On the afterglow from the receding jet of γ-ray bursts

According to popular progenitor models of gamma-ray bursts, twin jets should be launched by the central engine, with a forward jet moving toward the observer and a receding jet (or the counter jet) moving backwardly. However, in calculating the afterglows, usually only the emission from the forward jet is considered. Here we present a detailed numerical study on the afterglow from the receding jet. Our calculation is based on a generic dynamical description, and includes some delicate ingredients such as the effect of the equal arrival time surface. It is found that the emission from the receding jet is generally rather weak. In radio bands, it usually peaks at a time t >= 1000 d, with the peak flux nearly 4 orders of magnitude lower than the peak flux of the forward jet. Also, it usually manifests as a short plateau in the total afterglow light curve, but not as an obvious rebrightening as once expected. In optical bands, the contribution from the receding jet is even weaker, with the peak flux being similar to 23 mag lower than the peak flux of the forward jet. We thus argue that the emission from the receding jet is very difficult to detect. However, in some special cases, i.e., when the circum-burst medium density is very high, or if the parameters of the receding jet are quite different from those of the forward jet, the emission from the receding jet can be significantly enhanced and may still emerge as a marked rebrightening. We suggest that the search for receding jet emission should mostly concentrate on nearby gamma-ray bursts, and the observation campaign should last for at least several hundred days for each event.