The Microlensing Event Rate and Optical Depth toward the Galactic Bulge from MOA-II

We present measurements of the microlensing optical depth and event rate toward the Galactic Bulge (GB) based on two years of the MOA-II survey. This sample contains ~1000 microlensing events, with an Einstein radius crossing time of t _E <= 200 days in 22 bulge fields covering ~42 deg² between -5° < l < 10° and -7° < b < -1°. Our event rate and optical depth analysis uses 474 events with well-defined microlensing parameters. In the central fields with |l| < 5°, we find an event rate of Γ = [2.39 ± 1.1]e ^{[0.60 ± 0.05](3 - |b|)} × 10^-5 star^-1 yr^-1 and an optical depth (for events with t _E <= 200 days) of τ₂₀₀ = [2.35 ± 0.18]e ^{[0.51 ± 0.07](3 - |b|)} × 10^-6 for the 427 events, using all sources brighter than I_s <= 20 mag. The distribution of observed fields is centered at (l, b) = (0.°38, -3.°72). We find that the event rate is maximized at low latitudes and a longitude of l ≈ 1°. For the 111 events in 3.2 deg² of the central GB at |b| <= 3.°0 and 0.°0 <= l <= 2.°0, centered at (l, b) = (0.°97, -2.°26), we find \Gamma = 4.57_{-0.46}^{+0.51} \times 10^{-5} star^-1 yr^-1 and \tau _{200} = 3.64_{ -0.45}^{+ 0.51} \times 10^{-6}. We also consider a red clump giant (RCG) star sample with I_s < 17.5, and we find that the event rate for the RCG sample is slightly lower than but consistent with the all-source event rate. The main difference is the lack of long duration events in the RCG sample due to a known selection effect. Our results are consistent with previous optical depth measurements, but they are somewhat lower than previous all-source measurements, and slightly higher than previous RCG optical depth measurements. This suggests that the previously observed difference in optical depth measurements between all-source and RCG samples may largely be due to statistical fluctuations. These event rate measurements toward the central GB are necessary to predict the microlensing event rate and to optimize the survey fields in future space missions such as Wide Field Infrared Space Telescope.