Surface imaging by the Occamian approach Basic principles, simulations, and tests

The recently developed Occamian approach for solving inverse problems was applied to surface imaging of cool stars. With a set of tests the effects of data noise and uncertainties of the stellar parameters on the solution have been investigated. The spot locations and spot configuration are found to be well determined in most cases. The spot contrast can be successfully restored in case of adequate atmospheric models and line profile calculations. A formal error analysis of the solution is applied for the first time to the surface imaging problem. It is suggested that the pole-to-equator gradient of the temperature is a consequence of the information distribution on the stellar surface, which is determined by the available observational data. From the analysis of the error distribution on the stellar surface under different conditions two practical advices have been formulated for successful surface imaging. First, a total number points of data ought to be a few times the number of unknown parameters, since only in such a case most of the stellar surface can be restored realiably. Second, the S/N ratio should be as large as possible, since its value affects proportionally the size of the area of the stellar surface with an acceptable level of the errors.