Timo Niroma: The Cyclicity of Sunspots


Sunspots Image Courtesy of SOHO/EIT.
SOHO is a project of international cooperation
between ESA and NASA.

















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An Influence by Jupiter on the Sunspot cycle?

Analysis by Timo Niroma

Jupiter

It seems that during the Jovian perihelion the sunspot number is always low. This means that if the sunspot cycle maximum coincides with Jupiter's perihelion, the maximum is either delayed, making that cycle long, or it is very low, as in 1810's. Actually, there is an average rise of 10 in the Wolf Number at exactly the perihelion and the lowest values prevail two years before the perihelion.

There is nothing mystical about the relation between the solar activity and the Jupiter's orbit. Most easily the relation is explained by the Standard Model of Physics so that Jupiter is surrounded by a relatively powerful magnetic field that moves inside the Sun's still more powerful magnetic field that reaches beyond the trans-Neptunean areas. Jupiter is not the primary cause behind of sunspots but it twists the solar magnetic field in ways that affects them. Jupiter has a relatively great eccentricity which causes that distance between Jupiter and Sun vary greatly in 11.86 years intervals. Now it can be shown by a simple statistical analysis that Jupiter is near the Sun, the number of sunspots is in average lower than when Jupiter is at a longer distance. Actually it is the nearness that matters. When Jupiter is near its heliocentric perihelion (nearest point to Sun) it causes the sunspot activity to drop.

In the following table I have calculated average monthly Wolf numbers from 1762 to 1999. The cycle length is one Jovian year (11.86 years), so data for 20 cycles are included. For every month is calculated the arithmetic mean for 142 months, each containing the average of the 20 revolutions of Jupiter from 1762 to 1999.

From every third Jovian year one month is omitted. This negative leap month mechanism is due to the 142 months used, when actually one Jovian year is 142.34 month.

The results are as follows.

The overall picture doesn't change from the previous one. The rise begins 10-15 months before the perihelion, reaches its maximum speed about 15 months after the perihelion and the maximum value about 45 months after the perihelion. The fall has its first sharp part just before the aphelion. The second maximum rate of the fall is reached 20-30 months before the perihelion and the Wolf number is at its minimum 15-20 months before the perihelion.

The most interesting phases according to the index:

1. fall from 82 to 79 from perihelion to month 3
2. rise from 79 to 116 from month 3 to month 16 (100 in month 11)
3. rise from 117 to 135 from month 27 to month 31
4. a setback to 128-131 from month 33 to month 37 ("deviating mos")
5. MAXIMUM of 140 in months 44-45
--) the next months are months before the perihelion (aphelion = 71)
6. fall from 74 to 60 from month 27 to month 21
7. MINIMUM of 60-61 in months 17-21
8. rise from 75 to 82 from month 3 to perihelion

The rise rate reaches its highest speed from month 3 to month 16 after the perihelion.


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Sunspots and Jupiter:

PLOT OF WOLF NUMBERS VERSUS PERIOD OF JUPITER'S ORBIT

Wolf






























A 105 Year Oscillation in spots and climate?

If we take the Schove estimates of the maximum magnitudes (R(M)) from the period 1500-1750 and the measurements from 1750, we get:

1410-1500   ? cold (at end the Sporer minimum)
1510-1600 107 warm
1610-1700  61 cold (at end the Maunder minimum)
1710-1800 114 warm
1810-1900  95 cold (begins with the Dalton minimum)
1910-2000 146 warm
2010-2100     cold?

So the supercyclic rise is a very long process.

There are hints of a 1060-year cycle intertwined with a cycle of 2290 years. The Sun seems to be much more irregular than we ever have imagined. The historical data seem to show that the 200-year oscillation has been there at least since 200 AD. The even centuries seem to be have been cold, odd ones warm, not to the accuracy of year, but in the average anyway. If a spotless sun during the third century caused the process of the Great Roman Empire demise to begin, we have to write the history books anew.

The other thing that seems apparent is that the general warming trend has been going on at least 1,800 years so that the third century AD may be the coldest century for at least 2000 years. So much more dramatical appear the cold periods to have been during the first millennium AD than during the second one. On the other hand we may now live in the mildest climate Anno Domini. This may even have greater implications to the whole Holocene climate study and possibly to ice age theories also. Considering the evidence it looks like a megalomaniac idea that the recent rise of half a degree would have been caused by man. So great are the natural variations. But man has always wanted to be in the center of the world.

A 211 Year Cycle in Sunspots?

