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.
We propose the rest-frame 2-10 keV photon index, ga, acting as an indicator of the bolometric correction, lb/$L_{rm 2-10keV}$ (where lb~ is the bolometric luminosity and $L_{rm 2-10keV}$ is the rest-frame 2-10 keV luminosity), in radio-quiet active galactic nuclei (AGNs). Correlations between ga~ and both bolometric correction and Eddington ratio are presented, based on simultaneous X-ray, UV, and optical observations of reverberation -mapped AGNs. These correlations can be compared with those for high-redshift AGNs to check for any evolutionary effect. Assuming no evolutionary effect in AGNs spectral properties, together with the independent estimates of $L_{rm 2-10keV}$, the bolometric correction, Eddington ratio, and black hole (BH) mass can all be estimated from these correlations for high-redshift AGNs, with the mean uncertainty of a factor of 2-3. If there are independent estimates of BH masses, ga~ for high-redshift AGNs can be used to determine their true lb~ and $L_{rm 2-10keV}$, and in conjunction with the redshift, can be potentially used to place constraints on cosmology by comparison with the rest-frame 2-10 keV flux. We find that the true $L_{rm 2-10keV}$ estimated from ga~ for the brightest Type I AGNs with $z<1$ in the Lockman Hole is generally in agreement with the observed $L_{rm 2-10keV}$. However, there are still many uncertainties, such as the accurate determination of the intrinsic ga~ for distant AGNs and the large uncertainty in the luminosities obtained, which call for significant further study before ``AGN cosmology can be considered a viable technique.
