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 , \sigma \approx 660 km s ^ { -1 } .
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 , L _ { X } \approx 4.9 \times 10 ^ { 42 } erg s ^ { -1 } , and a temperature , kT \approx 0.9 keV .
The inferred mass of the cluster is 2.5 \times 10 ^ { 13 } M _ { \odot } , 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 3 \times 10 ^ { -14 } erg s ^ { -1 } cm ^ { -2 } , or M \lesssim 5 \times 10 ^ { 13 } M _ { \odot } 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 \sim 10 - 20 \% .