Formation rates of black hole accretion disk gamma-ray bursts

The cosmological origin of at least an appreciable fraction of classical ga mma-ray bursts (GRBs) is now supported by redshift measurements for a half- dozen faint host galaxies. Still, the nature of the central engine (or engi nes) that provide the burst energy remains unclear. While many models have been proposed, those currently favored are all based upon the formation of and/or rapid accretion into stellar-mass black holes. Here we discuss a var iety of such scenarios and estimate the probability of each. Population syn thesis calculations are carried out using a Monte Carlo approach in which t he many uncertain parameters intrinsic to such calculations are varied. We estimate the event rate for each class of model as well as the propagation distances for those having significant delay between formation and burst pr oduction, i.e., double neutron star (DNS) mergers and black hole-neutron st ar (BH/NS) mergers. One conclusion is a 1-2 order of magnitude decrease in the rate of DNS and BH/NS mergers compared to that previously calculated us ing invalid assumptions about common envelope evolution. Other major uncert ainties in the event rates and propagation distances include the history of star formation in the universe, the masses of the galaxies in which mergin g compact objects are born, and the radii of the hydrogen-stripped cores of massive stars. For reasonable assumptions regarding each, we calculate a d aily event rate in the universe for (1) merging neutron stars: similar to 1 00 day(-1); (2) neutron star-black hole mergers: similar to 450 day(-1); (3 ) collapsars: similar to 10(4) day(-1); (4) helium star black hole mergers: similar to 1000 day(-1); and (5) white dwarf-black hole mergers: similar t o 20 day(-1). The range of uncertainty in these numbers, however, is very l arge, typically 2-3 orders of magnitude. These rates must additionally be m ultiplied by any relevant beaming factor (f(Omega) < 1) and sampling fracti on (if the entire universal set of models is not being observed). Depending upon the mass of the host galaxy, one-half of the DNS mergers will happen within 60 kpc (for a galaxy with a mass comparable to that of the Milky Way ) to 5 Mpc (for a galaxy with negligible mass) from the Galactic center. Th e same numbers characterize BH/NS mergers. Because of the delay time, neutr on star and black hole mergers will happen at a redshift 0.5-0.8 times that of the other classes of models. Information is still lacking regarding the hosts of short, hard bursts, but we suggest that they are due to DNS and B H/NS mergers and thus will ultimately be determined to lie outside of galax ies and at a closer mean distance than long complex bursts (which we attrib ute to collapsars). In the absence of a galactic site, the distance to thes e bursts may be difficult to determine.