  We investigate the possibility of Photospheric Radius Expansion (PRE) during
magnetar bursts. Identification of PRE would enable a determination of the
magnetic Eddington limit (which depends on field strength and neutron star mass
and radius), and shed light on the burst mechanism. To do this we model
hydrostatic atmospheres in a strong radial magnetic field, determining both
their maximum extent and photospheric temperatures. We find that
spatially-extended atmospheres cannot exist in such a field configuration:
typical maximum extent for magnetar-strength fields is ~10 m (as compared to
200 km in the non-magnetic case). Achieving balance of gravitational and
radiative forces over a large range of radii, which is critical to the
existence of extended atmospheres, is rendered impossible in strong fields due
to the dependence of opacities on temperature and field strength. We conclude
that high luminosity bursts in magnetars do not lead to expansion and cooling
of the photosphere, as in the non-magnetic case. We also find the maximum
luminosity that can propagate through a hydrostatic magnetar atmosphere to be
lower than previous estimates. The proximity and small extent of the
photospheres associated with the two different polarization modes also calls
into question the interpretation of two blackbody fits to magnetar burst
spectra as being due to extended photospheres.
