken at 0.99R which is around 7000Km beneath the top of the Convection zone. It is thought these patterns (darker zones mostly) are generated at the Tachocline (a thin sheer layer between the radiative core and the Convection zone at around 0.71R) and they spiral out to the top of the Convection zone and are subject to spin momentum like a garden sprinkler. As we go deeper, like the graphic below (0.99R to 0.84R) the patterns break up, which is not what I would expect. The overall scale of the pattern seems to remain but loses clarity. Perhaps this is a condition of going deep with Doppler equipment or maybe the frequency is a lot higher as we go down?

Dr. Howe’s paper suggests that the travel time interval from Tachocline to the solar surface is around 2 years and, as we will see, these Doppler patterns align very closely to the sunspot butterfly image when overlayed. If so, then sunspot activity is a historical account of what happened at the Tachocline 2 years ago.

In the next graphic we go back further and it displays an apparant rotation change. During past grand minima, observations suggest a faster rotating Sun, as can be seen at the equator. After 2000 there is a greater acceleration occurring, but we need to keep in mind that the surface is not static. UPDATE May 2015, recent information suggests the opposite, ie the rotation rate has slowed during SC24

Also noted is the much longer length of cycle 23 (96- ?) compared to cycle 22 (86-96). So here we see two direct links to the highly possible effect from Angular Momentum created by the Gas Giants, ~~increased~~ decreased rotation rate and the stretching of the cycle length as the Sun takes its abnormal path every 172 years.

The last time this occurred was in SC4 just before the Dalton Minimum and the retrograde motion we are now part of is very similar to SC4. On average the retrograde orbit (purple) is around 9 years, SC23 & SC4 have orbits of over 11 years.

Below is a graphic I produced by rescaling the SIDC sunspot butterfly plots then overlaying over Dr. Howe’s graphic, as can be seen there is a direct correlation between the two sets of data. It is thought the sunspots are created at the poleward edge of the fast and slow zones (yellow /green), but I am sceptical. The slower zones are what travel all the way to the Tachocline (its like a “brakes on” feedback) and we might have to possibly shift the overlay to the right to allow for angular momentum as the Doppler image is taken from 7000Km below. I have asked Dr. Howe her opinion. UPDATE May 2015: New data suggests that sunspots are created on the yellow flows.

* Animation: Dr.Howe’s diagram with the SIDC butterfly sunspot scatter with re scaled X & Y coordinates to match..*

You can see in the pattern why early cycle sunspots appear at high latitudes then gravitate to the equator. Looking at butterfly graphs of solar activity, they suggest the majority of sunspots occurring between -40 & +40 latitude, ruling out the dark blue/blacks areas at high latitudes.I speculate they are reserved for Coronial Mass Ejections. The purple arrows show where a “flow” starts.

Some more speculation: Some suggest the modulation of a sunspot cycle is governed by the strength of the solar poles, which are a late product of the previous cycle (this product can also be severely downgraded as seen in SC19) . Maybe the poles are a player, but not the main influence as the main source of power is coming from the Tachocline. This is where the poles eventually get their flow from. But it may explain why we have a weak cycle after a grand minima cycle, as the following cycle after could have very low pole strength.

Worth saving and blowing up to see the detail.

Angular Momentum could vary the speed of the outer convection layer of the Sun, creating less torsion on the Tachocline sheer layer, resulting in reduced solar activity 2 years later. The Doppler diagrams will reveal some of this as we move forward and I believe these diagrams are an invaluable tool and would greatly appreciate access to this data easily, like the WSO polar strength graph and watch each move through the cycle. I informed Dr. Howe of this, lets hope it gets something going.

Geoff Sharp.

Geoff,

FYI, the barycenter diagram used in this post was created with my “Solar orbit simulator” software a.k.a. “Sim1”. It has just been brought to my attention that the Windows software provided at my page didn’t run on some machines, due to a bug. I have found the problem now and fixed it, so if you need to make more diagrams go ahead and download the fixed version give it a try:

http://arnholm.org/astro/sun/sc24/sim1/

REPLY:Thanks Carsten, all working perfectly now. This tool we be invaluable, now I can start building a reference library for those who might be interested.Geoff:

Before I ask a question, I would just like to say that it was a revelation to me when you produced the original pdf summarising your discussions on the original Landscheidt auditblog site. For the first time I felt comfortable with the explanations given for solar variations (as far as the explanations went at the time). My father, an extremely practical Professor of Engineering (in the UK), always used to say that if a solution in science wasn’t elegant then it was either largely incomplete or completely wrong. The direction you were and are going in, certainly seems to me to be elegant. Anyway, thank you for the time and thought you put in to this field.

