Wide-field high-precision photometric surveys such as Kepler have produced reams of data suitable for investigating stellar magnetic activity of cooler stars. Starspot activity produces quasi-sinusoidal light curves whose phase and amplitude vary as active regions grow and decay over time. Here we investigate, first, whether there is a correlation between the size of starspots - assumed to be related to the amplitude of the sinusoid - and their decay time-scale and, secondly, whether any such correlation depends on the stellar effective temperature. To determine this, we computed the auto-correlation functions of the light curves of samples of stars from Kepler and fitted them with apodised periodic functions. The light-curve amplitudes, representing spot size, were measured from the root-mean-squared scatter of the normalized light curves. We used a Monte Carlo Markov Chain to measure the periods and decay time-scales of the light curves. The results show a correlation between the decay time of starspots and their inferred size. The decay time also depends strongly on the temperature of the star. Cooler stars have spots that last much longer, in particular for stars with longer rotational periods. This is consistent with current theories of diffusive mechanisms causing starspot decay. We also find that the Sun is not unusually quiet for its spectral type - stars with solar-type rotation periods and temperatures tend to have (comparatively) smaller starspots than stars with mid-G or later spectral types.

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