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

Abstract 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 deg 2 between −5° &lt; l &lt; 10° and −7° &lt; b &lt; −1°. In the central region with ∣ l ∣ &lt; 5°, we estimate an optical depth of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>τ</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>1.75</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.04</mml:mn> <mml:mo stretchy="false">]</mml:mo> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> <mml:mi>exp</mml:mi> <mml:mo stretchy="false">[</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.34</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.02</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>∘</mml:mo> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:mo stretchy="false">∣</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy="false">∣</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">]</mml:mo> </mml:math> and an event rate of Γ = [16.08 ± 0.28] × 10 −6 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>exp</mml:mi> <mml:mo stretchy="false">[</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.44</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.02</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mn>3</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>−</mml:mo> <mml:mo stretchy="false">∣</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy="false">∣</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">]</mml:mo> <mml:msup> <mml:mi>star</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mi>yr</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> using a sample consisting of 3525 microlensing events, with Einstein radius crossing times of t E &lt; 760 days and a source star magnitude of I s &lt; 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 ∣ &lt; 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.