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We report optical and near-infrared broad band observations of theshort-duration GRB 050724 host galaxy, used to construct its spectral energydistribution (SED). Unlike the hosts of long-duration gamma-ray bursts (GRBs),which show younger stellar populations, the SED of the GRB 050724 host galaxyis optimally fitted with a synthetic elliptical galaxy template based on anevolved stellar population (age ~2.6 Gyr). The SED of the host is difficult toreproduce with non-evolving metallicity templates. In contrast, if the shortGRB host galaxy metallicity enrichment is considered, the synthetic templatesfit the observed SED satisfactorily. The internal host extinction is low (A_v\~< 0.4 mag) so it cannot explain the faintness of the afterglow. This shortGRB host galaxy is more massive (~5x10^10 Mo) and luminous (~1.1 L*) than mostof the long-duration GRB hosts. A statistical comparison based on the ages ofshort- and long-duration GRB host galaxies strongly suggests thatshort-duration GRB hosts contain, on average, older progenitors. These findingssupport a different origin for short- and long-duration GRBs.Comment: A&A in pres

The short-duration GRB 050724 host galaxy in the context of the long-duration GRB hosts