3 Results

The distribution of kick velocities a neutron star receives at birth is not very well known. Dewey & Cordes (1987) describe it as a weighted sum of 80% with the width of $175\,$km s^-1, and 20% with the width $700\,$km s^-1. We use the population synthesis code with four values of the kick velocity distribution width: with no kick velocites $\sigma_{\rm v}=0\,$km s^-1, and with $\sigma_{\rm v}= 200,\, 400,\, 800\,$km s^-1. The results are presented in Fig. 1. In the case of propagation in the empty space the mean distance travelled from the place of birth decreases with increasing the kick velocity distribution width $\sigma_{\rm v}$. This is due to the fact that with high kick velocities only tightly bound systems survive and their expected lifetimes are short. On the other hand the typical velocities of the binaries increase; however the dominant effect is that of the decrease of the lifetimes. While the mean of the distribution becomes smaller, the width of the distribution increases, so that the distribution always reaches a few Mpc. Depending on the kick velocity, between 80% and 40% of the mergers take place further than 100kpc (projected) distance from the place of birth, and between 25% and 15% travel beyond a Mpc.

In the case of propagation in the potential of a large galaxy, the mean distance from the center of the galaxy does not change with the kick velocity, and is about $10\,$kpc; i.e. the size of the galaxy in our simulations. This is because the slow systems are bound in the galactic potential and their distribution traces that of the matter in the galaxy, regardless of their lifetime. The width of the distribution increases with increasing $\sigma_{\rm v}$, as was the case above. The tail here is due to the systems that are unbound, and is nearly identical to the case of propagation in empty space. Between 5% and 30% of the systems travel further than 100kpc, and up to 7% of the mergers reach the distance of 1Mpc.

While the statistics of GRB afterglows that are detected and localized within the host galaxies is small, we note that in eight cases host galaxies have been identified, with two cases under discussion: 980425 may be a very unusal burst and 971227 was not searched for exhaustively (Hogg & Fruchter 1998). This indicates that bursts afterglows are correlated with faint ($R \sim 25$) galaxies. From our simulations we find that a significant fraction of the neutron star mergers should be ejected far from the hosts, and then the probability of chance association with a galaxy would be 10-15%. Thus continuing assciations of GRB afterglows with galaxies will disfavour the compact object merger model. On the other hand GRBs that take place outside host galaxies may not produce afterglows, thus preventing good localizations. In the compact object merger model the fraction of such bursts would be about 10-20%. GRBs detected by BeppoSAX are only those with durations longer than 6s, so perhaps the compact object mergers are connected with short bursts, while the long bursts are produced by a different physical mechanism (e.g., collapsars), that links them to galaxies. In conclusion, studies of the afterglows and their relations to the host galaxies can yield another important constraint on the models of GRBs.

Acknowledgements

This work has been funded by KBN grants 2P03D00911, 2P03D01113, and 2P03D00415; and also made use of the NASA Astrophysics Data System.