Dirt-cheap Gas Scaling Relations: Using Dust Absorption, Metallicity and
  Galaxy Size to Predict Gas Masses for Large Samples of Galaxies
  We apply novel survival analysis techniques to investigate the relationship
between a number of the properties of galaxies and their atomic
($M_\mathrm{HI}$) and molecular ($M_{\mathrm{H_2}}$) gas mass, with the aim of
devising efficient, effective empirical estimators of the cold gas content in
galaxies that can be applied to large optical galaxy surveys. We find that dust
attenuation, {\AV}, of both the continuum and nebular emission, shows
significant partial correlations with $M_{\mathrm{H_2}}$, after controlling for
the effect of star formation rate (SFR). The partial correlation between {\AV}
and $M_\mathrm{HI}$, however, is weak. This is expected because in poorly
dust-shielded regions molecular hydrogen is dissociated by far-ultraviolet
photons. We also find that the stellar half-light radius, $R_{50}$, shows
significant partial correlations with both $M_{\mathrm{H_2}}$ and
$M_\mathrm{HI}$. This hints at the importance of environment (e.g.,
galactocentric distance) on the gas content of galaxies and the interplay
between gas and SFR. We fit multiple regression to summarize the median, mean,
and the $0.15/0.85$ quantile multivariate relationships among
$M_{\mathrm{H_2}}$, {\AV}, metallicity, and/or $R_{50}$. A linear combination
of {\AV} and metallicity (inferred from stellar mass) or {\AV} and $R_{50}$,
can estimate molecular gas masses within $\sim 2.5-3$ times the observed
masses. If SFR is used in addition, $M_\mathrm{{H_2}}$ can be predicted to
within a factor $\lesssim 2$. In this case, {\AV} and $R_{50}$ are the two best
secondary parameters that improve the primary relation between
$M_\mathrm{{H_2}}$ and SFR. Likewise, $M_\mathrm{HI}$ can be predicted to
within a factor $\lesssim 3$ using $R_{50}$ and SFR.
