2007ApJ...670.1254B

I present an analysis of the γ-ray and afterglow energies of a complete sample of 16 short-duration GRBs with prompt X-ray follow-up. I find that 80% of the bursts exhibit a linear correlation between their γ-ray fluence and the afterglow X-ray flux normalized to t=1 day, a proxy for the kinetic energy of the blast wave (F_X,1∝F^1.01±0.27_γ). An even tighter correlation is evident between the isotropic γ-ray energy, E_γ,iso, and the X-ray luminosity at t=1 day, L_X,1, for the subset of 12 bursts with measured or constrained redshifts. The remaining 20% of the bursts have values of F_X,1/F_γ that are suppressed by about 3 orders of magnitude, likely as a result of low circumburst densities; this has been noted based on a smaller sample by Nakar ((ref???)2007). These results have several important implications: (1) the X-ray luminosity is generally a robust proxy for the blast wave kinetic energy, indicating ν_X>ν_c, and hence a circumburst density n≳0.05/cm3; (2) most short GRBs have a narrow range of γ-ray efficiency, with <ε_γ>~0.1 and a spread of 0.3 dex; and (3) the isotropic-equivalent energies span 10⁴⁸-10⁵³ erg. Furthermore, I find tentative evidence for jet collimation (opening angle, θ_j~6°) in GRB 061006 leading to E_γ~4x10⁴⁸ erg, similar to other short bursts with jet breaks. 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 low-density hypothesis for the outliers can be explained in the context of neutron star-neutron star (NS-NS) mergers in globular clusters (as opposed to large kick velocities), but present short GRB rate estimates may be an order of magnitude too large for this scenario to work.