The prompt gamma-ray and afterglow energies of short-duration gamma-ray bursts

I present an analysis of the gamma- 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 gamma- 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,F-1 proportional to F-gamma(1.01+/- 0.27)). An even tighter correlation is evident between the isotropic gamma-ray energy, E-gamma,E- iso, and the X-ray luminosity at t = 1 day, L-x,L-1, for the subset of 12 bursts with measured or constrained redshifts. The remaining 20% of the bursts have values of F-x,F-1/F-gamma 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 (2007). These results have several important implications: (1) 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 greater than or similar to 0.05 cm(-3); (2) most short GRBs have a narrow range of gamma- ray efficiency, with approximate to 0.1 and a spread of 0.3 dex; and (3) the isotropic-equivalent energies span 10(48)-10(53) erg. Furthermore, I find tentative evidence for jet collimation (opening angle, theta(j) approximate to 6 degrees) in GRB 061006 leading to E-gamma approximate to 4 x 10(48) 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.