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-to- metal ratios of distant galaxies from rest-frame optical spectra. The technique exploits the sensitivity of certain optical lines to changes in depletion of metals on to dust grains and uses photoionization models to constrain these physical ratios along with the metallicity and dust column density. We compare our gas column density estimates with HI 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 similar to 75M circle dot pc-2. Our technique is independent of the conversion factor of CO to II2 and we show that a metallicity-dependent XCO is required to achieve good agreement between our measurements and that provided by CO and HI. However, we also show that our method cannot be reliably aperture corrected to total integrated gas mass. We calculate dust-to- gas ratios for all star-forming galaxies in the Sloan Digital Sky Survey Data Release 7 and show that 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 similar to 70 000 star-forming galaxies from the Sloan Digital Sky Survey. We show that their central gas content and gas depletion time 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.