Single star progenitors of long gamma-ray bursts I: Model grids and redshift dependent GRB rate

We present grids of massive star evolution models at four different metallicities (Z=0. 004, 0. 002, 0. 001, 0. 00001). The effects of rotation on the stellar structure and the transport of angular momentum and chemical elements through the Spruit-Tayler dynamo and rotationally induced instabilities are considered. After discussing uncertainties involved with the adopted physics, we elaborate the final fate of massive stars as a function of initial mass and spin rate, at each considered metallicity. In particular, we investigate for which initial conditions long gamma-ray bursts (GRBs) are expected to be produced in the frame of the collapsar model. Then, using an empirical spin distribution of young massive metal-poor stars and a specified metallicity-dependent history of star-formation, we compute the expected GRB rate as function of metallicity and redshift based on our stellar evolution models. The GRB production in our models is limited to metallicities of Z 0. 004, with the consequence that about 50 % of all GRBs are predicted to be found at redshifts above z = 4, with most supernovae occurring at redshifts below z 2. 2. The average GRB/SN ratio predicted by our model is about 1/200 globally, and 1/1250 at low redshift. Future strategies for testing the considered GRB progenitor scenario are briefly discussed.