Gnevyshev–Ohl rule

The Gnevyshev–Ohl rule (GO rule) is an empirical rule according to which the sum of Wolf's sunspot numbers in odd cycles with preceding even cycles (E+O) are highly correlated and the correlation is lower if even cycles and preceding odd ones (O+E) are taken (see Figure 1).^[1] Sometimes a simplified formulation of the rule is used, according to which the sums over odd cycles exceeds those of the preceding even cycles^[2] (see Figure 2). The rule breaks down under certain conditions.^[3] In particular, it inverts sign across the Dalton minimum, but can be restored with the "lost cycle" in the end of the 18th century.^[4][5] The nature of the GO rule is still unclear.^[2]

Figure 2. Illustration of the simplified GO rule: Intensities of sunspot cycles in pairs of even (open circles) and odd (filled circles) numbered cycles.^[4] The GO rule is expresses in the connecting lines pointing up. The break of the rule for cycles 2–3 and 4–5 is visible.

Figure 1. Illustration of the GO rule. The blue circles are pairs of cycles, the dashed red lines are linear regressions (the pair 4-5 is excluded from the left regression). The Pearson correlation coefficients are R=0.91 for even-odd pairs (the left panel) and R=0.41 for odd-even ones (the right panel).

References

1. Gnevishev, M. N.; Ohl, A. I. (1948). "On the 22-year cycle of solar activity". Astronomicheskii Zhurnal (in Russian). 25 (1): 18–20.
2. Hathaway, D. (2015). "The solar cycle". Living Reviews in Solar Physics. 12 (1): 4. arXiv:1502.07020. Bibcode:2015LRSP...12....4H. doi:10.1007/lrsp-2015-4. PMC 4841188. PMID 27194958.
3. Komitov, Boris; Bonev, Boncho (2001). "Amplitude Variations of the 11 Year Cycle and the Current Solar Maximum 23". The Astrophysical Journal Letters. 554 (1): 119–122. Bibcode:2001ApJ...554L.119K. doi:10.1086/320908.
4. Usoskin, I.; Mursula, K.; Kovaltsov, G. (2001). "Was one sunspot cycle lost in late XVIII century?". Astronomy and Astrophysics. 370 (2): L31–L34. Bibcode:2001A&A...370L..31U. doi:10.1051/0004-6361:20010319.
5. Usoskin, I.; Mursula, K.; Arlt, R.; Kovaltsov, G. (2009). "A Solar Cycle Lost in 1793-1800: Early Sunspot Observations Resolve the Old Mystery". Astrophysical Journal Letters. 700 (2): L154–L157. arXiv:0907.0063. Bibcode:2009ApJ...700L.154U. doi:10.1088/0004-637X/700/2/L154. S2CID 14882350.