The Comptonisation of accretion disc X-ray emission: Consequences for X-ray reflection and the geometry of AGN coronae

We consider the Comptonisation of the photons that make up the relativistically blurred reflection that is commonly detected from the accretion discs of AGN by the coronae of energetic particles believed to give rise to the powerful X-ray continua by the inverse-Compton scattering of thermal seed photons from the disc. Recent measurements of the emissivity profiles of accretion discs as well as reverberation time lags between the primary X-ray continuum and the reflection suggest that this corona is situated at a low height above the disc and extends radially, tens of gravitational radii over the disc surface, hence should also Compton scatter the reflected X-rays. We find that the detection of blurred reflection from as close in as the innermost stable circular orbits (ISCOs) of maximally rotating black holes is consistent with such coronae, but requires that the corona be patchy, consisting perhaps of a number of isolated flares throughout the region. Considering only the requirement that it be possible to detect reflection from the ISCO, we find that at any given moment, the covering fraction of the inner part of the accretion disc by the corona needs to be less than 85 per cent, though allowing for the detection of 'reflection-dominated' spectra in which the total reflected flux exceeds that seen in the continuum requires covering fractions as low as 50 or 25 per cent.