Isothermal, Compton-heated coronae above accretion disks

We examine the structure of Compton-heated coronae above accretion disks by the development of both approximate analytic solutions and self-consistent numerical solutions to determine the direct and scattered radiation reaching the base of the corona for a range of central source luminosities. We generalize previous work by treating the case of a central X-ray source at a finite distance above the disk midplane, while allowing for both flat and flaring disks. The corona is assumed vertically isothermal, with temperature set to half of the local Compton temperature. Our solutions are self-consistent in that the attenuation of the radiation from the central source depends on the density distribution of the corona, which itself depends upon the attenuated central flux. Analytic solutions for the optical depth from source to disk in both optically thin and optically thick cases show excellent agreement with detailed numerical results. We treat only singly scattered radiation and evaluate the range of radii for which multiple scattering is not important, for a given luminosity. We find that the outer region of the corona is unaffected by multiple scattering in the interior, provided that the luminosity of the central source is sufficiently below the Eddington limit. For these luminosities, modification of the spectrum produced by the underlying disk due to the overlying corona is unimportant; for higher luminosities the effect may become significant. We determine how attenuation and scattering by the corona will affect the strength of chromospheric emission lines. We determine the condition for which the irradiation due to the central source exceeds the locally generated flux from the disk. Finally, we show that the stability analysis for irradiated accretion disks of Tuchman and coworkers is not substantially altered by the corona.