Lessons from cosmic history: The case for a linear star formation -- H2 relation

Abstract

Observations show that star formation in galaxies is closely correlated with the abundance of molecular hydrogen. Modeling this empirical relation from first principles proves challenging, however, and many questions regarding its properties remain open. For instance, the exact functional form of the relation is still debated and it is also unknown whether it applies at z>4, where CO observations are sparse. Here, we analyze how the shape of the star formation -- gas relation affects the cosmic star formation history and global galaxy properties using an analytic model that follows the average evolution of galaxies in dark matter halos across cosmic time. We show that a linear relation with an H2 depletion time of ~2.5 Gyr, as found in studies of nearby galaxies, results in good agreement with current observations of galaxies at both low and high redshift. These observations include the evolution of the cosmic star formation rate density, the z~4-9 UV luminosity function, the evolution of the mass -- metallicity relation, the relation between stellar and halo mass, and the gas-to-stellar mass ratios of galaxies. In contrast, the short depletion times that result from adopting a highly super-linear star formation -- gas relation lead to large star formation rates, substantial metal enrichment (~0.1 solar), and low gas-to-stellar mass ratios already at z~10, in disagreement with observations. These results can be understood in terms of an equilibrium picture of galaxy evolution in which gas inflows, outflows, and star formation drive the metallicities and gas fractions toward equilibrium values that are determined by the ratio of the accretion time to the gas depletion time. In this picture, the cosmic modulation of the accretion rate is the primary process that drives the evolution of stellar masses, gas masses, and metallicities of galaxies from high redshift until today.