Characterisation of starspot structure and differential rotation of Kepler-411

Starspots and their movements on stellar surfaces enable the mechanisms of stellar magnetic activity to be investigated. Information on the spot distribution and differential rotation provide important constraints for the behaviour of stellar magnetic dynamos. We analyse the Kepler photometry of Kepler-411, a known exoplanet host, to determine the distribution and properties of star spots on the stellar surface with two independent and complementary methods: modelling the photometric effect of the rotation of spots on the stellar surface and mapping spots by transiting planets. By constructing a spot model accounting for geometry, differential rotation, and spot evolution, we modelled the spots of the stellar surface giving rise to the observed brightness variations. We also searched for evidence for occultations of starspots in high-cadence photometry. Our spot models reproduce the observed photometric variations well and we are able to obtain information on the distribution and movement of spots on the stellar surface. We do not obtain evidence for differential rotation -- the rotational profile is consistent with rigid-body rotation with a period of 10.52±0.34 days. We detect three occultations of spots by planet c. The positions of these spots coincide well with the positions of larger spot structures identified by our modelling of the rotational modulation of the light curve.