Origin of the X-ray disc-reflection steep radial emissivity

Context. X-ray reflection off the accretion disc surrounding a black hole, together with the associated broad iron Kα line, has been widely used to constrain the innermost accretion-flow geometry and black hole spin. Some recent measurements have revealed steep reflection emissivity profiles in a number of active galactic nuclei and X-ray binaries. Aims. We explore the physically motivated conditions that give rise to the observed steep disc-reflection emissivity profiles. Methods. We perform a set of simulations based on the configuration of a possible future high-resolution X-ray mission. Computations are carried out for typical X-ray bright Seyfert-1 galaxies. Results. We find that steep emissivity profiles with q ~ 4−5 (where the emissivity is ϵ(r) ∝ r−q) are produced considering either i) a lamp-post scenario where a primary compact X-ray source is located close to the black hole, or ii) the radial dependence of the disc ionisation state. If both effects are taken into account, emissivity profiles as steep as q ~ 7 can be obtained from X-ray spectra modelled via conventional reflection models. We also highlight the role of the reflection angular emissivity: the radial emissivity index q is overestimated when the standard limb-darkening law is used to describe the data. Conclusions. Very steep emissivity profiles with q ≥ 7 are naturally obtained by applying reflection models that take into account the radial profile ξ(r) of the disc ionisation induced by a compact X-ray source located close to the central black hole