  We present the results of self-consistent models of Compton-heated accretion
disk coronae. The models are calculated using a new method for computing
monochromatic radiative transfer in two-dimensions. The method splits the
radiation into direct and scattered components. The direct radiation is
computed by calculating the optical depth along rays, while transfer of the
scattered radiation is approximated by flux-limited diffusion. The resulting
code agrees with more accurate treatments to within 50\%, and is highly
efficient, making it practical for use in large hydrodynamic simulations. The
coronal models are used to confirm the results of earlier work, and to extend
it to higher luminosities. In contrast to earlier work, which found the outer
disks to be shadowed by the inner corona at high luminosities, we find our
results to form an almost continuous extension of the models at lower
luminosities. This is due to the presence of multiply-scattered radiation,
which acts to partially offset the loss of direct radiation from the central
source. Although the analytic methods derived at lower luminosities cannot be
used to derive the coronal structure for $L/L\sr{Edd}\gapprox0.1$, the results
of the models are amenable to semiempirical fits. We also discuss possible
observational consequences of the results for coronal veiling and line
fluorescence from the disk.

Astrophysics