Optical depths and time-scale distributions in Galactic microlensing

Abstract

We present microlensing calculations for a Galactic model based on that of Han & Gould, which is empirically normalized by star counts. We find good agreement between this model and data recently published by the MACHO and OGLE collaborations for the optical depth in various Galactic fields, and the trends thereof with Galactic longitude l and latitude b. We produce maps of optical depth and, by adopting simple kinematic models, of average event time-scales for microlensing towards the Galactic bulge. We also find that our model predictions are in reasonable agreement with the OGLE data for the expected time-scale distribution. We show that the fractions of events with very long and short time-scales owing to a lens of mass M are weighted by M2n(M) dM and M−1n(M) dM, respectively, independent of the density and kinematics of the lenses.