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 scalelength 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 scalelength 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 scalelength is 3.5+ 2 − 1 degrees, or a linear scalelength of ∼25 000 km. This linear scalelength is similar to large sunspot groups, but two to five times smaller than the starspots recently deduced on an active G-dwarf using eclipse mapping by a transiting exoplanet. However, the best-fitting spot scalelength 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 scalelengths if the spot-filling factors are 0.9.