221 Year Sunspot Cycles

Wolf sunspot numbers smoothed by 12 years (appr. 1 Jovian yr)
An interval of 221 years, which corresponds a cycle of 211 years unsmoothed.
On the lower line between 1600-1820,and
On the upper line between 1821-1994
Sunspots for the years from 1600-1699 estimated by Schove from aurorae

Tentative suggestions:
20 sunspot cycles = 18 2/3 Jovian years
Average length of sunspot cycle = 11.07 years
14 Jovian years = 15 sunspot cycles
158 years = 75% * 211 years = 2 Gleissberg cycles
Gleissberg cycle (7 consecutive cycles):
- minimum length = 6.07 Jovian years,
- maximum length = 7 Jovian years

The lower line:
Minima 1694 and 1810 (15 Wolfs), maximum 1784
The upper line:
Minimum 1901, maxima 1833, 1953, (2003 estimated)

For more information about the influence of Jupiter on sunspots:
Click here.


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The above is a summary.
For more information:
Goto http://personal.inet.fi/tiede/tilmari/sunspots.html or
Click here.

Variation in the length of the sunspot cycles.
Two modes of sunspot cycle length distributions.
Table 1. The cycle lengths since 1745.
Table 2. The sunspot cycle lengths classified.
About the cycle lengths before 1889.
About the cycle lengths after 1889.
Table 3. A probabilistic distribution of the sunspot cycles.
The sunspot mean length is a mean of means.
How accurate is the estimated sunspot cycle length?
Table 4. The lengths of sunspot cycles 19-21 based on different smoothing periods.
Table 5. The minima of sunspot cycles 19-22 based on the 5 lowest months.
Sunspot cycle length estimates extended to 500 years by auroral numbers.
Supercycles of 13-15 basic cycles.
Length of several cycles combined.
Table 6. 4, 8, and 16 cycles combined.
Table 7. Every 15 cycles combined between 1689-1996.
How do the sunspot minima relate to the Jovian perihelion?
Table 8. Sunspot minima compared to Jovian perihelion.
Table 9. The distance between the sunspot minimum and the Jovian perihelion.
Table 10. The most attractive distances between minima and perihelia.
The sunspot minima prefer an area around the Jovian perihelion.
The distance between minimum and perihelion is quantisized.
The sunspot minimum and the Jovian perihelion never exactly meet.
Table 11. The minima v. Jovian perihelion graphically.
The relation of the length of the cycle to its magnitude.
Table 12. The magnitude and the rise period to maximum.
Table 13. R(M) compared with the time of rise to maximum.
The maximum possible sunspot number.
Table 14. The residuals of the actual maximum magnitude compared with the theoretical value.

  • PART 2: Jupiter and the Sun
  • - Average sunspot magnitude during 19 Jovian years 1762-1987.
    - Is the Jovian effect real or an artifact?
    - How many Jovian years are needed for the effect to show up?

  • PART 3: Minima, maxima and medians of the sunspots
  • - Magnitude minima.
    - Magnitude maxima.
    - Medians and quartiles.
    - The perihelian stability.

  • PART 4: From basic cycles to supercycles
  • - How long is the 11-year cycle?
    - The rules of Schove interpreted.
    -- The supercycle of 7 consecutive cycles.
    -- The supercycle of 14 consecutive cycles.
    - The Precambrian Elatina formation.
    - The Gleissberg cycle.

  • PART 5. The 200-year sunspot cycle is also a weather cycle.
  • - A 2000-year historical perspective.
    -- The Roman Empire and its demise.
    -- The Mayan Classic Period.
    -- When the Nile froze in 829 AD.
    -- Why is it Iceland and Greenland and not vice versa?
    -- Tambora did not cause it.
    -- The spotless century 200 AD.
    -- The recent warming caused by Sun.
    -- The 200-year weather pattern.
    - An autocorrelation analysis.
    -- Three variants of 200 years.
    -- The basic cycle length.
    -- The Gleissberg cycle put into place.
    - Some studies showing a 200-year cyclicity.
    - The periods of Cole.

  • PART 6: Searching supercycles by smoothing.
  • - Smoothing sunspot averages in 1768-1992 by one sunspot cycle.
    - Smoothing by the Hale cycle.
    - Smoothing by the Gleissberg cycle.
    - Double smoothing.
    - Omitting minima or taking into account only the active parts of the cycle.

    A double smoothed sunspot cycle





    One need not much wonder about the variation in temperature during the past 200 years,
    so much does it correlate with the activity of the Sun.
    The "greenhouse warming" gets here a natural (literally) explanation.

  • PART 7: Summary of supercycles and a hypercycle of 2289 years.



  • PART 8: Organizing the cycles into a web.