  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,
firstly, whether there is a correlation between the size of starspots - assumed
to be related to the amplitude of the sinusoid - and their decay timescale and,
secondly, whether any such correlation depends on the stellar effective
temperature. To determine this, we computed the autocorrelation 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 normalised light curves. We
used a Monte Carlo Markov Chain to measure the periods and decay timescales 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.
