Connecting the Gamma Ray Burst Rate and the Cosmic Star Formation History: Implications for Reionization and Galaxy Evolution

Abstract: (Abridged) The contemporary discoveries of galaxies and gamma ray bursts (GRBs) at high redshift have supplied the first direct information on star formation when the universe was only a few hundred million years old. The probable origin of long duration GRBs in the deaths of massive stars would link the universal GRB rate to the redshift-dependent star formation rate density, although exactly how is currently unknown. As the most distant GRBs and star-forming galaxies probe the reionization epoch, the potential rewards of understanding the redshift-dependent ratio Psi(z) of the GRB rate to star formation rate are significant and include addressing fundamental questions such as incompleteness in rest-frame UV surveys for determining the star formation rate at high redshift and time variations in the stellar initial mass function. Using an extensive sample of 112 GRBs above a fixed luminosity limit drawn from the Second Swift Burst Alert Telescope catalog, we compare the cumulative redshift distribution N(< z) of GRBs with the star formation density rho_sfr(z) measured from UV-selected galaxies over 0 < z < 4. Strong evolution (e.g., Psi(z) \propto (1+z)^{1.5}) is disfavored, while more modest evolution (e.g., Psi(z) \propto (1+z)^{0.5}) is consistent with the data. If such trends continue beyond z ~ 4, we find the discovery rate of distant GRBs implies a star formation rate density much higher than that inferred from UV-selected galaxies. We show that such a star formation history would over-predict the observed stellar mass density at z > 4 measured from rest-frame optical surveys. The resolution of this important disagreement is currently unclear, and the GRB production rate at early times is likely more complex than a simple function of star formation rate and progenitor metallicity.