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 $5.7^{+1.5}_{-1.1}\times10^{10}$ $\textrm{M}_\odot$.
