  We study local radiation magnetohydrodynamic instabilities in static,
optically thick, vertically stratified media with constant flux mean opacity.
We include the effects of vertical gradients in a horizontal background
magnetic field. Assuming rapid radiative diffusion, we use the zero gas
pressure limit as an entry point for investigating the coupling between the
photon bubble instability and the Parker instability. Apart from factors that
depend on wavenumber orientation, the Parker instability exists for wavelengths
longer than a characteristic wavelength lambda_{tran}, while photon bubbles
exist for wavelengths shorter than lambda_{tran}. The growth rate in the Parker
regime is independent of the orientation of the horizontal component of the
wavenumber when radiative diffusion is rapid, but the range of Parker-like
wavenumbers is extended if there exists strong horizontal shear between field
lines (i.e. horizontal wavenumber perpendicular to the magnetic field). Finite
gas pressure introduces an additional short wavelength limit to the Parker-like
behavior, and also limits the growth rate of the photon bubble instability to a
constant value at short wavelengths. We also consider the effects of
differential rotation with accretion disk applications in mind. Our results may
explain why photon bubbles have not yet been observed in recent stratified
shearing box accretion disk simulations. Photon bubbles may physically exist in
simulations with high radiation to gas pressure ratios, but higher spatial
resolution will be needed to resolve the asymptotically growing unstable
wavelengths.