The question I have is to do with Dr Howe’s doppler graphic. As you would expect there is bilateral symmetry about the equator. This being the case I would have expected the disturbances on the sun also to be bilaterally symmetrical but this does not seem to be the case. Sunspots and plages early in a solar cycle seem to be phenomena of the upper latitudes and not the lower. Have you any thouhghts about this? If this has been dealt with and I have missed it, I apologise.

p.s. I have somehow lost my copy of your original pdf. If it is still available I would appreciate a link. It will be interesting to have another look at it.

REPLY:Hi Roger, if you look at the shapes created by the deceleration on the doppler image there is an overlap….I would think the higher latitude has a chance to “earth” with the poles at the earliest stage of a new cycle which then follow the pattern towards the equator. North/South asymmetry is still an unknown at present, but there could be some clues. If we look at the latitude position of the big 4 at present only Saturn is below the solar equator. Also noted during past grand minima, limited sunspots were only observed in one hemisphere.The pdf file is now out of date, with new data coming available its hard to keep it up to date. I need to produce a pdf combining all the current info into one document, which I will do soon and forward you a copy via email.

This link is the most up to date version of the original pdf. http://landscheidt.auditblogs.com/2008/11/06/are-neptune-and-uranus-the-major-players-in-solar-grand-minima/

cheers

Geoff

Geoff:

Thanks for the link, although I rather fancied looking at the original. For no particular reason, I thought it would be interesting to see how your thinking had developed or changed! Things certainly seem to be moving quickly and it is interesting to see the way things progress.

In my question, when I said sunspots are “phenoma of upper latitudes and not the lower”, I had meant to write that they seem to be phenomena of the northern hemisphere and not the southern. Somehow you managed to divine that!

I have read these papers with great interest.You seem to use

the angular momentum of the planets vs sun as a value to

correlate with old time series of sunspots and observed

energy levels.

Has anyone done a computation of expected tides on the Sun, and

seen how this correlates with the time series we have?

Best regards,

Morten Reistad

REPLY:Yes and beyond Jupiter there is practically no tidal affect. There may be a case for some of the inner planets in relation to the 11 yr cycle but the forces involved are extremely weak.Morten Reistad, Norway said, May 13, 2009 @ 4:38 pmI have read these papers with great interest.You seem to use the angular momentum of the planets vs sun as a value to correlate with old time series of sunspots and observed energy levels.

Has anyone done a computation of expected tides on the Sun, and seen how this correlates with the time series we have?Tides are totally neglible (fractions of millimeters). I have done extensive calculations of angular momentum for all the planets, and it shows it is impossible to explain sunspots via angular momentum theories, because it (angular momentum) is all accounted for via accepted physics. If you want to know the details just contact me, you find my email at http://arnholm.org/ (Du kan også skrive på norsk om du vil, debattklimaet her er litt anstrengt).

Please mail me and i will send the worksheet

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

A Theoretical Calculation of the Sunspot Cycle

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 then the Northern Polarity field has a speed from 37.4075

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.

REPLY:Thanks Patrick….I need some time to absorb this, but on the surface it looks very encouraging.So what do you think of PG’s claim above here? Most of his claims are stolen from other cranks, and he doesn’t seem to understand elementary physics or anything that is non-intuitive. The “formulas” that he presents seem so incredibly basic that a solar physicist would probably fall over laughing at them. I know quite a few people, including children, that are worried about Patrick’s claims for 2012. I would greatly appreciate your opinions on him, and letting me know your experiences in dealing with him because I know he stole some of your “negative sunspot” ideas and literally copy-pasted them to his site. Seems slightly illegal to me.

REPLY:Not overly impressed is the mantra, and that is being kind. But we have those like Patrick that are promoting themselves selling books to the gullible public which is not that different from the select crew of solar and climate scientists promoting their own beat up propaganda in an effort to secure more funding.The challenge is to decipher the facts and achieve an informed opinion.