Stellar evolution with rotation. XIII. Predicted GRB rates at various Z

We present the evolution of rotation in models of massive single stars covering a wide range of masses and metallicities. These models reproduce observations during the early stages of the evolution very well, in particular Wolf-Rayet (WR) populations and ratio between type II and type Ib,c supernovae at different metallicities. Our models predict the production of fast-rotating black holes. Models with large initial masses or high metallicity end their lives with less angular momentum in their central remnant with respect to the break-up limit for the remnant. Many WR star models satisfy the three main criteria (black hole formation, loss of hydrogen-rich envelope, and enough angular momentum to form an accretion disk around the black hole) for gamma-ray bursts (GRB) production via Woosley's collapsar model. If we consider all types of WR stars as GRB progenitors, there would be too many GRBs compared to observations but if we consider only WO stars (type Ic supernovae as is the case for SN2003dh/GRB030329) as GRB progenitors, the GRB production rates are in much better agreement with observations. WO stars are produced only at low metallicities in the present series of models. This prediction can be tested by future observations.