Bursts from soft gamma repeaters (SGRs) have been shown to be super-Ed
dington by a factor of 1000 and have been persuasively associated with
compact objects. Super-Eddington radiation transfer on the surface of
a strongly magnetic (greater than or equal to 10(13) G) neutron star
is studied and related to the observational constraints on SGRs. In st
rong magnetic fields, Thompson scattering is suppressed in one polariz
ation state, so super-Eddington fluxes can be radiated while the plasm
a remains in hydrostatic equilibrium. We discuss a model which offers
a somewhat natural explanation for the observation that the energy spe
ctra of bursts with varying intensity are similar. The radiation produ
ced is found to be linearly polarized to one part in 1000 in a directi
on determined by the local magnetic field, and intensity variations be
tween bursts are understood as a change in the radiating area on the s
ource. The net polarization is inversely correlated with burst intensi
ty. Further, it is shown that for radiation transfer calculations in l
imit of superstrong magnetic fields, it is sufficient to solve the rad
iation transfer equations for the low opacity state rather than the co
upled equations for both. With this approximation, standard stellar at
mosphere techniques are utilized to calculate the model energy spectru
m.