Self-Consistent Thermal Accretion Disk Corona Models for Compact Objects: II. Application to Cygnus X-1

We apply our self-consistent accretion disk corona (ADC) model, with two different geometries, to the broad-band X-ray spectrum of the black hole candidate Cygnus X-1. As shown in a companion paper (Dove, Wilms, and Begelman), models where the Comptonizing medium is a slab surrounding the cold accretion disk cannot have a temperature higher than about 120 keV for optical depths greater than 0.2, resulting in spectra that are much softer than the observed 10-30 keV spectrum of Cyg X-1. In addition, the slab geometry models predict a substantial ``soft excess'' at low energies, a feature not observed for Cyg X-1, and Fe K\alpha fluorescence lines that are stronger than observed. Previous Comptonization models in the literature invoke a slab geometry with the optical depth \tau_T \gta 0.3 and the coronal temperature T_c \sim 150 keV, but they are not self-consistent. Therefore, ADC models with a slab geometry are not appropriate for explaining the X-ray spectrum of Cyg X-1. Models with a spherical corona and an exterior disk, however, predict much higher self-consistent coronal temperatures than the slab geometry models. The higher coronal temperatures are due to the lower amount of reprocessing of coronal radiation in the accretion disk, giving rise to a lower Compton cooling rate. Therefore, for the sphere+disk geometry, the predicted spectrum can be hard enough to describe the observed X-ray continuum of Cyg X-1 while predicting Fe fluorescence lines having an equivalent width of \sim 40 eV. Our best-fit parameter values for the sphere+disk geometry are \tau_T \approx 1.5 and T_c \approx 90 keV.