Estimation of the detectability of optical orphan afterglows

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 ǫe, and environment density n are insignificant. If Ej 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. Key words. gamma rays: bursts – ISM: jets and outflows – radiation mechanisms: non-thermal