On the correlation of short gamma-ray bursts and clusters of galaxies

We cross-correlate gamma-ray bursts (GRBs) and X-ray selected clusters of galaxies at z <= 0.45. We find a positive 2 sigma signal for the angular cross-correlation function w(bc)(theta) on scales theta <= 3 degrees. between short GRBs and clusters. Conversely, no correlation is found between clusters and the population of long GRBs. The comparison with the cluster autocorrelation function shows that short GRBs do not trace the cluster distribution, as not all short GRBs are found in clusters. A higher signal in wbc(.) is found if we only consider the cluster population up to z = 0.1. By comparing the short-burst autocorrelation function with model predictions, we then constrain short bursts to mostly originate within similar to 270 Mpc (i.e. z <= 0.06). Our analysis also reveals that short GRBs are better correlated with 'normal' galaxies. The double compact-object merger model for short GRBs would associate them preferentially with early-type galaxies, but the present statistics do not allow us to exclude that at least a fraction of these events might also take place in late-type galaxies, in agreement with recent evidence.