This analysis is based on a Sunspot number reconstruction from Radiocarbon C14 in Tree Rings by Solanki, S.K., et al. 2005, and the data was obtained from NOAA. C14 is generally accepted as being a proxy for solar activity, possibly because of affects in cosmic rays. It will be seen that there are similar cycles in C14 to what are found in climate reconstructions.
The data extends over the period 9455 BCE to 1895 CE at decade spacing. Therefore it is not suitable for studying the 11 and 22 year cycles but is suitable for studying cycles longer than 30 years. This is a spectrum of the time series.
Because of the long period of data, it is possible to determine the cycles periods found with high precision, except for the longer cycles. Noticeable in the spectrum are a cluster of peaks around 55 to 60 years, one near 88 years, two near 200 years, one near 350 years, two near 500 years, one near 2300 years and one at over 6000 years. Taking these in turn we can compare them to known cycles.
Firstly, the 55 to 60 year cluster of cycles may be understood as a cycle in that range which is not strictly rhythmic. The last several centuries of climate data show a strong variation with a period in this range with temperature maxima around 1940 and 1998 and minima near 1910 and 1970.
A period of 208 years or thereabouts has been reported in climate and solar activity and is called the de Vries (or sometimes Suess) cycle. In this C14 series we see a strong 208 year period along with a stronger 224 year period. these two together will therefore form beats over a long cycle.
A period of 355 years was reported by Chizhevsky in climate and here we have a 352 year period in C14 which would seem to be related. Likewise, Wheeler reported a cycle of 510 years in climate and we find 520 and 560 years in C14.
A 2245 year cycle in C14 is quite close to the reported 2300 year cycle in climate called the Hallstatt cycle. This cycle has been suggested to be related to a 2300 year in alignments of the outer planets by Lamb and others.
The time series is not long enough to say that it is real, but there is a definite sign of a 6600 year cycle. Again, this is close to a 6000 year cycle reported by Xapsos & Burke in solar variation.
To gain some perspective of where we are in the longer cycles, here is a fit of a 6600 year cycle and a 2245 year cycle. On these long time frames, the cycle are still increasing.
The 208 year period or thereabout is reported much more often than a 224 year period. Two such periods together would be expected to produce beats, so it is worth looking at the time series filtered by a 210 years cycle smoothed over 3 successive cycles.
It is possible to look at this cycle and see a modulation that might be the 2300 year cycle. If the 2300 year cycle is indeed connected to a cycle of alignments of the 4 gas giant planets, then there needs to be some explanation of why there should be a 208 year cycle because the shorter gas giant cycle should average 171 years with a possible 179 year component. There is a cycle of that period of 171.0 years but its amplitude is not very high.
The cycles near 60 years have also been associated with gas giant alignments, specifically Jupiter and Saturn. These have conjunctions every 19.86 years which repeat in the same part of the sky very close to every third cycle or every 59.6 years, although the long term average would be 61 years.