We use a sample of 36 galaxies from the KINGFISH (Herschel IR), HERACLES (IRAM CO), and THINGS (VLA HI) surveys to study empirical relations between Herschel infrared (IR) luminosities and the total mass of the interstellar gas (H2+HI). Such a comparison provides a simple empirical relationship without introducing the uncertainty of dust model fitting. We find tight correlations, and provide fits to these relations, between Herschel luminosities and the total gas mass integrated over entire galaxies, with the tightest, almost linear, correlation found for the longest wavelength data (SPIRE500). However, we find that accounting for the gas-phase metallicity (affecting the dust-to-gas ratio) is crucial when applying these relations to low-mass, and presumably high-redshift, galaxies. The molecular (H2) gas mass is found to be better correlated with the peak of the IR emission (e.g. PACS160), driven mostly by the correlation of stellar mass and mean dust temperature. When examining these relations as a function of galactocentric radius we find the same correlations, albeit with a larger scatter, up to a radius of 0.7 r_25 (within which most of the galaxys baryonic mass resides). However, beyond this radius the same correlations no longer hold, with the gas mass (predominantly HI) increasing relative to the infrared emission. The tight relations found for the bulk of the galaxys baryonic content suggest that the total gas masses of disk-like (non-merging) galaxies can be inferred from far-infrared continuum measurements in situations where only the latter are available, e.g. in ALMA continuum observations of high-redshift galaxies.
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