A Decade of Short-duration Gamma-ray Burst Broad-band Afterglows: Energetics, Circumburst Densities, and Jet Opening Angles

We present a comprehensive catalog and analysis of broad-band afterglow observations for 103 short-duration gamma-ray bursts (GRBs), comprised of all short GRBs from November 2004 to March 2015 with prompt follow-up observations in the X-ray, optical, near-infrared and/or radio bands. These afterglow observations have uncovered 71 X-ray detections, 30 optical/NIR detections, and 4 radio detections. Employing the standard afterglow synchrotron model, we perform joint probability analyses for a subset of 38 short GRBs with well-sampled light curves to infer the burst isotropic-equivalent energies and circumburst densities. For this subset, we find median isotropic-equivalent gamma-ray and kinetic energies of E_gamma,iso~2x10^51 erg, and E_K,iso~(1-3)x10^51 erg, respectively, depending on the values of the model input parameters. We further find that short GRBs occur in low-density environments, with a median density of n~(3-15)x10^-3 cm^-3, and that ~80-95% of bursts have densities of less than 1 cm^-3. We investigate trends between the circumburst densities and host galaxy properties, and find that events located at large projected offsets of >10 effective radii from their hosts exhibit particularly low densities of n<10^-4 cm^-3, consistent with an IGM-like environment. Using late-time afterglow data for 11 events, we find a median jet opening angle of theta_jet=16+/-10 deg. We also calculate a median beaming factor of f_b~0.04, leading to a beaming-corrected total energy release of E_true~1.6x10^50 erg. Furthermore, we calculate a beaming-corrected event rate of R_true=270 (+1580,-180) Gpc^-3 yr^-1, or ~8 (+47,-5) yr^-1 within a 200 Mpc volume, the Advanced LIGO/Virgo typical detection distance for NS-NS binaries.