Besançon Galactic model analysis of MOA-II microlensing: Evidence for a mass deficit in the inner bulge

Abstract

Galactic bulge microlensing surveys provide a probe of Galactic structure. We present the first field-by-field comparison between microlensing observations and the Besançon population synthesis Galactic model. Using an updated version of the model we provide maps of optical depth, average event duration and event rate for resolved source populations and for difference imaging analysis (DIA) events. We also compare the predicted event time-scale distribution to that observed. The simulation follows the selection criteria of the MOA-II survey. We modify the Besançon model to include M dwarfs and brown dwarfs. Our best-fitting model requires a brown dwarf mass function slope of -0.4. The model provides good agreement with the observed average duration, and respectable consistency with the shape of the timescale distribution (reduced Χ2 ≃ 2.2). The DIA and resolved source limiting yields bracket the observed number of events byMOA-II (2.17×and 0.83×the number observed, respectively). We perform a two-dimensional fit to the event spatial distribution to predict the optical depth and event rate across the Galactic bulge. The most serious difficulty for the model is that it provides only ~50 per cent of the measured optical depth and event rate per star at low Galactic latitude around the inner bulge (|b| < 3°). This discrepancy most likely is associated with known underestimated extinction and star counts in the innermost regions and therefore provides additional support for a missing inner stellar population.