Improved Estimates of the Milky Way's Stellar Mass and Star Formation
  Rate from Hierarchical Bayesian Meta-Analysis
  We present improved estimates of several global properties of the Milky Way,
including its current star formation rate (SFR), the stellar mass contained in
its disk and bulge+bar components, as well as its total stellar mass. We do so
by combining previous measurements from the literature using a hierarchical
Bayesian (HB) statistical method that allows us to account for the possibility
that any value may be incorrect or have underestimated errors. We show that
this method is robust to a wide variety of assumptions about the nature of
problems in individual measurements or error estimates. Ultimately, our
analysis yields a SFR for the Galaxy of $\dot{\mathrm{M}}_\star=1.65\pm0.19$
$\textrm{M}_\odot \textrm{yr}^{-1}$, assuming a Kroupa initial mass function
(IMF). By combining HB methods with Monte Carlo simulations that incorporate
the latest estimates of the Galactocentric radius of the Sun, $R_0$, the
exponential scale length of the disk, $L_d$, and the local surface density of
stellar mass, $\Sigma_\star(R_0)$, we show that the mass of the Galactic
bulge+bar is $\textrm{M}_\star^B=0.91\pm0.07\times10^{10}$ $\textrm{M}_\odot$,
the disk mass is $\textrm{M}_\star^D=5.17\pm1.11\times10^{10}$
$\textrm{M}_\odot$, and their combination yields a total stellar mass of
$\textrm{M}_\star=6.08\pm1.14\times10^{10}$ $\textrm{M}_\odot$ (assuming a
Kroupa IMF and an exponential disk profile). This analysis is based upon a new
compilation of literature bulge mass estimates, normalized to common
assumptions about the stellar initial mass function and Galactic disk
properties, presented herein. We additionally find a bulge-to-total mass ratio
for the Milky Way of $B/T=0.150^{+0.028}_{-0.019}$ and a specific star
formation rate of
$\dot{\mathrm{M}}_\star/\textrm{M}_\star=2.71\pm0.59\times10^{-11}
\textrm{yr}^{-1}$.
