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

We explore the consequences of new observational and theoretical evidencethat long gamma-ray bursts prefer low metallicity environments. Using recentlyderived 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 ofmassive stars formed below a given fraction of solar metallicity, $\epsilon$,as function of redshift. We demonstrate that about 1/10th of all stars formwith $\epsilon < 0.1$. Therefore, a picture where the majority of GRBs formwith $\epsilon < 0.1$ is not inconsistent with an empirical global SN/GRB ratioof 1/1000. It implies that (1) GRB's peak at a significantly higher redshiftthan supernovae; (2) massive star evolution at low metallicity may bequalitatively different and; (3) the larger the low-metallicity bias of GRBsthe less likely binary evolution channels can be significant GRB producers.Comment: 12 pages, 2 figures; accepted as ApJ Lette