The soft gamma repeaters as very strongly magnetized neutron stars - I. Radiative mechanism for outbursts
A radiative model for the soft gamma repeaters and the energetic 1979 March 5 burst is presented. We identify the sources of these bursts with neutron stars the external magnetic fields of which are much stronger than those of ordinary pulsars. Several independent arguments point to a neutron star with B_dipole~5x10^14 G as the source of the March 5 event. A very strong field can (i) spin down the star to an 8-s period in the ~10^4-yr age of the surrounding supernova remnant N49; (ii) provide enough energy for the March 5 event; (iii) undergo a large-scale interchange instability the growth time of which is comparable to the ~0.2-s width of the initial hard transient phase of the March 5 event; (iv) confine the energy that was radiated in the soft tail of that burst; (v) reduce the Compton scattering cross-section sufficiently to generate a radiative flux that is ~10^4 times the (non-magnetic) Eddington flux; (vi) decay significantly in ~10^4-10^5 yr, as is required to explain the activity of soft gamma repeater sources on this time-scale; and (vii) power the quiescent X-ray emission L_X~7x10^35 erg s^-1 observed by Einstein and ROSAT as it diffuses the stellar interior. We propose that the 1979 March 5 event was triggered by a large-scale reconnection/interchange instability of the stellar magnetic field, and the soft repeat bursts by cracking of the crust. The hard initial spike of the March 5 event is identified with an expanding pair fireball, and the soft tail of that burst, together with the short, soft repeat bursts, with a pair plasma trapped in the stellar magnetosphere. We construct a detailed radiative model that describes the cooling of such a plasma. The opacity is dominated by the electron-baryon contaminant in a cold surface layer, and the plasma releases energy as the edge of the pair-dominated region propagates inward, in a cooling wave. The rate at which the plasma volume contracts is limited either by the rate of advection of heat toward the stellar surface (where the field is strongest and the scattering opacity weakest), or by ablation of ions and electrons from the stellar surface. The effective temperature of the surface radiation depends only on the surface magnetic field strength in the regime where the radiative flux is limited by ablation from the neutron star surface (which is the regime of interest in the March 5 event), and otherwise is weakly dependent on the plasma energy density. We argue that the deposition of equivalent energy in a much weaker magnetic field (characteristic of ordinary pulsars) necessarily generates a very high scattering depth which chokes off the radiative flow on the observed ~0.1-s time-scale of soft gamma repeater bursts. Indeed, we suggest that the same basic magnetospheric emission mechanism operates at lower field strengths (B~10^12 G) in Type II X-ray bursts, which have much lower luminosities than soft gamma repeater bursts. Important magnetic radiative effects include the suppression of Compton scattering in the extraordinary polarization mode, and stimulated photon splitting. We derive the Boltzmann equations for the photon occupation number which describe simulated photon splitting, as well as photon merging. We show that the net splitting rate vanishes in thermal equilibrium. Radiative diffusion occurs primarily in the E-mode, although rapid scattering of the O-mode ensures convergence of the photon distribution function to a Bose-Einstein form. This allows us to write down diffusion equations for the photon energy flux and number flux as linear superpositions of gradients in the temperature and chemical potential. The transition from a Planck to a Bose-Einstein spectrum occurs at T~10 keV. Photon splitting at higher temperatures can impede free-streaming of photons across the magnetic field lines, but splitting of high-energy photons is impeded by the inverse process of photon merging. We demonstrate that only a small fraction of the pair bubble energy can be conducted into the crust during the lifetime of the burst. We discuss the radiative ablation of matter from the heated stellar surface after the magnetospheric pair plasma is dissipated. The ensuing surface afterglow is typically ~1 per cent of the burst luminosity. Direct pair neutrino cooling of the plasma is shown to be unimportant for soft gamma repeater bursts, but may help to determine the light curve of the March 5 event. Finally, we make a critical comparison between this model and models in which the soft gamma repeater bursts are triggered by accretion and/or involve surface cooling.