用主成分分析法将aa指数分离为太阳和海尔循环相关分量
Separating aa-index into Solar and Hale Cycle Related Components Using Principal Component Analysis
摘要：
我们使用主成分分析（PCA）分解周期10-23的月度aa指数。结果表明，第一分量（PC 1）与太阳活动周期有关，解释了数据方差的41.5%。第二个分量（PC 2）与22年海尔周期有关，解释了23.6%的数据方差。第10-23周的PC 1时间序列在其功率谱中只有一个峰值，其周期为10.95年，这是间隔SC 10-SC 23的平均太阳周周期。相同周期的PC 2时间序列在周期21.90（Hale周期）处有一个明显的峰值，在该周期的3/4处有一个较小的峰值。我们还研究了太阳黑子数（SSN）的主成分的第10-23周，并比较了AA指数和SSN主成分分析的PC 2分量的相互行为。我们注意到，它们在除第15和第20太阳周期之外的所有其他周期中都处于相同的相位。aa循环20在其形状上也不同于其他偶数aa循环，特别是在其下降阶段期间的异常高的峰。尽管aa指数和太阳黑子数的PC 2时间序列相位存在相干性，但这种影响太小，不可能导致所有奇偶aa周期形状的差异。我们估计，30%的AA指数的PC 2分量的形状是由于太阳黑子的数量和其他经常性的事件在太阳/太阳风。在太阳黑子活动最大期，aa数据的第一个极大值（典型的奇数周期）与日冕物质抛射（CME）有关，而第二个极大值（典型的偶数周期）在太阳黑子活动的下降期，可能与高速流（HSS）有关。最后的事件增加了活动水平，使得偶数-奇数周期对之间的最小值总是高于随后的奇数-偶数周期对之间的最小值。
英文摘要：
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.
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