Harmonically Related Solar Cycles in UV

There are many reported cycles in the Sun ranging from long to short periods, and often periods found are harmonically related to each other. Sometimes the reasons for this rather obvious, but at other times the related cycles have appeared inexplicable to those finding them.

The 11 and 22 year solar cycles are an obvious case once it is understood that the Sun’s North and South poles reverse every 11 years, leading to the 22 year Hale cycle.

In the space era, the structure of the solar wind and the nature of the Sun’s neutral current sheet has led to an understanding of why many geomagnetic measurements show cycles of 28, 14, 7 and 3.5 days. The simple reason is that the Solar rotation as seen from the moving Earth is about 28 days, and the current sheet shape means that we cross through the most active part of the solar wind usually 4 times per 28 days (2 N-S and 2 S-N) although sometimes 2, 6 or 8 times.

Less easy to understand are the set of harmonically related cycles including 154 and 77 days reported by Rieger, Bai and others, because they are sub-harmonics of the solar rotation and include ratio 3 harmonics as well as ratio 2. This type of pattern of cycles periods in ratios 2 and 3 was extensively studied by Edward R Dewey and included in his landmark paper “The Case for Cycles” first published in 1967.

This study of Solar Mg II core-to-wing ratio measurements, which are considered as an indicator of solar UV flux temporal variation uses 28 years of daily data obtained from NOAA covering the period late 1978 to late 2006.

References: Viereck and Puga, The NOAA Mg II core-to-wing solar index:
Construction of a 20-year time series of chromospheric variability from
multiple satellites., JGR, 104, pp9995-10005, May 1999.
Viereck et al., The Mg II Index: A proxy for Solar EUV., GRL, 28,
pp1343-1346, April 2001.

Solar MgII Index

Solar MgII Index

The spectrum was analyzed using CRI’s CATS Software.

There are a series of strong peaks in the spectrum, generally surrounded by a series of lesser peaks on each side. The strongest peaks include both harmonics and sub-harmonics of the solar rotation period. The strongest harmonics are 1, 2, 4 and 8 as expected from the neutral current sheet typical behaviour, and less string peaks at 3, 5 and 7 harmonics.

The strongest sub-harmonics are at 1, 2, 4, 6, 12 and 24 times the solar rotation period. This includes a period near to the commonly reported cycle around 155 days as well as 2 and 4 times that period. Altogether, this single analysis of one time series shows a very extensive set of harmonically related cycles. Normally a number of different series need to be examined to find such an extensive set of related cycles.

Observed cycles periods are 642, 321, 158.8, 114.7, 51.8, 26.74, 13.55, 8.92, 6.84, 5.35, 4.60 days. If the harmonic relationships were perfect with ratios 24, 12, 6, 4, 2, 1, 1/2, 1/3, 1/4, 1/5, 1/6 then the periods would be 642, 321, 160.5, 107.0, 53.5, 26.75, 13.38, 8.92, 6.69, 5.35, 4.46 days.

I know of no accepted physical reason why these particular sub-harmonics of the solar rotation should appear in this time series. However, if these cycles are all part of a cosmic pattern of cycles as I have suggested in the Harmonics theory, then all of these cycles are linked into the pattern reported by Dewey back in the 1960s.

Harmonics in Solar MgII Index

Harmonics in Solar MgII Index (click to enlarge)


About Ray Tomes

Ray's career was in computer software development including system software design, economic modeling, investments. He spent 15 years full time on cycles research and has spoken on cycles and related topics at conferences and seminars around the world. He retired at age 42 to study cycles full time and work out “The Formula for the Universe” and as a result developed the Harmonics Theory as an explanation for observed patterns of cycles and structure of the Universe. His current project is the development of CATS (Cycles Analysis & Time Series) software, and collecting and organizing large quantities of time series data and analyzing this data to test and confirm Dewey's findings in an organized way. Interested in all aspects of cycles especially climate change and causes.
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