Detailed Atmosphere Calculations of Accretion Disks Around Intermediate Mass Black Holes, and Their Application to Observations of Ultra-luminous X-ray Sources

We have calculated the structures and the emergent spectra of stationary, geometrically thin accretion disks around intermediate mass black holes (IMBH) in both the Schwarzschild and extreme Kerr metrics. Equations of radiative transfer, hydrostatic equilibrium, energy balance, ionization equilibrium, and statistical equilibrium are solved simultaneously and consistently. The six most astrophysically abundant elements (H, He, C, N, O, and Fe) are included, as well as energy transfer by Comptonization. The observed spectrum as a function of viewing angle is computed, incorporating all general relativistic effects. We find that, in contrast with the predictions of the commonly used multicolor disk (MCD) model, opacity associated with photoionization of heavy elements can significantly alter the spectrum near its peak. These ionization edges can create spectral breaks visible in the spectra of slowly spinning black holes viewed from almost all angles and in the spectra of rapidly spinning black holes seen approximately face-on. For fixed mass and accretion rate relative to Eddington, both the black hole spin and the viewing angle can significantly shift the observed peak energy of the spectrum, particularly for rapid spin viewed edge-on. We present a detailed test of the approximations made in various forms of the MCD model. Linear limb-darkening is confirmed to be a reasonable approximation for the integrated flux but not for many specific frequencies of interest.