Constraining the Beaming of Gamma-Ray Bursts With Radio Surveys

The degree of beaming in Gamma-Ray Bursts (GRBs) is currently unknown. The uncertainty in the gamma-ray beaming angle, theta, leaves the total energy release (proportional to theta^2) and the event rate per galaxy (proportional to 1/theta^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 counterpart can be used to set an upper limit on 1/theta^2. We find that a VLA survey with a sensitivity of 0.1 mJy at 10 GHz could identify more than 2e4/(theta/10degrees)^2 radio afterglows across the sky if each source is sampled at least twice over a period of one month or longer. From the total number of >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>6 degrees.