Formation rates of core-collapse supernovae and gamma-ray bursts

Abstract

Core collapse of massive stars with a relativistic jet expulsion along the rotation axis is a widely discussed scenario for gamma-ray burst (GRB) production. However the nature of the stellar progenitor remains unclear. We study the evolution of stars that may be the progenitors of long-soft GRBs - rotating naked helium stars presumed to have lost their envelopes to winds or companions. Our aim is to investigate the formation and development of single and binary systems and from this population evaluate the rates of interesting individual species. Using a rapid binary-evolution algorithm that enables us to model the most complex binary systems and to explore the effect of metallicity on GRB production, we draw the following conclusions. First, we find that, if we include an approximate treatment of angular momentum transport by mass loss, the resulting spin rates for single stars become too low to form a centrifugally supported disc that can drive a GRB engine, although they do have sufficiently massive cores to form black holes. Secondly, massive stars in binaries result in enough angular momentum -due to spin-orbit tidal interactions - to form a centrifugally supported disc and are thus capable of supplying a sufficient number of progenitors. This holds true even if only a small fraction of bursts are visible to a given observer and the GRB rate is several hundred times larger than the observed rate. Thirdly, low-metallicity stars aid the formation of rapidly rotating, massive helium cores at collapse and so their evolution is likely to be affected by the local properties of the interstellar medium (ISM). This effect could increase the GRB formation rate by a factor of 5-7 at Z = Z ○. /200. Finally we quantify the effects of mass loss, common-envelope evolution and black-hole formation and show that more stringent constraints to many of these evolution parameters are needed in order to draw quantitative conclusions from population synthesis work.