Gas-regulation of galaxies: the evolution of the cosmic sSFR, the metallicity-mass-SFR relation and the stellar content of haloes
A very simple physical model of galaxies, in which the formation of stars is instantaneously regulated by the mass of gas in a reservoir, links together three different aspects of the evolving galaxy population:(a) the cosmic time evolution of the specific star-formation rate sSFR relative to the growth of haloes, (b) the gas-phase metallicities across the galaxy population and over cosmic time, and (c) the ratio of the stellar to dark matter mass of haloes. If the SFR efficiency and wind mass loading are constant, the sSFR is set to the specific accretion rate of the galaxy: more realistic situations lead to an sSFR which is perturbed from this identity. The metallicity is set by the instantaneous operation of the regulator system rather than by the past history of the system. The regulator system naturally produces a Z(mstar, SFR) relation, with SFR as a second parameter in the mass-metallicity relation. This will be the same at all epochs unless the efficiency and mass-loading change with time, naturally producing a so-called "fundamental metallicity relation". The observed Z(mstar) relation of SDSS galaxies implies a strong dependence of stellar mass on halo mass that reconciles the different faint end slopes of the stellar and halo mass-functions in standard ΛCDM. It also boosts the sSFR relative to the specific accretion rate and produces a different dependence on mass, both of which are observed. The derived Z(mstar, SFR) relation for the regulator system is fit to published Z(mstar, SFR) data. The fitted efficiency is consistent with observed molecular gas-depletion timescales in galaxies while the fitted mass-loading is also plausible. The model also successfully reproduces the mass-metallicity relation of star-forming galaxies at z ~ 2.