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.

我们使用主成分分析（PCA）分解了周期10至23的每月aa指数。我们表明，第一个分量（PC1）与11年太阳周期有关，占数据方差的41.5％。第二部分（PC2）与22年的Hale周期相关，并解释了数据的23.6％的方差。循环10 – 23的aa指数的PC1时间序列在其功率谱中只有一个峰值处于10.95年，这是SC10 – SC23间隔的平均太阳周期（SC）周期。相同周期的PC2时间序列在周期21.90（Hale周期）有一个清晰的峰值，在该周期的3/4处有一个较小的峰值。我们还研究了10-23周期太阳黑子数（SSN）的主要成分，并比较了aa指数和SSN PCA分析中PC2成分的相互行为。我们注意到它们在除太阳周期15和20以外的所有其他周期中处于同一阶段。周期20的aa指数在形状上也与其他甚至aa指数周期不同，尤其是在其下降阶段异常高的峰值时。即使在PC2时间序列阶段中，aa指数和太阳黑子数具有连贯性，但这种影响仍然很小，无法成为偶数和奇数aa周期形状之间所有差异的起因。我们估计，aa指数PC2分量的形状的30％是由于太阳黑子数的PC2的形状，而其余部分是由于太阳和太阳风中的其他复发事件引起的。太阳黑子最大值期间，aa指数的第一个最大值（典型到奇数周期）已显示与冠状物质抛射（CME）有关，而在循环下降阶段的第二个最大值（通常为偶数循环）可能与高速流（HSS）有关。最后的事件会增加活动级别，以使偶数和奇数对周期之间的最小值始终大于后续的奇数和偶数对周期之间的最小值。