  It has been known for nearly three decades that the energy spectra of
thermonuclear X-ray bursts are often well-fit by Planck functions with
temperatures so high that they imply a super-Eddington radiative flux at the
emitting surface, even during portions of bursts when there is no evidence of
photospheric radius expansion. This apparent inconsistency is usually set aside
by assuming that the flux is actually sub-Eddington and that the fitted
temperature is so high because the spectrum has been distorted by the
energy-dependent opacity of the atmosphere. Here we show that the spectra
predicted by currently available conventional atmosphere models appear
incompatible with the highest-precision measurements of burst spectra made
using the Rossi X-ray Timing Explorer, such as during the 4U 1820-30 superburst
and a long burst from GX 17+2. In contrast, these measurements are well-fit by
Bose-Einstein spectra with high temperatures and modest chemical potentials.
Such spectra are very similar to Planck spectra. They imply surface radiative
fluxes more than a factor of three larger than the Eddington flux. We find that
segments of many other bursts from many sources are well-fit by similar
Bose-Einstein spectra, suggesting that the radiative flux at the emitting
surface also exceeds the Eddington flux during these segments. We suggest that
burst spectra can closely approximate Bose-Einstein spectra and have fluxes
that exceed the Eddington flux because they are formed by Comptonization in an
extended, low-density radiating gas supported by the outward radiation force
and confined by a tangled magnetic field.
