  We derive an analytic model for nonlinear "photon bubble" wave trains driven
by buoyancy forces in magnetized, radiation pressure-dominated atmospheres.
Continuous, periodic wave solutions exist when radiative diffusion is slow
compared to the dynamical timescale of the atmosphere. We identify these waves
with the saturation of a linear instability discovered by Arons - therefore,
these wave trains should develop spontaneously. The buoyancy-driven waves are
physically distinct from photon bubbles in the presence of rapid diffusion,
which evolve into trains of gas pressure-dominated shocks as they become
nonlinear.
  Like the gas pressure-driven shock trains, buoyancy-driven photon bubbles can
exhibit very large density contrasts, which greatly enhance the flow of
radiation through the atmosphere. However, steady-state solutions for
buoyancy-driven photon bubbles exist only when an extra source of radiation is
added to the energy equation, in the form of a flux divergence. We argue that
this term is required to compensate for the radiation flux lost via the
bubbles, which increases with height. We speculate that an atmosphere subject
to buoyancy-driven photon bubbles, but lacking this compensating energy source,
would lose pressure support and collapse on a timescale much shorter than the
radiative diffusion time in the equivalent homogeneous atmosphere.
