I present an analysis of the \gamma -ray and afterglow energies of the complete sample of 17 short-duration GRBs with prompt X-ray follow-up .
I find that 80 \% of the bursts exhibit a linear correlation between their \gamma -ray fluence and the afterglow X-ray flux normalized to t = 1 d , a proxy for the kinetic energy of the blast wave ( F _ { X, 1 } \propto F _ { \gamma } ^ { 1.01 \pm 0.09 } ) .
An even tighter correlation is evident between E _ { \gamma, { iso } } and L _ { X, 1 } for the subset of 13 bursts with measured or constrained redshifts .
The remaining 20 \% of the bursts have values of F _ { X, 1 } / F _ { \gamma } that are suppressed by about three orders of magnitude , likely because of low circumburst densities ( Nakar 2007 ) .
These results have several important implications : ( i ) The X-ray luminosity is generally a robust proxy for the blast wave kinetic energy , indicating \nu _ { X } > \nu _ { c } and hence a circumburst density n \gtrsim 0.05 cm ^ { -3 } ; ( ii ) most short GRBs have a narrow range of \gamma -ray efficiency , with \langle \epsilon _ { \gamma } \rangle \approx 0.85 and a spread of 0.14 dex ; and ( iii ) the isotropic-equivalent energies span 10 ^ { 48 } -10 ^ { 52 } erg .
Furthermore , I find tentative evidence for jet collimation in the two bursts with the highest E _ { \gamma, { iso } } , perhaps indicative of the same inverse correlation that leads to a narrow distribution of true energies in long GRBs .
I find no clear evidence for a relation between the overall energy release and host galaxy type , but a positive correlation with duration may be present , albeit with a large scatter .
Finally , I note that the outlier fraction of 20 \% is similar to the proposed fraction of short GRBs from dynamically-formed neutron star binaries in globular clusters .
This scenario may naturally explain the bimodality of the F _ { X } / F _ { \gamma } distribution and the low circumburst densities without invoking speculative kick velocities of several hundred km s ^ { -1 } .