Luminous accreting stellar mass and supermassive black holes produce power-law continuum X-ray emission from a compact central corona. Reverberation time lags occur due to light travel time-delays between changes in the direct coronal emission and corresponding variations in its reflection from the accretion flow. Reverberation is detectable using light curves made in different X-ray energy bands, since the direct and reflected components have different spectral shapes. Larger, lower frequency, lags are also seen and are identified with propagation of fluctuations through the accretion flow and associated corona. We review the evidence for X-ray reverberation in active galactic nuclei and black hole X-ray binaries, showing how it can be best measured and how it may be modelled. The timescales and energy-dependence of the high frequency reverberation lags show that much of the signal is originating from very close to the black hole in some objects, within a few gravitational radii of the event horizon. We consider how these signals can be studied in the future to carry out X-ray reverberation mapping of the regions closest to black holes.

The illumination pattern (or emissivity profile) of the accretion disc due to the reflection of X‐rays in active galactic nucleus can be understood in terms of relativistic effects on the rays propagating from a source in a corona surrounding the central black hole, both on their trajectories and on the accretion disc itself. Theoretical emissivity profiles due to isotropic point sources as well as simple extended geometries are computed in general relativistic ray‐tracing simulations performed on graphics processing units (GPUs). Such simulations assuming only general relativity naturally explain the accretion disc emissivity profiles determined from relativistically broadened emission lines which fall off steeply (with power‐law indices of between 6 and 8) over the inner regions of the disc, then flattening off to almost a constant before tending to a constant power law of index 3 over the outer disc. Simulations for a variety of source locations, extents and geometries show how the emissivity profiles depend on these properties, and when combined with reverberation time lags allow the location and extent of the primary X‐ray source to be constrained. Comparing the emissivity profile determined from the broadened iron K emission line in spectra of 1H 0707−495 obtained in 2008 January to theoretical emissivity profiles and applying constraints from reverberation lags suggest that there exists an extended region of primary X‐ray emission located as low as 2rg above the accretion disc, extending outwards to a radius of around 30rg.

The recent detection of X-ray reverberation lags, especially in the Fe Kα line region, around Active Galactic Nuclei (AGN) has opened up the possibility of studying the time-resolved response (reflection) of hard X-rays from the accretion disk around supermassive black holes. Here, we use general relativistic transfer functions for reflection of X-rays from a point source located at some height above the black hole to study the time lags expected as a function of frequency and energy in the Fe Kα line region. We explore the models and the dependence of the lags on key parameters such as the height of the X-ray source, accretion disk inclination, black hole spin and black hole mass. We then compare these models with the observed frequency and energy dependence of the Fe Kα line lag in NGC 4151. Assuming the optical reverberation mapping mass of 4.6 × 10 7 M ⊙ we get a best fit to the lag profile across the Fe Kα line in the frequency range (1 − 2) × 10 −5 Hz for an X-ray source located at a height h = 7 +2.9 −2.6 R G with a maximally spinning black hole and an inclination i < 30 • .

When considering the X‐ray spectrum resulting from the reflection off the surface of accretion discs of AGN, it is necessary to account for the variation in reflected flux over the disc, i.e. the emissivity profile. This will depend on factors including the location and geometry of the X‐ray source and the disc characteristics. We directly obtain the emissivity profile of the disc from the observed spectrum by considering the reflection component as the sum of contributions from successive radii in the disc and fitting to find the relative weightings of these components in a relativistically broadened emission line. This method has successfully recovered known emissivity profiles from synthetic spectra and is applied to XMM–Newton spectra of the Narrow Line Seyfert 1 galaxy 1H 0707‐495. The data imply a twice‐broken power‐law form of the emissivity law with a steep profile in the inner regions of the disc (index 7.8) and then a flat region between 5.6 and 34.8rg before tending to a constant index of 3.3 over the outer regions of the disc. The form of the observed emissivity profile is consistent with theoretical predictions, thus reinforcing the reflection interpretation.