Constraints on Hydrostatic Models of Soft Gamma-Ray Repeaters

All three soft gamma-ray repeaters (SGRs) are associated with supernova remnants; consequently, models of SGRs involving young neutron stars have attracted close attention. From the distances to the supernova remnants and the observed burst fluxes, the luminosity of a typical burst from an SGR is ~10 41 -10 42 ergs s -1 ; the 1979 March 5 event from SGR 0526-66 had an inferred peak luminosity of ~5 × 10 44 ergs s -1 . These luminosities are orders of magnitude larger than the Eddington luminosity L E ~ 2 × 10 38 ergs s -1 for a neutron star. Many models of SGRs assume that the atmosphere is hydrostatic. To reconcile this requirement with the large luminosities of SGRs, it has been suggested that the neutron stars that produce SGRs have extremely high magnetic fields. Then for a photon with frequency ω much less than the electron cyclotron frequency ω c , the scattering cross section (and thus the radial radiation force) in the perpendicular polarization mode is decreased by a factor ~(ω/ω c ) 2 compared to the magnetic field B = 0 case. It has been assumed that if essentially all of the radiation emerges in the perpendicular mode, then the maximum hydrostatic luminosity rises to L crit ~ (ω c /ω) 2 L E . Thus, to allow a hydrostatic atmosphere for a burst luminosity ~10 42 ergs s -1 and a typical photon energy ℏω ~ 50 keV, it has been thought that a magnetic field B ~ 5 × 10 14 G would suffice. We show that this is not correct. Although most of the luminosity emerges in the perpendicular mode, the fraction ~(ω/ω c ) that scatters into the parallel mode dominates the radiation force. Hence the maximum luminosity is only L crit ~ 5(ω c /ω) L E . Thus, for a typical SGR burst, the magnetic field must be at least B ~ 10 16 G to ensure a hydrostatic atmosphere, and for the March 5 event B > 5 × 10 18 G is required. These field strengths are unreasonably high. We therefore suggest that SGRs do not have hydrostatic atmospheres and that models which invoke magnetic confinement are more promising.