In our previous paper (Jørgensenet al. 1995) we had computed by population synthesis the NS+NS coalescence time distribution. This allowed us to obtained a good fit to the observed distribution of the BATSE GRB. Transition from the coalescence time distribution to the requires knowledge of the star formation rate (SFR) history, which was approximated by a simple two-parametric model including an intensive burst (in which of all the stars were born, at a redshift ), and a subsequent constant SFR.
Since that time our knowledge of cosmic SFR history increased by the works of Madau et al. (1996) and others. Now it has become evident that the star formation rate is far from being constant and strongly rises with redshift up to .To account for the realistic SFR, we used the cosmic SFR history taken from Madau et al. (1996). However, the SFR at higher redshifts z>1.5 is still poorly known, so we introduce an additional SFR burst at to account for the early formation of the elliptical galaxies and spheroidal components of the spiral galaxies. The fraction of the stellar matter formed in this burst we denote by .We attribute the star formation burst to the galactic spheroidals and the subsequent star formation - to the galactic disks. The ratio of the amount of the visible matter in galactic disks and spheroidals is (Fukugita et al. 1998), which corresponds to our .
The coalescence time distributions were computed by the "Scenario Machine'' population synthesis engine (Lipunov et al. 1996a, 1996b) with an ordinary set of model parameters. The stellar evolution model was based on the results of Vanbeveren et al. (1998), which reproduce most accurately the observed galactic WR star distributions and stellar wind mass loss in massive stars.
As the main parameter influencing the result was the kick velocity, we display the result for several possible values of the mean kick velocity.
Figure 1 shows the coalescence time distributions for different values of mean kick. Note that the distributions have a power-law behaiviour, which implies a significant part of the coalescences time to be long. If there is no kick, the neutron star coalescence times are preferably long (there should be no coalescences in young stellar population), and the NS+BH binaries coalescence times are even longer than the Hubble time, so the observable event rate should be negligible.
The coalescence time distributions can be used for calculating the GRB rates. As relative rates are easier to observe than the absolute ones, here we show (see Fig. 2) the relative rate of coalescences in spiral and elliptical galaxies, obtained in a standard cosmological model (H0=75 km s-1/Mpc, and ).
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