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Rotational modulation of stellar light curves due to dark spots enclosesinformation on spot properties and, thus, on magnetic activity. In particular,the decay of the autocorrelation function (ACF) of light curves is presumed tobe linked to spot/active-region lifetimes, given that some coherence of thesignal is expected throughout their lifetime. In the literature, an exponentialdecay has been adopted to describe the ACF. Here, we investigate the relationbetween the ACF and the active-region lifetimes. For this purpose, we produceartificial light curves of rotating spotted stars with different observation,stellar, and spot properties. We find that a linear decay and respectivetimescale better represent the ACF than the exponential decay. We thereforeadopt a linear decay. The spot/active-region timescale inferred from the ACF isstrongly restricted by the observation length of the light curves. For 1-yearlight curves our results are consistent with no correlation between theinferred and the input timescales. The ACF decay is also significantly affectedby differential rotation and spot evolution: strong differential rotation andfast spot evolution contribute to a more severe underestimation of theactive-region lifetimes. Nevertheless, in both circumstances the observedtimescale is still correlated with the input lifetimes. Therefore, our analysissuggests that the ACF decay can be used to obtain a lower limit of theactive-region lifetimes for relatively long-term observations. However,strategies to avoid or flag targets with fast active-region evolution ordisplaying stable beating patterns associated with differential rotation shouldbe employed.

On the relation between active-region lifetimes and the autocorrelation function of light curves