SIMBAD references

We present measurements of the microlensing optical depth and event rate toward the Galactic bulge using the data set from the 2006 to 2014 MOA-II survey, which covers 22 bulge fields spanning ∼42 deg² between -5° < l < 10° and -7° < b < -1°. In the central region with ∣l∣ < 5°, we estimate an optical depth of $\tau =[1.75\pm 0.04]\times 1{0}^{-6}\exp [(0.34\pm 0.02)({3}^{\circ }-| b| )]$ and an event rate of Γ = [16.08 ± 0.28] × 10^–6$\exp [(0.44\pm 0.02)({3}^{\circ }-| b| )]{\mathrm{star}}^{-1}\,{\mathrm{yr}}^{-1}$ using a sample consisting of 3525 microlensing events, with Einstein radius crossing times of t_E < 760 days and a source star magnitude of I_s < 21.4 mag. We confirm our results are consistent with the latest measurements from the OGLE-IV 8 yr data set. We find our result is inconsistent with a prediction based on Galactic models, especially in the central region with ∣b∣ < 3°. These results can be used to improve the Galactic bulge model, and more central regions can be further elucidated by upcoming microlensing experiments, such as the PRime-focus Infrared Microlensing Experiment and Nancy Grace Roman Space Telescope.