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 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 between -5 <l< 10 degree and -7 <b< -1 degree. Our event rate
and optical depth analysis uses 474 events with well defined microlensing
parameters. In the central fields with |l|< 5 degree, we find an event rates of
\Gamma = [2.39+/-1.1]e^{[0.60\pm0.05](3-|b|)}x 10^{-5}/star/yr and an optical
depth of \tau_{200} = [2.35+/-0.18]e^{[0.51+/-0.07](3-|b|)}x 10^{-6} for the
427 events using all sources brighter than I_s = 20 mag 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 degree. For the 111 events in 3.2 deg^2 of the central
Galactic Bulge at |b| < 3.0 degree and 0.0 < l < 2.0, centered at (l,b)=(0.97,
-2.26), we find \Gamma = 4.57_{-0.46}^{+0.51} x 10^{-5}/star/yr and \tau_{200}
= 3.64_{-0.45}^{+ 0.51} x 10^{-6}. We also consider a Red Clump Giant (RCG)
star sample with I_s<17.5 mag. Our results are consistent with previous optical
depth measurements. We find that the previously observed difference in optical
depth measurements between all-source and RCG samples may be largely due to
statistical fluctuations. These event rate measurements towards the central
galactic bulge are necessary to predict the microlensing event rate and to
optimize the survey fields in the future space mission such as WFIRST.
