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 very well observations during the early stages of the evolution (in particular WR populations and ratio between type II and type Ib,c at different metallicities, see Meynet & Maeder 2005).   Our models predict the production of fast rotating black holes. Models with large initial masses or high metallicity end their life 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 the collapsar model (Woosley 1993). Considering all types of WR stars as GRB progenitors, there would be too many GRBs compared to observations. If we consider only WO stars (type Ic supernovae as is the case for SN2003dh/GRB030329, see Matheson et al. 2003) as GRBs progenitors, the GRBs production rates are in much better agreement with observations. WO stars are produced only at low metallicities in the present grid of models. This prediction can be tested by future observations. 
R. Hirschi (1), G. Meynet (2), A. Maeder (2) ((1) University of Basel,   (2) Geneva Observatory, Switzerland)