On the relationship between the size and surface coverage of starspots on magnetically active low-mass stars

We present a model that predicts the light curve amplitude distribution for an ensemble of low-mass magnetically active stars, under the assumptions that stellar spin axes are randomly orientated and that cool starspots have a characteristic scale length and are randomly distributed across the stellar surfaces. The model is compared with observational data for highly magnetically active M-dwarfs in the young cluster NGC 2516. We find that the best fitting starspot scale length is not constrained by these data alone, but requires assumptions about the overall starspot filling factor and starspot temperature. Assuming a spot coverage fraction of 0.4+/-0.1 and a starspot to unspotted photosphere temperature ratio of 0.7+/-0.05, as suggested by the inflated radii of these stars compared to evolutionary model predictions and by TiO band measurements on other active cool stars of earlier spectral type, the best-fitting starspot angular scale length is 3.5(+2)(-1) degrees, or a linear scale length of \\sim 25000 km. This linear scale length is similar to large sunspot groups, but 2--5 times smaller than the starspots recently deduced on an active G-dwarf using eclipse mapping by a transiting exoplanet. However, the best-fitting spot scale length in the NGC 2516 M-dwarfs increases with the assumed spot temperature ratio and with the inverse square root of the assumed spot filling factor. Hence the light curve amplitude distribution might equally well be described by these larger spot scale lengths if the spot filling factors are <0.1 or the spot temperature ratio is >0.9.