Gamma-ray bursts (GRBs) are the most brilliant objects in the Universe but efforts to estimate the total energy released in the explosion -- a crucial physical quantity -- have been stymied by their unknown geometry: spheres or cones. We report on a comprehensive analysis of GRB afterglows and derive their conical opening angles. We find that the gamma-ray energy release, corrected for geometry, is narrowly clustered around 5x10**50 erg. We draw three conclusions. First, the central engines of GRBs release energies that are comparable to ordinary supernovae, suggesting a connection. Second, the wide variation in fluence and luminosity of GRBs is due entirely to a distribution of opening angles. Third, only a small fraction of GRBs are visible to a given observer and the true GRB rate is at least a factor of 500 times larger than the observed rate.Comment: Nature, submitte

Past studies have suggested that long-duration gamma-ray bursts have a 'standard' energy of E(gamma) approximately 10(51) erg in the ultra-relativistic ejecta, after correcting for asymmetries in the explosion ('jets'). But a group of sub-energetic bursts, including the peculiar GRB980425 associated with the supernova SN1998bw (E(gamma) approximately 10(48) erg), has recently been identified. Here we report radio observations of GRB030329 that allow us to undertake calorimetry of the explosion. Our data require a two-component explosion: a narrow (5 degrees opening angle) ultra-relativistic component responsible for the gamma-rays and early afterglow, and a wide, mildly relativistic component that produces the radio and optical afterglow more than 1.5 days after the explosion. The total energy release, which is dominated by the wide component, is similar to that of other gamma-ray bursts, but the contribution of the gamma-rays is energetically minor. Given the firm link of GRB030329 with SN2003dh, our result indicates a common origin for cosmic explosions in which, for reasons not yet understood, the energy in the highest-velocity ejecta is extremely variable.

We employ a fireball model of the gamma-ray burst explosion to constrain intrinsic and environmental parameters of four events with good broadband afterglow data; GRB 970508, GRB 980329, GRB 980703, and GRB 000926. Using the standard assumptions of constant circumburst density and no evolution of the fraction of the explosion energy in the post-shock magnetic field, we investigate the uniformity of the derived explosion and shock physics parameters among these events. We find a variety of parameters: densities that range from those of the ISM to diffuse clouds, energies comparable to the total GRB γ-ray energy, collimations from near-isotropy to 0.04 radians, substantial electron energy fractions of 10-30% with energy distribution indices of 2.1-2.9 and magnetic energy fractions from 0.2-25%. We also investigate the level to which the data constrain the standard model assumptions, such as the magnetic field evolution, and the allowed density profiles of the medium. Fits generally improve slightly with an increasing magnetic energy fraction ǫ B . Good fits can be produced with magnetic energy accumulating or decaying with the shock strength over the afterglow as ǫ B ∝ γ x ; −2 ≤ x ≤ +1 . The data are not very sensitive to increasing density profiles, allowing good fits even with density ∝ r 10 . Some parameter values change by up to an order of magnitude under such altered assumptions; the parameters of even good fits cannot be taken at face value. The data are sensitive to decreasing densities; r −2 profiles may produce reasonable fits, but steeper profiles, even r −2.5 , will not fit the data.

Over the six years since the discovery of the gamma-ray burst GRB 980425, which was associated with the nearby (distance approximately 40 Mpc) supernova 1998bw, astronomers have debated fiercely the nature of this event. Relative to bursts located at cosmological distance (redshift z approximately 1), GRB 980425 was under-luminous in gamma-rays by three orders of magnitude. Radio calorimetry showed that the explosion was sub-energetic by a factor of 10. Here we report observations of the radio and X-ray afterglow of the recent GRB 031203 (refs 5-7), which has a redshift of z = 0.105. We demonstrate that it too is sub-energetic which, when taken together with the low gamma-ray luminosity, suggests that GRB 031203 is the first cosmic analogue to GRB 980425. We find no evidence that this event was a highly collimated explosion viewed off-axis. Like GRB 980425, GRB 031203 appears to be an intrinsically sub-energetic gamma-ray burst. Such sub-energetic events have faint afterglows. We expect intensive follow-up of faint bursts with smooth gamma-ray light curves (common to both GRB 031203 and 980425) to reveal a large population of such events.

We report late-time observations of the radio afterglow of GRB 030329. The light curves show a clear achromatic flattening at 50 days after the explosion. We interpret this flattening as resulting from the blast wave becoming transrelativistic. Modeling of this transition enables us to make estimates of the energy content of the burst, regardless of the initial jet structure or the distribution of initial Lorentz factors of the ejecta. We find, in accordance with other events, that GRB 030329 is well described by an explosion with total energy of a few ; 10 51 ergs expanding into a circumburst medium with a density of order unity.