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X-ray reflection off the accretion disc surrounding a black hole, togetherwith the associated broad iron K$\alpha$ line, has been widely used toconstrain the innermost accretion-flow geometry and black hole spin. Somerecent measurements have revealed steep reflection emissivity profiles in anumber of active galactic nuclei and X-ray binaries. We explore the physicallymotivated conditions that give rise to the observed steep disc-reflectionemissivity profiles. We perform a set of simulations based on the configurationof a possible future high-resolution X-ray mission. Computations are carriedout for typical X-ray bright Seyfert-1 galaxies. We find that steep emissivityprofiles with $q\sim 4-5$ (where the emissivity is $\epsilon (r) \proptor^{-q}$) are produced considering either i) a lamp-post scenario where aprimary compact X-ray source is located close to the black hole, or ii) theradial dependence of the disc ionisation state. We also highlight the role ofthe reflection angular emissivity: the radial emissivity index $q$ isoverestimated when the standard limb-darkening law is used to describe thedata. Very steep emissivity profiles with $q \geq 7$ are naturally obtained byapplying reflection models that take into account radial profile $\xi (r)$ ofthe disc ionisation induced by a compact X-ray source located close to thecentral black hole.

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