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 compar
ison 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.
(Abridged) We present a comprehensive analysis of the relationship between star formation rate surface density (SFR SD) and gas surface density (gas SD) at sub-kpc resolution in a sample of 18 nearby galaxies. We use high resolution HI data from THIN
GS, CO data from HERACLES and BIMA SONG, 24 micron data from the Spitzer Space Telescope, and UV data from GALEX. We target 7 spiral galaxies and 11 late-type/dwarf galaxies and investigate how the star formation law differs between the H2-dominated centers of spiral galaxies, their HI-dominated outskirts and the HI-rich late-type/dwarf galaxies. We find that a Schmidt-type power law with index N=1.0+-0.2 relates the SFR SD and the H2 SD across our sample of spiral galaxies, i.e., that H2 forms stars at a constant efficiency in spirals. The average molecular gas depletion time is ~2*10^9 yrs. We interpret the linear relation and constant depletion time as evidence that stars are forming in GMCs with approximately uniform properties and that the H2 SD may be more a measure of the filling fraction of giant molecular clouds than changing conditions in the molecular gas. The relationship between total gas SD and SFR SD varies dramatically among and within spiral galaxies. Most galaxies show little or no correlation between the HI SD and the SFR SD. As a result, the star formation efficiency (SFE = SFR SD / gas SD) varies strongly across our sample and within individual galaxies. We show that in spirals the SFE is a clear function of radius, while the dwarf galaxies in our sample display SFEs similar to those found in the outer optical disks of the spirals. Another general feature of our sample is a sharp saturation of the HI SD at ~9 M_sol/pc^2 in both the spiral and dwarf galaxies.
