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 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 \citet{kewley2005} and \citet{savaglio2005} we derive expressions for the the relative number of massive stars formed below a given fraction of solar metallicity, $\epsilon$, as function of redshift. We demonstrate that about 1/10th of all stars form with $\epsilon < 0.1$. Therefore, a picture where the majority of GRBs form with $\epsilon < 0.1$ is not inconsistent with an empirical global SN/GRB ratio of 1/1000. It implies that (1) GRB's 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.