Optical Depths and Timescale Distributions in Galactic Microlensing

Abstract

We present microlensing calculations for a Galactic model based on Han & Gould (2003), which is empirically normalised 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 timescales for microlensing towards the Galactic bulge. We also find that our model predictions are in reasonable agreement with the OGLE data for the expected timescale distribution. We show that the fractions of events with very long and short timescales due to a lens of mass M are weighted by M^2 n(M)dM and M^(-1) n(M)dM respectively, independent of the density and kinematics of the lenses.