Estimating gas masses and dust-to-gas ratios from optical spectroscopy

We present a method to estimate the total gas column density, dust-to-gas and dust-tometal ratios of distant galaxies from rest-frame optical spectra. The technique exploits the sensitivity of certain optical lines to changes in depletion of metals onto dust grains and uses photo-ionization models to constrain these physical ratios along with the metallicity and dust column density. We compare our gas column density estimates with H i and CO gas mass estimates in nearby galaxies to show that we recover their total gas mass surface density to within a factor of 2 up to a total surface gas mass density of ∼ 75 M⊙ pc . Our technique is independent of the conversion factor of CO to H2 and we show that a metallicity dependent XCO is required to achieve good agreement between our measurements and that provided by CO and H i. However we also show that our method can not be reliably aperture corrected to total gas mass. We calculate dust-to-gas ratios for all star-forming galaxies in the Sloan Digital Sky Survey Data Release 7 and show the resulting dependence on metallicity agrees well with the trend inferred from modelling of the dust emission of nearby galaxies using far-IR data. We also present estimates of the variation of the dust-to-metal ratio with metallicity and show that this is poorly constrained at metallicities below 50 per cent solar. We conclude with a study of the inventory of gas in the central regions, defined both in terms of a fixed physical radius and as a fixed fraction of the half-light radius, of ∼ 70, 000 star-forming galaxies from the Sloan Digital Sky Survey. We show that their central gas content and gas depletion times are not accurately predicted by a single parameter, but in agreement with recent studies we find that a combination of the stellar mass and some measure of central concentration provides a good predictor of gas content in galaxies. We also identify a population of galaxies with low surface densities of stars and very long gas depletion times.