Figure Rotation and the Mass of the Galactic Bulge

Abstract

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 $\theta$ $=$ 20\deg \ 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, $\theta$ $\sim$ 40\deg, 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$_{\odot}$).