Measuring limb darkening of stars in high-magnification microlensing events by the Finite Element Method

Abstract

ABSTRACT The finite-size effect in gravitational microlensing provides a possibility to measure the limb darkening of distant stars. We use the Finite Element Method (FEM) as an inversion tool for discretization and inversion of the magnification–limb darkening integral equation. This method makes no explicit assumption about the shape of the brightness profile more than the flatness of the profile near the centre of the stellar disc. From the simulation, we investigate the accuracy and stability of this method and we use regularization techniques to stabilize it. Finally, we apply this method to the single lens, high-magnification transit events of OGLE-2004-BLG-254 (SAAO-I), MOA-2007-BLG-233/OGLE-2007-BLG-302 (OGLE-I, MOA-R), MOA-2010-BLG-436 (MOA-R), MOA-2011-BLG-93 (Canopus-V), MOA-2011-BLG-300/OGLE-2011-BLG-0990 (Pico-I), and MOA-2011-BLG-325/OGLE-2011-BLG-1101 (LT-I) in which light curves have been observed with a high cadence near the peak (Choi et al. 2012). The recovered intensity profile of stars from our analysis for five light curves is consistent with the linear and square-root limb darkening profiles and two events with the square-root profile. The advantage of FEM is to extract limb darkening of stars without any assumption about the limb darkening model.