  The vertical structure of black hole accretion disks in which radiation
dominates the total pressure is investigated using a three-dimensional
radiation-MHD calculation. The domain is a small patch of disk centered 100
Schwarzschild radii from a black hole of 10^8 Solar masses, and the stratified
shearing-box approximation is used. Magneto-rotational instability converts
gravitational energy to turbulent magnetic and kinetic energy. The gas is
heated by magnetic dissipation and by radiation damping of the turbulence, and
cooled by diffusion and advection of radiation through the vertical boundaries.
The resulting structure differs in several fundamental ways from the standard
Shakura-Sunyaev picture. The disk consists of three layers. At the midplane,
the density is large, and the magnetic pressure and total accretion stress are
less than the gas pressure. In lower-density surface layers that are optically
thick, the magnetic pressure and stress are greater than the gas pressure but
less than the radiation pressure. Horizontal density variations in the surface
layers exceed an order of magnitude. Magnetic fields in the regions of greatest
stress are buoyant, and dissipate as they rise, so the heating rate declines
more slowly with height than the stress. Much of the dissipation occurs at low
column depth, and the interior is cooler and less radiation-dominated than in
the Shakura-Sunyaev model with the same surface mass density and flux. The mean
structure is convectively stable.
