2 The model

We use the population synthesis code (Belczynski & Bulik 1999), which concentrates on the population of massive star binaries; i.e., those that may eventually lead to formation of compact objects and compact object binaries. There are many parameters that describe the evolution of binaries; however, we concentrate here on one of them - the width of the kick velocity distribution $\sigma_{\rm v}$ (we assume that the kick velocity distribution is a three dimensional maxwellian). In this paper we do not distinguish between black neutron star and double neutron star systems. A more detailed discussion is presented in Bulik et al. (1999).

Since little is known about the host galaxies of gamma-ray bursts, in particular their types and masses, we will present two extreme cases: (i) propagation in the potential of large spiral galaxy like the Milky Way, and (ii) propagation in empty space corresponding to e.g. globular cluster origin. The potential of a spiral galaxy can be described as the sum of three components: bulge, disk, and halo. A convenient way to describe the Galactic potential has been proposed by Miyamoto & Nagai (1975), while a series of more detailed models were constructed by Kuijken & Gilmore (1989). We assume that the distribution of binaries in our model galaxy follows the mass distribution in the young disk (Paczynski 1990). Our calculation follows the approach used by Bulik et al. (1998)

Each binary moves initially with the local rotational velocity in the galactic disk. After a supernova explosion we add an appropriate velocity, provided that the system survives the explosion. We calculate the orbit of each system until it merges, provided that the merger time is smaller than the Hubble time (20 Gyrs here).