On the collapsar Model of Long Gamma-Ray Bursts: Constraints from Cosmic Metallicity Evolution

We explore the consequences of new observational and theoretical evidence that long gamma-ray bursts (GRBs) prefer low-metallicity environments. Using recently derived mass-metallicity correlations and the mass function from SDSS studies, and adopting an average cosmic metallicity evolution from Kewley & Kobulnicky and Savaglio et al., we derive expressions for the relative number of massive stars formed below a given fraction of solar metallicity, e, as a function of redshift. We demonstrate that about 1/10 of all stars form with e ! 0.1. Therefore, a picture in which the majority of GRBs form with e ! 0.1 is not inconsistent with an empirical global SN/GRB ratio of 1/1000. It implies that (1) GRBs peak at a significantly higher redshift than supernovae; (2) massive star evolution at low metallicity may be qualitatively different; and (3) the larger the low-metallicity bias of GRBs, the less likely binary evolution channels can be significant GRB producers.