Two short (<2 s) γ-ray bursts (GRBs) have recently been localized1-4 and fading afterglow counterparts detected 2-4. The combination of these two results left unclear the nature of the host galaxies of the bursts, because one was a star-forming dwarf, while the other was probably an elliptical galaxy. Here we report the X-ray localization of a short burst (GRB 050724) with unusual γ-ray and X-ray properties. The X-ray afterglow lies off the centre of an elliptical galaxy at a redshift of z = 0.258 (ref. 5), coincident with the position determined by ground-based optical and radio observations6-8. The low level of star formation typical for elliptical galaxies makes it unlikely that the burst originated in a supernova explosion. A supernova origin was also ruled out for GRB 050709 (refs 3, 31), even though that burst took place in a galaxy with current star formation. The isotropic energy for the short bursts is 2-3 orders of magnitude lower than that for the long bursts. Our results therefore suggest that an alternative source of bursts - the coalescence of binary systems of neutron stars or a neutron star-black hole pair - are the progenitors of short bursts.
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