  We consider the effects of "photon bubble" shock trains on the vertical
structure of radiation pressure-dominated accretion disks. These density
inhomogeneities are expected to develop spontaneously in radiation-dominated
accretion disks where magnetic pressure exceeds gas pressure, even in the
presence of magnetorotational instability. They increase the rate at which
radiation escapes from the disk, and may allow disks to exceed the Eddington
limit by a substantial factor. We first generalize the theory of photon bubbles
to include the effects of finite optical depths and radiation damping.
Modifications to the diffusion law at low optical depth tend to fill in the
low-density regions of photon bubbles, while radiation damping inhibits the
formation of photon bubbles at large radii, small accretion rates, and small
heights above the equatorial plane. Accretion disks dominated by photon bubble
transport may reach luminosities of 10 to >100 times the Eddington limit (L_E),
depending on the mass of the central object, while remaining geometrically
thin. However, photon bubble-dominated disks with alpha-viscosity are subject
to the same thermal and viscous instabilities that plague standard radiation
pressure-dominated disks, suggesting that they may be intrinsically unsteady.
Photon bubbles can lead to a "core-halo" vertical disk structure. In
super-Eddington disks the halo forms the base of a wind, which carries away
substantial energy and mass, but not enough to prevent the luminosity from
exceeding L_E. Photon bubble-dominated disks may have smaller color corrections
than standard accretion disks of the same luminosity. They remain viable
contenders for some ultraluminous X-ray sources and may play a role in the
rapid growth of supermassive black holes at high redshift.
