Dirt-cheap Gas Scaling Relations: Using Dust Absorption, Metallicity and Galaxy Size to Predict Gas Masses for Large Samples of Galaxies

Abstract

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.