A fundamental relation between the metallicity, gas content and stellar mass of local galaxies

Recent results have suggested that the well-known mass-metallicity relation has a strong dependence on the star formation rate (SFR), to the extent that a three-dimensional 'fundamental metallicity relation' (FMR) exists which links the three parameters with minimal scatter. In this work, we use a sample of 4253 local galaxies observed in atomic hydrogen from the Arecibo Legacy Fast ALFA survey to demonstrate, for the first time, that a similar fundamental relation (the H i FMR) also exists between stellar mass, gas-phase metallicity and H i mass. This latter relation is likely more fundamental, driving the relation between metallicity, SFR and mass. At intermediate masses, the behaviour of the gas FMR is very similar to that expressed via the SFR. However, we find that the dependence of metallicity on H i content persists to the highest stellar masses, in contrast to the 'saturation' of metallicity with SFR. It is interesting to note that the dispersion of the relation is very low at intermediate stellar masses [9 < log (M-*/M-circle dot) < 11], suggesting that in this range galaxies evolve smoothly, in an equilibrium between gas inflow, outflow and star formation. At high and low stellar masses, the scatter of the relation is significantly higher, suggesting that merging events and/or stochastic accretion and star formation may drive galaxies outside the relation. We also assemble a sample of galaxies observed in CO. However, due to a small sample size, strong selection bias and the influence of a metallicity-dependent CO/H-2 conversion factor, the data are insufficient to test any influence of molecular gas on metallicity.