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

Abstract

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 (SFR) density, although exactly how is currently unknown. As the most distant GRBs and star-forming galaxies probe the reionization epoch, the potential reward of understanding the redshift-dependent ratio Ψ(z) of the GRB rate to SFR is significant and includes addressing fundamental questions such as incompleteness in rest-frame UV surveys for determining the SFR 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 and accounting for uncertainty in their redshift distribution by considering the contribution of "dark" GRBs, we compare the cumulative redshift distribution N(< z) of GRBs with the star formation density ρ˙_* (z) measured from UV-selected galaxies over 0 < z < 4. Strong evolution (e.g., Ψ(z)∝(1 + z)^(1.5)) is disfavored (Kolmogorov-Smirnov test P < 0.07). We show that more modest evolution (e.g., Ψ(z)∝(1 + z)^(0.5)) is consistent with the data (P ≈ 0.9) and can be readily explained if GRBs occur primarily in low-metallicity galaxies which are proportionally more numerous at earlier times. If such trends continue beyond z sime 4, we find that the discovery rate of distant GRBs implies an SFR density much higher than that inferred from UV-selected galaxies. While some previous studies of the GRB-SFR connection have concluded that GRB-inferred star formation at high redshift would be sufficient to maintain cosmic reionization over 6< z <9 and reproduce the observed optical depth of Thomson scattering to the cosmic microwave background, we show that such a star formation history would overpredict 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 SFR and progenitor metallicity.

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