2010ApJ...720L.206Z

We propose the rest-frame 2-10 keV photon index, Γ_2-10 keV_, acting as an indicator of the bolometric correction, L_bol/L_2-10 keV _(where L_bol is the bolometric luminosity and L_2-10 keV_is the rest-frame 2-10 keV luminosity), in radio-quiet active galactic nuclei (AGNs). Correlations between Γ_2-10 keV_ 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_2-10 keV_, 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, Γ_2-10 keV_ for high-redshift AGNs can be used to determine their true L_bol and L_2-10 keV_, 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 _2-10 keV_ estimated from Γ_2-10 keV_for the brightest Type I AGNs with z < 1 in the Lockman Hole is generally in agreement with the observed L_2-10 keV_. However, there are still many uncertainties, such as the accurate determination of the intrinsic Γ_2-10 keV_ 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.