  We present the properties of accretion disk corona (ADC) models, where the
radiation field, the temperature, and the total opacity of the corona are
determined self-consistently. We use a non-linear Monte Carlo code to perform
the calculations. As an example, we discuss models where the corona is situated
above and below a cold accretion disk with a plane-parallel (slab) geometry,
similar to the model of Haardt and Maraschi. By Comptonizing the soft radiation
emitted by the accretion disk, the corona is responsible for producing the
high-energy component of the escaping radiation. Our models include the
reprocessing of radiation in the accretion disk. Here, the photons either are
Compton reflected or photo-absorbed, giving rise to fluorescent line emission
and thermal emission. The self-consistent coronal temperature is determined by
balancing heating (due to viscous energy dissipation) with Compton cooling,
determined using the fully relativistic, angle-dependent cross-sections. The
total opacity is found by balancing pair productions with annihilations. We
find that, for a disk temperature kT_bb \lta 200 eV, these coronae are unable
to have a self-consistent temperature higher than \sim 120 keV if the total
optical depth is \gta 0.2, regardless of the compactness parameter of the
corona and the seed opacity. This limitation corresponds to the angle-averaged
spectrum of escaping radiation having a photon index \gta 1.8 within the 5 keV
- 30 keV band. Finally, all models that have reprocessing features also predict
a large thermal excess at lower energies. These constraints make explaining the
X-ray spectra of persistent black hole candidates with ADC models very
problematic.
