Sizing Up the Milky Way: A Bayesian Mixture Model Meta-Analysis of Photometric Scale Length Measurements

The exponential scale length ($L_d$) of the Milky Way's (MW's) disk is a critical parameter for describing the global physical size of our Galaxy, important both for interpreting other Galactic measurements and helping us to understand how our Galaxy fits into extragalactic contexts. Unfortunately, current estimates span a wide range of values and often are statistically incompatible with one another. Here, we perform a Bayesian meta-analysis to determine an improved, aggregate estimate for $L_d$, utilizing a mixture-model approach to account for the possibility that any one measurement has not properly accounted for all statistical or systematic errors. Within this machinery we explore a variety of ways of modeling the nature of problematic measurements, and then employ a Bayesian model averaging technique to derive net posterior distributions that incorporate any model-selection uncertainty. Our meta-analysis combines 29 different (15 visible and 14 infrared) photometric measurements of $L_d$ available in the literature; these involve a broad assortment of observational datasets, MW models and assumptions, and methodologies, all tabulated herein. Analyzing the visible and infrared measurements separately yields estimates for $L_d$ of $2.71^{+0.22}_{-0.20}$ kpc and $2.51^{+0.15}_{-0.13}$ kpc, respectively, whereas considering them all combined yields $2.64\pm0.13$ kpc. The ratio between the visible and infrared scale lengths determined here is very similar to that measured in external spiral galaxies. We use these results to update the model of the Galactic disk from our previous work, constraining its stellar mass to be $4.8^{+1.5}_{-1.1}\times10^{10}$ $\textrm{M}_\odot$, and the MW's total stellar mass to be $5.7^{+1.5}_{-1.1}\times10^{10}$ $\textrm{M}_\odot$.