The sun's magnetic (Hale) cycle and 27 day recurrences in the aa Geomagnetic Index

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 yr Hale (magnetic polarity) cycle, using the Hilbert transform of daily sunspot numbers (SSNs) since 1818. The occurrences of solar maxima show almost no discernible Hale cycle dependence, consistent with the clock being synchronized to polarity reversals. We reengineer the Sargent 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, with an upper bound of a few solar rotations. 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.