Analyzing the brightness distributions of the components of eclipsing variables using precise photometric data

We present the results of numerical simulations aimed at studying ways to analyze the brightness distributions of eclipsing-binary components from the high-precision photometric data that will be provided by the planned specialized orbital COROT and Kepler missions. We consider a simple model of an eclipsing binary with spherical components in circular orbits, with a linear limb-darkening law. We fit the light curves using a non-linear model with limb-darkening coefficients, as well as without placing stringent constraints on the shapes of the distributions. Our estimates demonstrate that, if the uncertainties in the measured light curves become as low as 10^?4 (a factor of ten better than the precision of ground-based photometry), the limb-darkening coefficients can be found with a relative uncertainty of 0.01. The uncertainties of the restored brightness distributions across the stellar disks are approximately the same.