Analysis of the spatial distribution of gamma-ray bursts in their host galaxies

We compare the radial distributions of known localized gamma-ray bursts (GRBs) relative to the centers of their host galaxies with the distributions of known objects in nearby galaxies (supernovae of various types, X-ray binaries), the hypothetical dark-matter profiles, and the distribution of luminous matter in galaxies in the model of an exponential disk. By comparing the moments of empirical distributions, we show that the radial distribution of GRBs in galaxies differs significantly from that of other sources. We suggest a new statistical method for comparing empirical samples that is based on estimating the number of objects within a given radius. The exponential disk profile was found to be in best agreement with the radial distribution of GRBs. The distribution of GRBs relative to the centers of their host galaxies also agrees with the dark matter profile at certain model parameters.