Spatial Distribution of Gamma-Ray Burst Sources

Abstract

The spatial distribution of sources of gamma-ray bursts (GRB) with known red shifts is analyzed by the conditional density and pairwise distance methods. The sample of GRB is based on data from the Swift mission and contains fluxes, coordinates, and red shifts for 384 GRB sources. Selection effects that distort the true source distribution are taken into account by comparing the observed distribution with fractal and uniform model catalogs. The Malmqvist effect is modeled using an approximation for the visible luminosity function of the GRB. The case of absorption in the galactic plane is also examined.This approach makes it possible to study the spatial structure of the entire sample at one time without artificial truncations. The estimated fractal dimensionality is $D=2.55\pm0.06$ on scales of $2\div6$ Gpc.