The high-redshift star formation rate derived from gamma-ray bursts: possible origin and cosmic reionization

The collapsar model of long gamma-ray bursts (GRBs) indicates that they may trace the star formation history, so long GRBs may be a useful tool for measuring the high-redshift star formation rate (SFR). The collapsar model explains GRB formation via the collapse of a rapidly rotating massive star with M > 30 M-circle dot into a black hole, which may imply a decrease in SFR at high redshift. However, we find that the Swift GRBs during 2005 to 2012 are biased when tracing the SFR, including a factor about (1 + z)(0.5), which agrees with recent results. After taking this factor, the SFR derived from GRBs does not show a steep drop up to z similar to 9.4. We consider the GRBs produced by rapidly rotating metal-poor stars with low masses to explain the high-redshift GRB rate excess. The chemically homogeneous evolution scenario (CHES) of rapidly rotating stars with mass higher than 12 M-circle dot is recognized as a promising path towards collapsars in connection with long GRBs. Our results indicate that the stars in the mass range 12 M-circle dot < M < 30 M-circle dot for low enough metallicity Z <= 0.004 with the GRB efficiency factor 10(-5) can fit the derived SFR with good accuracy. Combining these two factors, we find that the conversion efficiency from massive stars to GRBs is enhanced by a factor of 10, which may explain the excess of the high-redshift GRB rate. We also investigate the cosmic reionization history using the derived SFR. The GRB-inferred SFR would be sufficient to maintain cosmic reionization over 6 < z < 10 and reproduce the observed optical depth of Thomson scattering to the cosmic microwave background.