Starspot mapping with parallel tempering for M-dwarf flare stars

We implemented a code to decipher stellar surface information from Kepler/TESS light curves specified by many stellar/spot parameters with a parallel tempering (Ikuta et al. 2020) because it has been suggested that there are many spots on the surface. The code enables to deduce parameters, such as the spot location, size, emergence/decay rates, and the stellar differential rotation, and to calculate the model evidence in the Bayesian framework. We show degeneracies between all the parameters and the comparison of the number of spots by revisiting synthetic light curves emulating Kepler/TESS data. Then, we applied the code to TESS light curves of M-dwarf flare stars, AU Mic, EV Lac, and YZ CMi (Ikuta et al. 2021, to be submitted). As results, the spot location and size are uniquely deduced and almost consistent with those in other studies; the spot location is suggested to be uncorrelated with flares in the light curve; the variation of the light curve structure for AU Mic and YZ CMi in two TESS Cycles can be explained by the stellar differential rotation or spot emergence/decay. We also verify the validity of starspot mapping and propose other approaches to resolve the conundrum