Ionization structure and Fe K$\alpha$ energy for irradiated accretion disks

We study the radial ionization structure at the surface of an X-ray illuminated accretion disk. We plot the expected iron K$\alpha$ line energy as a function of the Eddington ratio and of the distance of the emitting matter from the central source, for a non-rotating and a maximally-rotating black hole. We compare the predicted disk line energies with those measured in an archival sample of active galactic nuclei observed with {\it Chandra}, {\it XMM-Newton} and {\it Suzaku}, and discuss whether the line energies are consistent with the radial distances inferred from reverberation studies. We also suggest using rapidly-variable iron K$\alpha$ lines to estimate the viscosity parameter of an accretion disk. There is a forbidden region in the line energy versus Eddington ratio plane, at low Eddington ratios, where an accretion disk cannot produce highly-ionized iron K$\alpha$ lines. If such emission is observed in low-Eddington-ratio sources, it is either coming from a highly-ionized outflow, or is a blue-shifted component from fast-moving neutral matter.