Model-independent restoration of the brightness distribution across the disks of stars from high precision eclipsing light curves

Abstract

Estimates are made of the accuracy with which the brightness distributions across the disks of stars can be reconstructed through analysis of data from high precision space-based photometry of classical eclipsing systems and observations of the transit of planets across stellar disks. The ill-posed reconstruction problem was solved on a compact set of monotonically nonincreasing, upwardly convex, non-negative functions. One of the difficulties with this method in the case of stars with thin photospheres is the poor convergence of the solution at the point where the brightness distribution has a discontinuity at the edge of the star's disk. Nevertheless, the use of this method for analysis of high precision observational data is justified, since it can be used to obtain an estimate of the limb darkening that is independent of any model assumptions. The reconstructed brightness distribution for the star HD 209458, for which the transit of a planet over its disk was observed with the HST space telescope, is in good agreement with the results of a nonlinear model fit.