A model of gamma-ray bursts

Abstract

We present a model that reproduces the basic spectral properties of classical gamma-ray bursts with essentially no free parameters. It is an elaboration of the scenario for cosmological gamma-ray bursts outlined by Duncan & Thompson. The starting point is a Poynting-flux-dominated, relativistic, MHD wind of extremely high luminosity, L ~ 1050 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 ~ 1012. The wind emanates from a rapidly rotating neutron star, or neutron disc, in which a poloidal field ≳ 1014 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 Alfvén 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 Alfvén 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 β = – 2 (vFv = constant), extending from an energy Ebreak ~ 1 (Lγ/1050 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 ~ 103mec2. 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 Ebreak is also a power law, with index α = – 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 Alfvén 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 ~ 109 cm from the source, without the need for any interaction with an external medium.