Microlensing optical depth & event rates from MOA-II

We estimate {tau} and {Gamma} by correcting this incompleteness. In the central fields with |l|<5{deg}, we find {Gamma}=[18.74+/-0.91]x10^-6^exp[(0.53+/-0.05)(3-|b|)]/star/yr and {tau}_200_=[1.84+/-0.14]x10^-6^exp[(0.44+/-0.07)(3-|b|)] for the 427 events with t_E_<=200 days using all sources brighter than I_s_<=20mag. Our revised all-source {tau} measurements are about 2{sigma} smaller than the other all-source measurements and are consistent with the RCG measurements within 1{sigma}.

We conclude that the long-standing problem on discrepancy between the high {tau} with all-source samples by DIA and low {tau} with RCG samples can probably be explained by the incompleteness of the stellar number count. A model fit to these measurements predicts {Gamma}=4.60+/-0.25x10^-5^/star/yr at |b|~-1.4{deg} and -2.25{deg}<l<3.75{deg} for sources with I<=20, where the future space mission, Wide Field Infrared Space Telescope, will observe.