Estimation of the detectability of optical orphan afterglows

¹ Department of Astronomy, Nanjing University, Nanjing 210093, PR China e-mail: [zouyc;dzg]@nju.edu.cn
² Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, PR China e-mail: xfwu@pmo.ac.cn
³ Joint Center for Particle, Nuclear Physics and Cosmology (J-CPNPC) between Nanjing University and Purple Mountain Observatory, Nanjing 210008, PR China

Received: 13 January 2006
Accepted: 22 August 2006

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 . 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  are important but that the effects of the electron-energy distribution index p, electron energy equipartition factor , and environment density n are insignificant. If E_j and  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  , if the observed limiting magnitude is 20 in R-band.