A Comparison of the Afterglows of Short- and Long-Duration Gamma-Ray Bursts

We present a comparative study of the observed properties of the optical and X-ray afterglows of short- and long-duration gamma-ray bursts (GRBs). Using a large sample of 37 short and 421 long GRBs, we find a strong correlation between the afterglow brightness measured after 11 hours and the observed fluence of the prompt emission. Both the optical (R band) and X-ray flux densities (F_R and F_X) scale with the gamma-ray fluence, F_gamma. For bursts with a known redshift, a tight correlation exists between the afterglow flux densities at 11 hours (rest-frame) and the total isotropic gamma-ray energy, Egi: F_{R,X} ~ Egi^{alpha}, with alpha ~ 1. The constant of proportionality is nearly identical for long and short bursts, when Egi is obtained from the Swift data. Additionally, we find that for short busts with F_gamma >10^{-7} erg cm^{-2}, optical afterglows are nearly always detected by reasonably deep early observations. Finally, we show that the ratio F_R/F_X has very similar values for short and long bursts. These results are difficult to explain in the framework of the standard scenario, since they require that either (1) the number density of the surrounding medium of short bursts is typically comparable to, or even larger than the number density of long bursts; (2) short bursts explode into a density profile, n(r)\alpha r^{-2} or (3) the prompt gamma-ray fluence depends on the density of the external medium. We therefore find it likely that either basic assumptions on the properties of the circumburst environment of short GRBs or else the standard models of GRB emission must be re-examined. We believe that the most likely solution is that the ambient density surrounding typical short bursts is higher than has generally been expected: a typical value of ~1 per cm^{-3} is indicated.