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

Abstract

We decompose the monthly aa-index of Cycles 10 to 23 using principal component analysis (PCA). We show that the first component (PC1) is related to the 11-year 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 the aa-index for Cycles 10 – 23 has only one peak in its power spectrum at the period 10.95 years, which is the average solar cycle (SC) 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 components of the sunspot number (SSN) for Cycles 10 – 23, and compare the mutual behavior of the PC2 components of the aa-index and SSN PCA analyses. We note that they are in the same phase in all other cycles but Solar Cycles 15 and 20. The aa-index of Cycle 20 also differs from other even aa-index 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 the aa-index and sunspot number, this effect is too small to be the origin of all the differences between the shape of even and odd aa cycles. We estimate that 30% of the shape of the PC2 component of the aa-index is due to the shape of the PC2 of the sunspot number and the rest to other recurrent events in the Sun and solar wind. The first maximum of the aa-index (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 cycle descending phase, is probably related to high-speed streams (HSS). The last events increase the activity level such that the minimum between even and odd cycle pairs is always higher than the minimum between succeeding odd and even cycle pairs.

Spatial and Temporal Distribution of Solar Green Line Corona for Solar Cycles 18-24

“…Another guestion is, does corona exhibit so-called Gnevyshev gap (GG), which has been reported in many solar phenomana (Gnevyshev, 1977;Feminella and Storini, 1997;Ahluwalia and Kamide, 2004;Bazilevskaya, Makhmutov, and Sladkova, 2006;Kane, 2008;Norton and Gallagher, 2010;Du, 2015;Mursula, 2018, 2020) and even in the geomagnetic indices (Takalo, 2021b). This has not been reported earlier.…”

“…PCA finds combinations of variables, that describe major trends in the data. PCA has earlier been applied, e.g., to studies of the geomagnetic field (Bhattacharyya and Okpala, 2015), geomagnetic activity Takalo, 2021b), ionosphere (Lin, 2012), the solar background magnetic field (Zharkova et al, 2015), variability of the daily cosmic-ray count rates (Okpala and Okeke, 2014), and atmospheric correction to cosmic-ray detectors Savić et al (2019).…”

“…To this end, we estimate that the average length of the cycle is 130 months, and use it as a representative Solar Cycle. We first resample the monthly data such that all cycles have the same length of 130 time steps (months), i.e about the average length of the Solar Cycles 19 -24 Mursula, 2018, 2020;Takalo, 2021b). This effectively elongates or abridges the cycles to the same length.…”

Prediction of even and odd sunspot cycles

“…Gnevyshev & Ohl, 1948;Takalo & Mursula, 2018;Leamon et al, 2022) and geomagnetic phenomena (e.g. Chernosky, 1966;Takalo, 2021;Chapman et al, 2021). However, some recent studies have considered the even/odd cycle parity in the context of sunspot cycle prediction (e.g.…”

Prediction of even and odd sunspot cycles

“…Gnevyshev and Ohl, 1948;Takalo and Mursula, 2018;Leamon, McIntosh, and Title, 2022) and geomagnetic phenomena (e.g. Chernosky, 1966;Takalo, 2021;Chapman et al, 2021). Here we study the prediction of sunspot cycles accounting for the 22-year Hale cycle by considering the differences in the even and odd numbered sunspot cycles.…”