Rotational modulation of stellar light curves due to dark spots encloses information on spot properties and, thus, on magnetic activity. In particular, the decay of the autocorrelation function (ACF) of light curves is presumed to be linked to spot/active-region lifetimes, given that some coherence of the signal is expected throughout their lifetime. In the literature, an exponential decay has been adopted to describe the ACF. Here, we investigate the relation between the ACF and the active-region lifetimes. For this purpose, we produce artificial light curves of rotating spotted stars with different observation, stellar, and spot properties. We find that a linear decay and respective time-scale better represent the ACF than the exponential decay. We therefore adopt a linear decay. The spot/active-region time-scale inferred from the ACF is strongly restricted by the observation length of the light curves. For 1-yr light curves our results are consistent with no correlation between the inferred and the input time-scales. The ACF decay is also significantly affected by differential rotation and spot evolution: strong differential rotation and fast spot evolution contribute to a more severe underestimation of the active-region lifetimes. Nevertheless, in both circumstances the observed time-scale is still correlated with the input lifetimes. Therefore, our analysis suggests that the ACF decay can be used to obtain a lower limit of the active-region lifetimes for relatively long-term observations. However, strategies to avoid or flag targets with fast active-region evolution or displaying stable beating patterns associated with differential rotation should be employed.

中文翻译：

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活性区寿命与光变曲线自相关函数的关系

由暗点引起的恒星光曲线的旋转调制包含了关于光斑特性的信息，因此也包含了关于磁活动的信息。特别是，假设光变曲线的自相关函数 (ACF) 的衰减与光斑/活性区域的寿命有关，因为在其整个寿命期间预期信号的一些相干性。在文献中，已采用指数衰减来描述 ACF。在这里，我们研究了 ACF 和有源区寿命之间的关系。为此，我们生成了具有不同观测、恒星和光斑特性的旋转点星的人造光变曲线。我们发现线性衰减和相应的时间尺度比指数衰减更能代表 ACF。因此，我们采用线性衰减。从 ACF 推断的光斑/活动区域时间尺度受到光变曲线观察长度的强烈限制。对于 1 年的光曲线，我们的结果与推断的时间尺度和输入的时间尺度之间没有相关性是一致的。ACF 衰减也受到微分旋转和光斑演化的显着影响：强烈的微分旋转和快速光斑演化导致对活性区寿命的更严重低估。然而，在这两种情况下，观察到的时间尺度仍然与输入寿命相关。因此，我们的分析表明，ACF 衰减可用于获得相对长期观察的有源区寿命的下限。然而，