  We use the available radio, optical and X-ray measurements for the afterglows
of the short bursts 050709 and 050724 to constrain the blast-wave energy, its
collimation and the density of the circumburst medium. For GRB 050709 (whose
duration was 0.07 s), we identify two models: i) a high-density solution, where
the ejecta are collimated in a jet of half-angle theta_{jet} > 6 deg and
interact with a medium of particle density 10^{-4}/cc < n < 0.1/cc, and ii) a
low-density solution with theta_{jet} > 2 deg and n < 10^{-5}/cc. These density
ranges are compatible with those expected in the vicinity of the host galaxy
and in the intergalactic medium, lending support to the hypothesis that the
progenitor of GRB 050907 is a NS-NS or NS-BH merger. For GRB 050724 (which last
3 s), we obtain 0.1/cc < n < 1000/cc and theta_{jet} > 8 deg. The range of
allowed densities shows that this burst occurred in the intragalactic
environment. The dynamical parameters of the high-density model for the GRB
afterglow 050709 are similar to those for 050724. If these parameters are
representative for short-GRB outflows, then these jets are less collimated and
have a lower kinetic energy than those of long bursts, which suggests that GRB
jets are not magnetically collimated and are powered by the gravitational
energy of the torus. Evidently, the analysis of more short-GRB afterglows is
required for a more robust conclusion.

Astrophysics