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 densites ( 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 , { E } _ { \gamma, ISO } : F _ { R,X } \propto { { E } _ { \gamma, ISO } } ^ { \alpha } , with \alpha \simeq 1 .
The constant of proportionality is nearly identical for long and short bursts , when { E } _ { \gamma, ISO } is obtained from the Swift data .
Additionally , we find that for short busts with F _ { \gamma } \gtrsim 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 ) \propto 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 \sim 1 per cm ^ { -3 } is indicated .
We discuss recent modifications to the standard binary merger model for short bursts which may be able to explain the implied density .