The Microlensing Event Rate and Optical Depth from MOA-II 9 Yr Survey Toward the Galactic Bulge

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 similar to 42 deg(2 )between -5 degrees < l < 10 degrees and -7 degrees < b < -1 degrees. In the central region with divided by l divided by < 5 degrees, we estimate an optical depth of tau=[1.75 +/- 0.04]x10(-6)exp[(0.34 +/- 0.02)(3 degrees-divided by b divided by)] and an event rate of Gamma = [16.08 +/- 0.28] x 10(-6) exp[(0.44 +/- 0.02)(3 degrees-divided by b divided by)]star(-1)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 divided by b divided by < 3 degrees. 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.