SIMBAD references

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. This estimation is carried out by calculating the durations of off-axis optical afterglows whose flux density exceeds a certain observational limit. 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 θ_j=0.1. We also considered the effects of other parameters, and find that the effects of the ejecta energy E_j and post-jet-break temporal index -α₂ are important but that the effects of the electron-energy distribution index p, electron energy equipartition factor ε_e, 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 1.3x10^–2/deg²/yr, if the observed limiting magnitude is 20 in R-band.