Constraining the Beaming of Gamma-Ray Bursts with Radio Surveys

Abstract

The degree of beaming in gamma-ray bursts (GRBs) is currently unknown. The uncertainty in the gamma-ray-beaming angle, theta(b), leaves the total energy release (proportional to theta(b)(2)) and the event rate per galaxy (proportional to theta(b)(-2)) unknown to within orders of magnitude. Since the delayed radio emission of GRB sources originates from a mildly relativistic shock and receives only weak relativistic beaming, the rate of radio-selected transients with no GRB counterparts can be used to set an upper limit on theta(b)(-2). We find that a VLA survey with a sensitivity of similar to 0.1 mJy at 10 GHz could identify greater than or similar to 2 x 10(4) (theta(b)/10 degrees)(-2) radio afterglows across the sky if each source is sampled at least twice over a period of 1 month or longer. From the total number of greater than or similar to 0.1 mJy sources observed at 8.44 GHz and the fraction of fading sources at 1.44 GHz, we get the crude limit theta(b) greater than or similar to 6 degrees.