Optical afterglows from cylindrical jets of short gamma-ray bursts

Abstract

Observations of extragalactic radio jets and young stellar jets show that the jets are cylindrical; i.e., they maintain a nearly constant cross section on large scales. It has been suggested that the afterglow behaviors of some long-duration gamma-ray bursts (GRBs) are consistent with the cylindrical jet model of GRBs. Here we study the afterglow emission of cylindrical jets from short-duration GRBs. For the usual conical jet geometry, it is argued that, because of the low fluence of short GRBs, the prospects of detecting the optical afterglow 10 hr after the burst are not promising. However, in the present work we find that if the jets are cylindrical, the chance for detecting the optical afterglow will be increased, even if the burst occurs in a low-density (n ∼ 10-3 cm-3) medium. Since the jets are expected to not be well collimated initially and the time when they change from conical to cylindrical is not exactly known, we discuss two cases for the afterglow of cylindrical jets: the jets becoming cylindrical (1) after the gamma-ray - emitting phase and (2) before the gamma-ray - emitting phase. In both cases, the light-curve behaviors, especially the peak time, are sensitive to the cross section radius of the cylindrical jet. In the former case we find that for viewing angles less than ∼0.03 rad relative to the jet axis, typical short GRBs have a late-time R-band afterglow with a maximum apparent magnitude of mR ≲ 23, given that the efficiency for producing gamma rays and the shock microphysical parameters of the afterglow are the same in short and long bursts. For the latter case the optical afterglows can always be readily detected with mR < 23 at 10 hr after the burst. Comparison between model light curves and observational upper limits of the optical afterglow flux of a few short GRBs are also made. © 2005. The American Astronomical Society. All rights reserved.