Ionised accretion discs in active galactic nuclei: the effects of a lamppost with a variable height

Abstract

Abstract The X-ray emitting corona irradiates and ionizes the surface of the inner accretion disc in active galactic nuclei (AGNs). The ionization parameter of the inner disc at a radius r from the black hole, ξ(r), can be used to infer information about the location of the corona. Here, a new formula is derived that predicts ξ(r, h) for a disc irradiated by an X-ray source at a height h above the black hole symmetry axis (i.e. a lamppost geometry). The equation is independent of the black hole mass and the X-ray spectrum, and accounts for the effects of gravitational light-bending on the ionization state and a variable coronal dissipation factor. We predict a strong ionization gradient across the surface of the inner disc that depends on the black hole spin and lamppost height. For a fixed h, the ionization parameter is also expected to increase as λ3, where λ is the observed bolometric Eddington ratio of the AGN. Comparing this formula to the observed ξ-λ relationship for Mrk 335 yields h ∝ λ0.5–0.6, supporting the view of a dynamic X-ray corona in AGNs.