A Decade of Short-duration Gamma-Ray Burst Broadband Afterglows: Energetics, Circumburst Densities, and Jet Opening Angles

We present a comprehensive catalog and analysis of broadband afterglow observations for 103 short-duration gamma-ray bursts (GRBs), comprised of all short GRBs from 2004 November to 2015 March with prompt follow-up observations in the X-ray, optical, near-infrared (NIR), 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 γ-ray and kinetic energies of E_γ,iso ≈ 2 × 10⁵¹ erg, and E_K,iso ≈ (1-3) × 10⁵¹ 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) × 10^-3 cm^-3, and that ≈80%-95% of bursts have densities of n ≲ 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 intergalactic medium-like environment. Using late-time afterglow data for 11 events, we find a median jet opening angle of θ_j = 16 ± 10°. We also calculate a median beaming factor of f_b ≈ 0.04, leading to a beaming-corrected total energy release of E_true ≈ 1.6 × 10⁵⁰ erg. Furthermore, we calculate a beaming-corrected event rate of {{R}}_{{true}}={270}_-180⁺¹⁵⁸⁰ Gpc^-3 yr^-1, or ≈ {8}_-5⁺⁴⁷ yr^-1 within a 200 Mpc volume, the Advanced LIGO/Virgo typical detection distance for NS-NS binaries.