Estimation of the detectability of optical orphan afterglows

Abstract

Aims. By neglecting sideways expansion of gamma-ray burst (GRB) jets and assuming their half-opening angle distribution, we estimate the detectability of orphan optical afterglows. Methods. This estimation is carried out by calculating the durations of off-axis optical afterglows whose flux density exceeds a certain observational limit. Results. We show that the former assumption leads to more detectable orphans, while the latter suppresses the detectability strongly compared with the model with half-opening angle θj = 0.1. We also considered the effects of other parameters, and find that the effects of the ejecta energy Ej and post-jet-break temporal index -α2 are important but that the effects of the electron-energy distribution index p, electron energy equipartition factor εe, and environment density n are insignificant. If E j and α2 are determined by other methods, one can constrain the half-opening angle distribution of jets by observing orphan afterglows. Adopting a set of "standard" parameters, the detectable rate of orphan afterglows is about 1.3 × 10-2 deg-2 yr-1, if the observed limiting magnitude is 20 in R-band. © ESO 2006.