Aims. We study the effects of X-ray reprocessing in the power spectra (PSDs) of active galactic nuclei (AGNs). Methods. We compute fully relativistic disc response functions in the case of lamp-post geometry using the full observed reflection spectrum for various X-ray source heights, disc inclination, and spin values of the central black hole. Since the observed PSD is equal to the product of the intrinsic power spectrum with the transfer function (i.e. the Fourier transform of the disc response function), we are able to predict the observed PSDs in the case of X-ray illumination of the inner disc.Results. The observed PSD should show a prominent dip at high frequencies and an oscillatory behaviour with a decreasing amplitude at higher frequencies. The reverberation echo features should be more prominent in energy bands where the reflection component is more pronounced. The frequency of the dip is independent of energy, and it is mainly determined by the black hole mass and the X-ray source height. The amplitude of the dip increases with increasing black hole spin and inclination angle, as long as the height of the lamp is smaller than ∼10 gravitational radii. Conclusions. The detection of the X-ray reverberation signals in the PSDs can provide further evidence for X-ray illumination of the inner disc in AGN. Our results are largely independent of the assumed geometry of the disc-corona system, as long as it does not change with time, and the disc response function is characterized by a sharp rise, a plateau, and a decline at longer times. Irrespective of the geometry, the frequency of the main dip should decrease with increasing mean time of the response function, and the amplitude of the dip should increase with increasing reflection fraction.

We present the results of a detailed study of the X-ray power spectra density (PSD) functions of twelve X-ray bright AGN, using almost all the archival XMM-Newton data. The total net exposure of the EPIC-pn light curves is larger than 350 ks in all cases (and exceeds 1 Ms in the case of 1H 0707-497). In a physical scenario in which X-ray reflection occurs in the inner part of the accretion disc of AGN, the X-ray reflection component should be a filtered echo of the X-ray continuum signal and should be equal to the convolution of the primary emission with the response function of the disc. Our primary objective is to search for these reflection features in the 5 − 7 keV (iron line) and 0.5 − 1 keV (soft) bands, where the X-ray reflection fraction is expected to be dominant. We fit to the observed periodograms two models: a simple bending power law model (BPL) and a BPL model convolved with the transfer function of the accretion disc assuming the lamp-post geometry and X-ray reflection from a homogeneous disc. We do not find any significant features in the best-fitting BPL model residuals either in individual PSDs in the iron band, soft and full band (0.3 − 10 keV) or in the average PSD residuals of the brightest and more variable sources (with similar black hole mass estimates). The typical amplitude of the soft and full-band residuals is around 3 − 5 per cent. It is possible that the expected general relativistic effects are not detected because they are intrinsically lower than the uncertainty of the current PSDs, even in the strong relativistic case in which X-ray reflection occurs on a disc around a fast rotating black hole having an X-ray source very close above it. However, we could place strong constrains to the X-ray reflection geometry with the current data sets if we knew in advance the intrinsic shape of the X-ray PSDs, particularly its high frequency slope.

We present the first results obtained by the application of the KYNREFREV-reverberation model, which is ready for its use in XSPEC. This model computes the time dependent reflection spectra of the disc as a response to a flash of primary power-law radiation from a point source corona located on the axis of the black hole accretion disc (lamp-post geometry). Full relativistic effects are taken into account. The ionisation of the disc is set for each radius according to the amount of the incident primary flux and the density of the accretion disc. We tested the model by fitting model predictions to the observed time-lag spectra of three Narrow-Line Seyfert 1 galaxies (ARK 564, MCG-6-30-15 and 1H 0707-495), assuming either a rapidly or zero spinning black hole (BH). The time-lags strongly suggest a compact X-ray source, located close to the BH, at a height of ∼ 4 gravitational radii. This result does not depend either on the BH spin or the disc ionization. There is no significant statistical difference between the quality of the best-fits in the rapidly and zero spinning BH scenarios in Ark 564 and MCG-6-30-15. But there is an indication that the hypothesis of a non-rotating BH in 1H 0707-495 is not consistent with its time-lag spectrum. Finally, the best-fits to the Ark 564 and 1H 0707-495 data are of rather low quality. We detect wavy-residuals around the best-fit reverberation model time-lags at high frequencies. This result suggests that the simple lamp-post geometry does not fully explain the X-ray source/disc configuration in Active Galactic Nuclei.

