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We present the properties of accretion disk corona (ADC) models, where theradiation field, the temperature, and the total opacity of the corona aredetermined self-consistently. We use a non-linear Monte Carlo code to performthe calculations. As an example, we discuss models where the corona is situatedabove and below a cold accretion disk with a plane-parallel (slab) geometry,similar to the model of Haardt and Maraschi. By Comptonizing the soft radiationemitted by the accretion disk, the corona is responsible for producing thehigh-energy component of the escaping radiation. Our models include thereprocessing of radiation in the accretion disk. Here, the photons either areCompton reflected or photo-absorbed, giving rise to fluorescent line emissionand thermal emission. The self-consistent coronal temperature is determined bybalancing heating (due to viscous energy dissipation) with Compton cooling,determined using the fully relativistic, angle-dependent cross-sections. Thetotal opacity is found by balancing pair productions with annihilations. Wefind that, for a disk temperature kT_bb \lta 200 eV, these coronae are unableto have a self-consistent temperature higher than \sim 120 keV if the totaloptical depth is \gta 0.2, regardless of the compactness parameter of thecorona and the seed opacity. This limitation corresponds to the angle-averagedspectrum 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 predicta large thermal excess at lower energies. These constraints make explaining theX-ray spectra of persistent black hole candidates with ADC models veryproblematic.Comment: 15 pages, Latex, 9 .eps figures, uses emulateapj.sty (included). To  be published in ApJ, October 1, 1997, Vol. 48

Self‐consistent Thermal Accretion Disk Corona Models for Compact Objects. I. Properties of the Corona and the Spectrum of Escaping Radiation