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We consider the Comptonisation of the photons that make up therelativistically blurred reflection that is commonly detected from theaccretion discs of AGN by the coronae of energetic particles believed to giverise to the powerful X-ray continua by the inverse-Compton scattering ofthermal seed photons from the disc. Recent measurements of the emissivityprofiles of accretion discs as well as reverberation time lags between theprimary X-ray continuum and the reflection suggest that this corona is situatedat a low height above the disc and extends radially, tens of gravitationalradii over the disc surface, hence should also Compton scatter the reflectedX-rays. We find that the detection of blurred reflection from as close in asthe innermost stable circular orbits (ISCOs) of maximally rotating black holesis 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 fromthe ISCO, we find that at any given moment, the covering fraction of the innerpart 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 whichthe total reflected flux exceeds that seen in the continuum requires coveringfractions as low as 50 or 25 per cent.

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