Reconstruction of the brightness distribution across a stellar disk from gravitational lensing caustic passage observations

This paper describes a method for analyzing observations of the passage of a star through a,gravitational lensing caustic that enables the derivation of information about the brightness distribution across the stellar disk wi thout knowledge of the lens parameters. The ill-posed inverse problem of re constructing a one-dimensional strip brightness distribution across the ste llar disk is solved using a regularization method, taking into account the non-negative nature of this function. Assuming the source is circularly sym metric, the search for the radial brightness distribution is carried out ov er compact sets of upward-convex, non-negative functions or functions that do not grow with distance from the stellar center. The method is used to an alyze the gravitational microlensing event MACHO 98-SMC-1, of a star in the Small Magellanic Cloud, obtained by the PLANET international group. The re sulting brightness distribution is compared with computations of limb darke ning for model stellar atmospheres. (C) 2000 MAIK "Nauka/Interperiodica".