Improved Estimates of the Milky Way's Stellar Mass and Star Formation Rate from Hierarchical Bayesian Meta-Analysis (1407.1078v3)

Abstract: 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 $\dot{\mathrm{M}}\star/\textrm{M}\star=2.71\pm0.59\times10^{-11} \textrm{yr}^{-1}$.

• The paper employs hierarchical Bayesian meta-analysis to derive robust estimates of the Milky Way's stellar mass and star formation rate.
• The methodology integrates decades of measurements, normalizing differing assumptions to account for uncertainties and outliers effectively.
• Results indicate a total stellar mass of approximately 6.08×10^10 M⊙ with a bulge-to-total ratio aligning with similar spiral galaxies.

Improved Estimates of the Milky Way's Stellar Mass and Star Formation Rate: A Hierarchical Bayesian Approach

The paper by Licquia and Newman provides a comprehensive evaluation of the Milky Way (MW) by analyzing its stellar mass and star formation rate (SFR) using hierarchical Bayesian (HB) meta-analysis techniques. This methodology meticulously combines past measurements to yield more robust estimates, accommodating potential inaccuracies or underestimated errors in individual studies.

Hierarchical Bayesian Meta-Analysis

The authors adopt a hierarchical Bayesian framework to synthesize various independent estimates of global MW properties, such as SFR and stellar mass. This approach is particularly adept at handling disparate datasets and can account for outliers or measurements potentially impacted by unquantified systematics. The major strength of this analysis is its ability to produce statistically rigorous consensus values from existing literature.

Star Formation Rate

The paper estimates the MW's current SFR to be $1.65 \pm 0.19 \, M_\odot/\text{yr}$, assuming a Kroupa initial mass function (IMF). This estimate is synthesized from a wide array of studies spanning three decades. The analysis reveals minimal tension among these studies once normalized to common assumptions, indicating the robustness of their approach. This result provides a critical reference for comparing the MW's star-forming activity to other galaxies, using consistently defined parameters.

Stellar Mass Estimates

The paper also provides detailed estimates of the MW's stellar mass, separating it into distinct components—bulge+bar and the disk. By integrating HB methods with Monte Carlo simulations, the authors account for uncertainties in parameters like the Solar radius ($R_0$), the scale length ($L_d$), and the local surface density. The Galactic bulge+bar mass is estimated at $0.91 \pm 0.07 \times 10^{10} \, M_\odot$, while the disk mass is $5.17 \pm 1.11 \times 10^{10} \, M_\odot$. The total stellar mass combines these to yield $6.08 \pm 1.14 \times 10^{10} \, M_\odot$.

Bulge-to-Total Mass Ratio

Additionally, the authors calculate the bulge-to-total mass ratio ($B/T$) as $0.150^{+0.028}_{-0.019}$, aligning the MW within the distribution typical of galaxies of similar morphological type. This result serves as a benchmark for understanding the structural makeup of spiral galaxies.

Theoretical and Practical Implications

The paper provides significant insights into the Milky Way's place in the broader galactic ecosystem. By using the HB meta-analysis for galaxy parameters, the authors add reliability and consistency to measurements that often suffer from methodological variations. This refined understanding aids in calibrating models of galactic evolution and improves comparisons with external galaxies.

Future Directions

With forthcoming surveys like Gaia expected to further refine these measurements, the HB methodology employed here sets a precedent for incorporating future datasets into cohesive analyses, potentially leading to even more precise determinations of galactic parameters. The approach facilitates an evolving framework that can adapt to the increasingly precise measurements available in contemporary astronomical research.

Licquia and Newman's integration of statistical rigor into astrophysical measurements represents a significant contribution to our understanding of the MW, illustrating a pathway forward for future large-scale galactic analyses.