A search for X-ray reprocessing echoes in the power spectral density functions of AGN

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.Comment: Accepted for publication in MNRAS. The paper is 15 pages long and contains 7 figures and 6 table

The model constraints from the observed trends for the quasi-periodic oscillation in RE J1034+396

We analyze the time variability of the X-ray emission of RE J1034+396 -- an active galactic nucleus with the first firm detection of a quasi-periodic oscillations (QPO). Based on the results of a wavelet analysis, we find a drift in the QPO central frequency. The change in the QPO frequency correlates with the change in the X-ray flux with a short time delay. The data specifically suggest a linear dependence between the QPO period and the flux, and this gives important constraints on the QPO models. In particular, it excludes explanation in terms of the orbiting hot spot model close to a black hole. Linear structures such as shocks, spiral waves, or very distant flares are favored.Comment: Astronomy & Astrophysics, in pres

Signatures of X-ray reverberation in the power spectra of AGN

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 fractio

The flare model for X-ray variability of NGC 4258

We study the variability mechanism of active galactic nuclei (AGN) within the framework of the flare model. To this end we examine the case of Seyfert/LINER galaxy NGC 4258, which is observed at high inclination angle and exhibits rapid fluctuations of the X-ray light curve. We construct a model light curve based on the assumption of magnetic flares localized in the equatorial plane and orbiting with Keplerian speed at each given radius. We calculate the level of variability as a function of the inclination of an observer, taking into account all effects of general relativity near a rotating supermassive black hole. The variability level is a monotonic function of the source inclination. It rises more rapidly for larger values of the black hole spin (Kerr parameter) and for steeper emissivity (index beta of the radial profile). We compare the expected level of variability for the viewing angle 81.6 deg, as inferred for NGC 4258, with the case of moderate viewing angles about 30 deg, typical for Seyfert type-1 galaxies. Highly inclined sources such as this one are particularly suitable to test the flare model because the effects of orbital motion, Doppler boosting and light bending are all expected to have maximum when the accretion disk is seen almost edge-on. The model is consistent with the NGC 4258 variability, where the obscuring material is thought to be localized mainly towards the equatorial plane rather than forming a geometrically thick torus. Once the intrinsic time-scales of the flare duration are determined to better precision, this kind of highly inclined objects with a precisely known mass of the black hole can be used to set independent constraints on the spin parameter.Comment: 7 pages, 3 figures; Astronomy & Astrophysics (this version includes minor language corrections

The relativistic shift of narrow spectral features from black-hole accretion discs

Transient spectral features have been discovered in the X-ray spectra of Active Galactic Nuclei, mostly in the 5--7 keV energy range. Several interpretations were proposed for the origin of these features. We examined a model of Doppler boosted blue horns of the iron line originating from a spot in a black hole accretion disc, taking into account different approximations of general relativistic light rays and the resulting shift of energy of photons. We provide a practical formula for the blue horn energy of an intrinsically narrow line and assess its accuracy by comparing the approximation against an exact value, predicted under the assumption of a planar accretion disc. The most accurate approximation provides excellent agreement with the spot orbital radius down to the marginally stable orbit of a non-rotating black hole.Comment: Accepted for publication in A&A; 8 pages, 5 figure

Hot-spot model for accretion disc variability as random process

Theory of random processes provides an attractive mathematical tool to describe the fluctuating signal from accreting sources, such as active galactic nuclei and Galactic black holes observed in X-rays. These objects exhibit featureless variability on different timescales, probably originating from an accretion disc. We study the basic features of the power spectra in terms of a general framework, which permits semi-analytical determination of the power spectral density (PSD) of the resulting light curve. We consider the expected signal generated by an ensemble of spots randomly created on the accretion disc surface. Spot generation is governed by Poisson or by Hawkes processes. We include general relativity effects shaping the signal on its propagation to a distant observer. We analyse the PSD of a spotted disc light curve and show the accuracy of our semi-analytical approach by comparing the obtained PSD with the results of Monte Carlo simulations. The asymptotic slopes of PSD are 0 at low frequencies and they drop to -2 at high frequencies, usually with a single frequency break. More complex two-peak solutions also occur. The amplitude of the peaks and their frequency difference depend on the inherent timescales of the model. At intermediate frequencies, the intrinsic PSD is influenced by the individual light curve profile as well as by the type of the underlying process. However, even in cases when two Lorentzians seem to dominate the PSD, it does not necessarily imply that two single oscillation mechanisms operate simultaneously. Instead, it may well be the manifestation of the avalanche mechanism. The main advantage of our approach is an insight in the model functioning and the fast evaluation of the PSD.Comment: 18 pages, 9 figures; Astronomy & Astrophysics accepte

Relativistický posuv spektrálních čar akrečních disků černých děr

We study gravitational redshift of spectral lines

Sestupující orbity v okolí rotující černé díry

We consider orbits of a test body near a rotating black hole. The orbits are perturbed by two effects which drive them away from purely geodesic motion