The Sun's magnetic (Hale) cycle and 27 day recurrences in the $aa$ geomagnetic index

TL;DR

This paper introduces a new solar cycle phase clock based on Hilbert transform analysis of sunspot data, revealing detailed timing of Hale cycle features and their relation to geomagnetic and cosmic ray activity.

Contribution

It develops a normalized epoch clock for solar cycles, re-engineers the R27 index for high-resolution recurrence analysis, and uncovers new timing relationships in solar and geomagnetic phenomena.

Findings

Hale cycle dependence of solar maxima is negligible.

Transition to 27-day recurrence occurs within 2-3 solar rotations.

Odd cycles have extended minimum-terminator intervals.

Abstract

We construct a new solar cycle phase clock which maps each of the last 18 solar cycles onto a single normalized epoch for the approximately 22 year Hale (magnetic polarity) cycle, using the Hilbert transform of daily sunspot numbers (SSN) since 1818. The occurrences of solar maxima show almost no Hale cycle dependence, confirming that the clock is synchronized to polarity reversals. The odd cycle minima lead the even cycle minima by ~ 1.1 normalized years, whereas the odd cycle terminators (McIntosh et al. (2019)) lag the even cycle terminators by ~ 2.3 normalized years. The mimimum-terminator interval is thus relatively extended for odd cycles and shortened for even ones. We re-engineer the Sargent(1985,2021) R27 index and combine it with our epoch analysis to obtain a high time resolution parameter for 27 day recurrence in aa, <acv(27)>. This reveals that the transition to recurrence, that is, to an ordered solar wind dominated by high speed streams, is fast, occurring within 2-3 solar rotations or less. It resolves an extended late declining phase which is approximately twice as long on even Schwabe cycles as odd. Galactic Cosmic Ray flux rises in step with <acv(27)> but then stays high. Our analysis also identifies a slow timescale trend in SSN that simply tracks the Gleissberg cycle. We find that this trend is in phase with the slow timescale trend in the modulus of sunspot latitudes, and in antiphase with that of the R27 index.