Measuring Stellar Limb Darkening by Gravitational Microlensing

Observations of microlensing transit events can be used to measure the limbdarkening of the lensed star. We discuss the advantages and drawbacks ofseveral microlensing light curve inversion methods. The method of choice inthis work is inversion by means of decomposition of the stellar surfacebrightness profile. We construct an ideal basis by principal component analysisof brightness profiles obtained from model atmosphere calculations. Limbdarkening approximations using such a basis are superior to those usingstandard power-law limb darkening laws. We perform a full analysis of simulatedsingle-lens microlensing transit events including a detailed error analysis ofthe method. In realistic events with a low impact parameter the brightnessprofile of the source can be recovered with a relative accuracy of 2% from thecenter of the source disk to 0.9 of the disk radius. We show that in theparticular case of the observed MACHO Alert 95-30 event the intrinsic complexvariability of the lensed red giant hinders efforts to recover its surfacefeatures.Comment: 47 pages, 11 figures - accepted by The Astrophysical Journa