The cosmological origin of at least an appreciable fraction of classical gamma-ray bursts ( GRBs ) is now supported by redshift measurements for a half-dozen faint host galaxies .
Still , the nature of the central engine ( or engines ) 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 variety of such scenarios and estimate the probability of each .
Population synthesis calculations are carried out using a Monte Carlo approach in which the many uncertain parameters intrinsic to such calculations are varied .
We estimate the event rate for each class of model as well as the propagation distance for those having significant delay between formation and burst production , i.e. , double neutron star ( DNS ) mergers and black hole – neutron star ( BH/NS ) mergers .
One conclusion is a one to two order of magnitude decrease in the rate of DNS and BH/NS mergers compared to that previously calculated using invalid assumptions about common envelope evolution .
Other major uncertainties in the event rates and propagation distances include the history of star formation in the universe , the masses of the galaxies where merging compact objects are born , and the radii of the hydrogen stripped cores of massive stars .
For reasonable assumptions regarding each , we calculate a daily event rate in the universe for i ) merging neutron stars : \sim 100/day ; ii ) neutron-star black hole mergers : \sim 450/day ; iii ) collapsars : \sim 10 ^ { 4 } /day ; iv ) helium star black hole mergers : \sim 1000/day ; and v ) white dwarf black hole mergers : \sim 20/day .
The range of uncertainty in these numbers however , is very large , typically two to three orders of magnitude .
These rates must additionally be multiplied by any relevant beaming factor ( f _ { \Omega } < 1 ) and sampling fraction ( if the entire universal set of models is not being observed ) .
Depending upon the mass of the host galaxy , 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 .
The same numbers characterize BH/NS mergers .
Because of the delay time , neutron star and black hole mergers will happen at a redshift 0.5 to 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 BH/NS mergers and thus will ultimately be determined to lie outside of galaxies and at a closer mean distance than long complex bursts ( which we attribute to collapsars ) .
In the absence of a galactic site , the distance to these bursts may be difficult to determine .