1 Introduction

The discovery of GRB afterglows by BeppoSAX (Costa et al. 1997) introduced the standard astronomical methods to the GRB field. It led to subsequent identification of host galaxies (Groot et al. 1997), and to measurement of the distance through redshift. At the time of writing we know two redshifts of afterglows, and a few of host galaxies. In three cases it was possible to locate the afterglow within the host galaxy. GRB 970228 lies $\approx 0.4\hbox{$^{\prime\prime}$}$ from the center of its host galaxy (Fruchter et al. 1997), GRB 970508 and GRB 971214 lie within $0.01\hbox{$^{\prime\prime}$}$ and $0.05\hbox{$^{\prime\prime}$}$(Kulkarni et al. 1998) of the centroid of the host galaxies respectively.

There are two major physical models for cosmological GRBs: the compact object merger model, and the collapsar model. Both models predict a relation bewtween GRB sites and their galaxies. However, this relation is less strict in the case of the compact object merger model. In this paper we present a calculation of compact object population properties and the consequent distribution of their mergers in relation to the host galaxies. We present our model in Sect. 2, and show the results and compare them with observations in Sect. 3.

  

Figure 1: Cumulative distribution of projected distances on the sky: the left panel shows the distribution of distances travelled by a compact object binary in the case of propagation in an empty space, while the right panel shows the distribution of the distances between the center of the massive host galaxy and the merger site. The solid line corresponds to the case $\sigma_{\rm v}=0\,$kms-1, the dotted line $\sigma_{\rm v}=200\,$kms-1, the short-dashed line $\sigma_{\rm v}=400\,$kms-1, and the long dashed line $\sigma_{\rm v}=800\,$kms-1