Separating aa-index into Solar and Hale Cycle Related Components Using Principal Component Analysis

TL;DR

This study uses principal component analysis to decompose the aa-index into components related to the solar and Hale cycles, revealing their distinct contributions and phase relationships, and comparing them with sunspot numbers.

Contribution

The paper introduces a PCA-based method to separate solar and Hale cycle components in the aa-index and compares these with sunspot number behavior.

Findings

PC1 accounts for 41.5% of variance, related to the solar cycle.

PC2 accounts for 23.6% of variance, related to the Hale cycle.

Phase coherence exists between aa-index and sunspot number PC2 components.

Abstract

We decompose the monthly aa-index of cycles 10-23 using principal component analysis (PCA). We show that the first component (PC1) is related to solar cycle, and accounts for 41.5 % of the variance of the data. The second component (PC2) is related to 22-year Hale cycle, and explains 23.6% of the variance of the data. The PC1 time series of aa cycles 10-23 has only one peak in its power spectrum at the period 10.95 years, which is the average solar cycle period for the interval SC10-SC23. The PC2 time series of the same cycles has a clear peak at period 21.90 (Hale cycle) and a smaller peak at 3/4 of that period. We also study the principal component of sunspot numbers (SSN) for cycles 10-23, and compare mutual behavior of the PC2 components of aa-index and SSN PCA analyses. We note that they are in the same phase in all other cycles than Solar Cycles 15 and 20. The aa cycle 20 also differs from other even aa cycles in its shape, especially in anomalously high peaks during its descending phase. Even though there is a coherence in the PC2 time series phases of aa-index and sunspot number, this effect is too small to cause all of the difference of the shape of even and odd aa cycles. We estimate that 30% of the shape of the PC2 component of aa-index is due to sunspot number and the rest to other recurrent events in Sun/solar-wind. The first maximum of aa-data (typical to odd cycles), during sunspot maximum, has been shown to be related to coronal mass ejections (CME), while the second maximum (typical to even cycles) in the declining phase of cycle, is probably related to high-speed streams (HSS). The last events increase the activity level such that the minimum between even-odd cycle-pair is always higher than the minimum between succeeding odd-even cycle pair.