The Giant Flare of 1998 August 27 from SGR 1900+14: II. Radiative Mechanism and Physical Constraints on the Source

(ABBREVIATED) The extraordinary 1998 August 27 giant flare places strong constraints on the physical properties of its source, SGR 1900+14. We make detailed comparisons of the published data with the magnetar model. The giant flare evolved through three stages, whose radiative mechanisms we address in turn. A triggering mechanism is proposed, whereby a helical distortion of the core magnetic field induces large-scale fracturing in the crust and a twisting deformation of the crust and exterior magnetic field. The envelope of the pulsating tail of the August 27 flare can be accurately fit, after ~40 s, by the contracting surface of a relativistically hot, but inhomogeneous, trapped fireball. We quantify the effects of direct neutrino-pair emission, thereby deducing a lower bound ~ 10^{32} G-cm^3 to the magnetic moment of the confining field. The radiative flux during the intermediate ~40 s of the burst appears to exceed the trapped fireball fit. The spectrum and lightcurve of this smooth tail are consistent with heating in an extended pair corona, possibly powered by continuing seismic activity in the star. We consider in detail the critical luminosity, below which a stable balance can be maintained between heating and radiative cooling in a confined, magnetized pair plasma; but above which the confined plasma runs away to local thermodynamic equilibrium. In the later pulsating tail, the best fit temperature equilibrates at a value which agrees well with the regulating effect of photon splitting. The remarkable four-peaked substructure within each 5.16-s pulse provides strong evidence for the presence of higher magnetic multipoles in SGR 1900+14. The corresponding collimation of the X-ray flux is related to radiative transport in a super-QED magnetic field.