A MODEL OF GAMMA-RAY BURSTS

We present a model that reproduces the basic spectral properties of classical gammaray bursts with essentially no free parameters. It is an elaboration of the scenario for cosmological gamma-ray bursts outlined by Duncan and Thompson. The starting point is a Poynting-flux-dominated, relativistic, MHD wind of extremely high luminosity, L similar to 10(50) erg s(-1). The compactness parameter measured at the base of the wind exceeds that of the Crab pulsar, or that of a luminous AGN, by a factor of similar to 10(12). The wind emanates from a rapidly rotating neutron star, or neutron disc, in which a poloidal field greater than or similar to 10(14) G has been generated by a helical dynamo. Scenarios that could produce such an object include a failed Type Ib supernova, accretion-induced collapse of a white dwarf, or perhaps a binary neutron star merger. The wind is safely in the MHD limit as the result of neutrino-driven and centrifugally driven mass loss. Mildly relativistic Alfven turbulence is excited in the wind by reconnection, or by hydrodynamical instabilities triggered by magnetic tension. Gamma-rays are generated via Comptonization at moderate to high scattering depth. The amplitude of the turbulence is itself limited by Compton drag and the y-parameter of the Alfven motions is regulated to a value near 1/4, with a weak dependence on parameters such as radius, luminosity and the amount of baryon loading. The resulting spectrum is a power law with spectral index close to beta = - 2 (vF(v) = constant), extending from an energy E(break) similar to 1 (L(gamma)/10(50) erg s(-1))(1/4) MeV (close to the spectral peak of a thermal fireball carrying the same flux) up to an energy as high as similar to 10(3) m(e)c(2). This power law steepens when the amplitude of the turbulence declines, or when the turbulence is generated outside the scattering photosphere. The spectrum below energy E(break) is also a power law, with index alpha = - 1, which is cut off from below by stimulated scattering terms. Heavy baryon loading causes much less adiabatic softening of the spectrum than in thermal fireballs, so long as the Alfven turbulence is generated out to the scattering photosphere. We show explicitly that the broken power law spectrum is an attractor, and that neither power law is altered by relativistic corrections to the Kompane'ets equation (except near the high-energy cut-off). The emergent gamma-ray spectrum is generated at a distance as small as similar to 10(9) cm from the source, without the need for any interaction with an external medium.