Context. Theoretical modelling of time-lags between variations in the Fe Kα emission and the X-ray continuum might shed light on the physics and geometry of the X-ray emitting region in active galaxies (AGN) and X-ray binaries. We here present the results from a systematic analysis of time-lags between variations in two energy bands (5−7 vs. 2−4 keV) for seven X-ray bright and variable AGN. Aims. We estimate time-lags as accurately as possible and fit them with theoretical models in the context of the lamp-post geometry. We also constrain the geometry of the X-ray emitting region in AGN. Methods. We used all available archival XMM-Newton data for the sources in our sample and extracted light curves in the 5−7 and 2−4 keV energy bands. We used these light curves and applied a thoroughly tested (through extensive numerical simulations) recipe to estimate time-lags that have minimal bias, approximately follow a Gaussian distribution, and have known errors. Using traditional χ 2 minimisation techniques, we then fitted the observed time-lags with two different models: a phenomenological model where the time-lags have a power-law dependence on frequency, and a physical model, using the reverberation time-lags expected in the lamppost geometry. The latter were computed assuming a point-like primary X-ray source above a black hole surrounded by a neutral and prograde accretion disc with solar iron abundance. We took all relativistic effects into account for various X-ray source heights, inclination angles, and black hole spin values. Results. Given the available data, time-lags between the two energy bands can only be reliably measured at frequencies between ∼5 × 10 −5 Hz and ∼10 −3 Hz. The power-law and reverberation time-lag models can both fit the data well in terms of formal statistical characteristics. When fitting the observed time-lags to the lamp-post reverberation scenario, we can only constrain the height of the X-ray source. The data require, or are consistent with, a small ( < ∼ 10 gravitational radii) X-ray source height. Conclusions. In principle, the 5−7 keV band, which contains most of the Fe Kα line emission, could be an ideal band for studying reverberation effects, as it is expected to be dominated by the X-ray reflection component. We here carried out the best possible analysis with XMM-Newton data. Time-lags can be reliably estimated over a relatively narrow frequency range, and their errors are rather large. Nevertheless, our results are consistent with the hypothesis of X-ray reflection from the inner accretion disc.

We present the results from a systematic analysis of the X-ray continuum ('hard') time-lags and intrinsic coherence between the 2−4 keV and various energy bands in the 0.3−10 keV range, for ten X-ray bright and highly variable active galactic nuclei (AGN). We used all available archival XMM-Newton data, and estimated the time-lags following Epitropakis & Papadakis (2016). By performing extensive numerical simulations, we arrived at useful guidelines for computing intrinsic coherence estimates that are minimally biased, have known errors, and are (approximately) Gaussian distributed.Owing to the way we estimated the time-lags and intrinsic coherence, we were able to do a proper model fitting to the data. Regarding the continuum time-lags, we are able to demonstrate that they have a power-law dependence on frequency, with a slope of −1, and that their amplitude scales with the logarithm of the light-curve mean-energy ratio. We also find that their amplitude increases with the square root of the X-ray Eddington ratio. Regarding the intrinsic coherence, we found that it is approximately constant at low frequencies. It then decreases exponentially at frequencies higher than a characteristic 'break frequency.' Both the low-frequency constant intrinsic-coherence value and the break frequency have a logarithmic dependence on the light-curve meanenergy ratio. Neither the low-frequency constant intrinsic-coherence value, nor the break frequency exhibit a universal scaling with either the central black hole mass, or the the X-ray Eddington ratio. Our results could constrain various theoretical models of AGN X-ray variability.