The Observed Cosmic Star Formation Rate Density Has an Evolution that Resembles a Γ(a, bt) Distribution and Can Be Described Successfully by Only Two Parameters

Abstract

A debate is emerging regarding the recent inconsistent results of different studies for the cosmic star formation rate density (CSFRD) at high-z. We employ UV and IR data sets to investigate the SFR function (SFRF) at z ∼ 0–9. We find that the SFRFs derived from the dust-corrected UV (UVcorr) data contradict those from IR on some key issues because they are described by different distributions (Schechter versus double power law), imply different physics for galaxy formation (UVcorr data suggest an SFR limit/strong mechanism that diminish the number density of highly star-forming systems with respect to IR) and compare differently with the stellar mass density evolution obtained from spectral energy distribution fitting (UVcorr is in agreement, while IR differs up to 0.5 dex). However, both tracers agree on a constant CSFRD evolution at z ∼ 1–4 and point to a plateau instead of a peak. In addition, using both indicators, we demonstrate that the evolution of the observed CSFRD can be described by only two parameters and a function that has the form of a Gamma distribution (Γ(a, bt)). In contrast to previous parameterizations used in the literature, our framework connects the parameters to physical properties such as the SFR depletion time and cosmic baryonic gas density. The build-up of stellar mass occurs in Γ(a, bt) distributed steps and is the result of gas consumption up to the limit at which no eligible gas for SF at t = ∞ remains, resulting in a final cosmic stellar mass density of ∼ 0.5×109M⊙Mpc3 .