标题： 利用主成分分析将aa指数分解为与太阳活动周期和 Hale 周期相关的分量 显示英文标题

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

摘要： 我们利用主成分分析（PCA）方法分解了第10至23个太阳活动周的月aa指数。 结果显示，第一主成分（PC1）与太阳活动周相关，并占数据方差的41.5%。 第二主成分（PC2）与22年哈雷周期有关，解释了数据方差的23.6%。 aa指数第10至23周的PC1时间序列功率谱只有一个峰值，出现在10.95年周期，这是SC10-SC23期间平均太阳活动周周期。 同一周期的PC2时间序列在21.90年（哈雷周期）有一个明显的峰值，且在该周期的3/4处还有一个较小的峰值。 我们还研究了第10至23个太阳活动周的黑子数（SSN）的主成分，并比较了aa指数和SSN主成分分析中PC2分量的行为。 我们注意到，在除第15和20个太阳活动周外的所有其他周期中，它们都处于相同相位。 aa周期20与其他偶数aa周期相比形状不同，特别是在下降阶段异常高的峰值。 尽管aa指数和黑子数的PC2时间序列相位存在一致性，但这种效应太小，不足以导致奇数和偶数aa周期形状差异的所有变化。 我们估计，aa指数PC2分量形状的30%归因于黑子数，其余部分则归因于太阳/太阳风中的其他周期性事件。 典型的奇数周期的aa数据第一个极大值（出现在太阳黑子极大期），已被证明与日冕物质抛射（CME）有关，而偶数周期典型情况下在周期下降阶段的第二个极大值可能与高速流（HSS）有关。 后一事件提高了活动水平，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。 显示英文摘要

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.