A Beaming-Independent Estimate of the Energy Distribution of Long Gamma-Ray Bursts: Initial Results and Future Prospects

We present single-epoch radio afterglow observations of 24 long-duration gamma-ray burst (GRB) on a timescale of >100 d after the burst. These observations trace the afterglow evolution when the blastwave has decelerated to mildly- or non-relativistic velocities and has roughly isotropized. We infer beaming-independent kinetic energies using the Sedov-Taylor self-similar solution, and find a median value for the sample of detected bursts of about 7x10^51 erg, with a 90% confidence range of 1.1x10^50-3.3x10^53 erg. Both the median and 90% confidence range are somewhat larger than the results of multi-wavelength, multi-epoch afterglow modeling (including large beaming corrections), and the distribution of beaming-corrected gamma-ray energies. This is due to bursts in our sample with only a single-frequency observation for which we can only determine an upper bound on the peak of the synchrotron spectrum. This limitation leads to a wider range of allowed energies than for bursts with a well-measured spectral peak. Our study indicates that single-epoch centimeter-band observations covering the spectral peak on a timescale of ~1 yr can provide a robust estimate of the total kinetic energy distribution with a small investment of telescope time. The substantial increase in bandwidth of the EVLA (up to 8 GHz simultaneously with full coverage at 1-40 GHz) will provide the opportunity to estimate the kinetic energy distribution of GRBs with only a few hours of data per burst.