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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, $Σ_\star(R_0)$, 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 $\dot{\mathrm{M}}_\star/\textrm{M}_\star=2.71\pm0.59\times10^{-11} \textrm{yr}^{-1}$.