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 kinds of models : i ) a high-density solution , where the ejecta are collimated in a jet of half-angle \theta _ { jet } > 6 ^ { o } and interact with a medium of particle density 10 ^ { -4 } cm ^ { -3 } < n < 0.1 cm ^ { -3 } , ii ) a low-density solution with \theta _ { jet } > 2 ^ { o } and n < 10 ^ { -5 } cm ^ { -3 } .
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 cm ^ { -3 } < n < 10 ^ { 3 } cm ^ { -3 } and \theta _ { jet } > 8 ^ { o } .
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 .