Bimodality and the Hale cycle

Abstract

Because of the bimodal distribution of sunspot cycle periods, the Hale cycle (or double sunspot cycle) should show evidence of modulation between 20 and 24 yr, with the Hale cycle having an average length of about 22 yr. Indeed, such a modulation is observed. Comparison of consecutive pairs of cycles strongly suggests that even-numbered cycles are preferentially paired with odd-numbered following cycles. Systematic variations are hinted in both the Hale cycle period and Rsum (the sum of monthly mean sunspot numbers over consecutively paired sunspot cycles). The preferred even-odd cycle pairing suggests that cycles 22 and 23 form a ‘new’ Hale cycle pair (Hale cycle 12), that cycle 23 will be larger than cycle 22 (in terms of RM, the maximum smoothed sunspot number, and of the individual cycle value of Rsum), and that the length of Hale cycle 12 will be longer than 22 yr. Because of the strong correlation (r = 0.95) between individual sunspot cycle values of Rsum and RM, having a good estimate of RMfor the present sunspot cycle (22) allows one to predict its Rsum, which further allows an estimation of both RMand Rsum for cycle 23 and an estimation of Rsum for Hale cycle 12. Based on Wilson's bivariate fit (r = 0.98), sunspot cycle 22 should have an RMequal to 144.4 ± 27.3 (at the 3-σ level), implying that its Rsum should be about 8600 ± 2200; such values imply that sunspot cycle 23 should have an Rsum of about 10500 ± 2000 and an RMof about 175 ± 40, and that Hale cycle 12 should have an Rsum of about 19100 ± 3000.