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Figure Rotation and the Mass of the Galactic Bulge

The mass of the Galactic bulge, $M_B$, is estimated from the tensor virial theorem. By including the effects of a barred stellar distribution and figure rotation (81 \kms kpc $^{-1}$) and by assuming that the bar is oriented at $θ$ $=$ 20°\ to our line of sight, $M_B$ is found to be as high as 2.8$\times$10$^{10}$ M$_{\odot}$. This estimate is in good agreement with the total mass inferred from the observed optical depth to microlensing for stars toward the inner Galaxy. For larger angles, $θ$ $\sim$ 40°, or smaller pattern speeds (20 \kms kpc $^{-1}$), $M_B$ is found to be $\sim$ 1.7 $-$ 1.9$\times$10$^{10}$ M$_{\odot}$, similar to previous estimates for a barred bulge (2$\times$10$^{10}$ M$_{\odot}$) and axisymmetric bulge (1.8$\times$10$^{10}$ M$_{\odot}$).