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Galaxy Clusters Associated with Short GRBs. I. The Fields of GRBs 050709, 050724, 050911 and 051221a

We present a search for galaxy clusters in the fields of three bona-fide short GRBs (050709, 050724, and 051221a) and the putative short burst GRB 050911 using multi-slit optical spectroscopy. These observations are part of a long-term program to constrain the progenitor age distribution based on the fraction of short GRBs in galaxy clusters and early-type galaxies. We find no evidence for cluster associations at the redshifts of the first three bursts, but we confirm the presence of the cluster EDCC 493 within the error circle of GRB 050911 and determine its redshift, z=0.1646, and velocity dispersion, ~660 km/s. In addition, our analysis of Swift/XRT observations of this burst reveals diffuse X-ray emission coincident with the optical cluster position, with a luminosity, 4.9e42 erg/s, and a temperature, kT=0.9 keV. The inferred mass of the cluster is 2.5e13 Msun, and the probability of chance coincidence is about 0.1-1%, indicating an association with GRB 050911 at the 2.6-3.2 sigma confidence level. A search for diffuse X-ray emission in coincidence with the fifteen other short GRBs observed with XRT and Chandra reveals that with the exception of the previously noted cluster ZwCl 1234.0+02916 likely associated with GRB 050509b, no additional associations are evident to a typical limit of 3e-14 erg/s/cm^2, or M<5e13 Msun assuming a typical z=0.3. The resulting fraction of short GRBs hosted by galaxy clusters of about 20% is in rough agreement with the fraction of stellar mass in clusters of ~10-20%.