  The first arcsecond localization of a short gamma-ray burst, GRB 050509B, has
enabled detailed studies of a short burst environment. We here report on
studies of the environment of GRB 050509B using the Swift X-ray Telescope
(XRT). The XRT error circle of the burst overlaps with an elliptical galaxy in
the cluster of galaxies ZwCl 1234.0+02916. Based on the measured X-ray flux of
the cluster we estimate that the probability for a chance superposition of GRB
050509B and a cluster at least as X-ray bright as this cluster is $< 2\times
10^{-3}$, presenting the first strong case of a short burst located in a
cluster of galaxies. We also consider the case for GRB 050509B being located
behind ZwCl 1234.0+02916 and gravitationally lensed. From the velocity
dispersion of the elliptical galaxy and the temperature of hot intracluster
gas, we model the mass distribution in the elliptical galaxy and the cluster,
and calculate the gravitational lensing magnification within the XRT error
circle. We find that, if GRB050509B would be positioned significantly behind
the cluster, it is most likely magnified by a factor less than two, but that
the burst could be strongly lensed if it is positioned within 2 arcsec of the
center of the bright elliptical galaxy. Further mapping of arcsecond size short
burst error boxes is a new promising route to determine the spatial
distribution of old stars throughout the Universe.
