Optical emission from GRB 050709: A short/hard GRB in a star-forming galaxy

We present optical observations of the short/hard gamma-ray burst GRB 050709, the first such event with an identified optical counterpart. The object is coincident with a weak X-ray source and is located inside a galaxy at redshift $z = 0.1606 \pm 0.0002$. Multiband photometry allowed us to study the broad-band spectral energy distribution. Late-time monitoring places strong limits on any supernova simultaneous with the GRB. The host galaxy is not of early type. Spectra show that the dominant stellar population is relatively young ($\sim $1 Gyr), and that ongoing star formation is present at a level of $2\mbox{--}3\,L/L_*~M_\odot$ yr-1. This is at least 2 orders of magnitude larger than that observed in the elliptical hosts of the short GRB 050509B and GRB 050724. This shows that at least some short GRBs originate in a young population. Short/hard GRB models based on the merger of a binary degenerate system are compatible with the host galaxy characteristics, although there is still the possibility of a connection between young stars and at least a fraction of such events.