The production of artificial light curves with known statistical and variability properties is of great importance in astrophysics. Consolidating the confidence levels during cross-correlation ...studies, understanding the artefacts induced by sampling irregularities, establishing detection limits for future observatories are just some of the applications of simulated data sets. Currently, the widely used methodology of amplitude and phase randomization is able to produce artificial light curves which have a given underlying power spectral density (PSD) but which are strictly Gaussian distributed. This restriction is a significant limitation, since the majority of the light curves, e.g. active galactic nuclei, X-ray binaries, gamma-ray bursts, show strong deviations from Gaussianity exhibiting 'burst-like' events in their light curves yielding long-tailed probability density functions (PDFs). In this study, we propose a simple method which is able to precisely reproduce light curves which match both the PSD and the PDF of either an observed light curve or a theoretical model. The PDF can be representative of either the parent distribution or the actual distribution of the observed data, depending on the study to be conducted for a given source. The final artificial light curves contain all of the statistical and variability properties of the observed source or theoretical model, i.e. the same PDF and PSD, respectively. Within the framework of Reproducible Research, the code and the illustrative example used in this paper are both made publicly available in the form of an interactive mathematica notebook.
ABSTRACT
Thermal reverberation in accretion discs of active galactic nuclei is thought to be the reason of the continuum UV/optical time lags seen in these sources. Recently, we studied thermal ...reverberation of a standard Novikov-Thorne accretion disc illuminated by an X–ray point-like source, and we derived an analytic prescription for the time lags as function of wavelength. In this work, we use this analytic function to fit the time-lags spectra of seven Seyferts, that have been intensively monitored, in many wave-bands, in the last few years. We find that thermal reverberation can explain the observed UV/optical time lags in all these sources. Contrary to previous claims, the magnitude of the observed UV/optical time-lags is exactly as expected in the case of a standard accretion disc in the lamp-post geometry, given the black hole mass and the accretion rate estimates for the objects we study. We derive estimates of the disc accretion rates and corona height for a non-spinning and a maximally spinning black hole scenarios. We also find that the modelling of the continuum optical/UV time-lags can be used to estimate the black hole spin, when combined with additional information. We also find that the model under-predicts the observed X–ray to UV time-lags, but this difference is probably due to the broad X-ray auto-correlation function of these sources.
The long-term X-ray spectral variability of AGN Sobolewska, M. A.; Papadakis, I. E.
Monthly notices of the Royal Astronomical Society,
November 2009, Letnik:
399, Številka:
3
Journal Article
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We present the results from the spectral analysis of more than 7500 Rossi X-ray Timing Explorer (RXTE) spectra of 10 active galactic nuclei (AGN). Our main goal was to study their long-term X-ray ...spectral variability. The sources in the sample are nearby, X-ray bright, and they have been observed by RXTE regularly over a long period of time (∼7–11 yr). High-frequency breaks have been detected in their power spectra, and these characteristic frequencies imply time-scales of the order of a few days or weeks. Consequently, the RXTE observations we have used most probably sample most of the flux and spectral variations that these objects exhibit. Thus, the RXTE data are ideal for our purpose. Fits to the individual spectra were performed in the 3–20 keV energy band. We modelled the data in a uniform way using simple phenomenological models (a power law with the addition of Gaussian line and/or edge to model the iron Kα emission/absorption features, if needed) to consistently parametrize the shape of the observed X-ray continuum of the sources in the sample. We found that the average spectral slope does not correlate with source luminosity or black hole mass, while it correlates positively with the average accretion rate. We have also determined the (positive) spectral slope–flux relation for each object, over a flux range larger than before. We found that this correlation is similar in all objects, except for NGC 5548 which displays limited spectral variations for its flux variability. We discuss this global spectral slope–flux trend in the light of current models for spectral variability. We consider (i) intrinsic variability, expected, for example, from Comptonization processes, (ii) variability caused by absorption of X-rays by a single absorber whose ionization parameter varies proportionally to the continuum flux variations, (iii) variability resulting from the superposition of a constant reflection component and an intrinsic power law which is variable in flux but constant in shape and (iv) variability resulting from the superposition of a constant reflection component and an intrinsic power law which is variable both in flux and in shape. Our final conclusion is that scenario (iv) provides the best fit to the data of all objects, except for NGC 5548.
Hard X-ray spectra of 28 bright Seyfert galaxies observed with INTEGRAL were analysed together with the X-ray spectra from XMM–Newton, Suzaku and RXTE. These broad-band data were fitted with a model ...assuming a thermal Comptonization as a primary continuum component. We tested several model options through a fitting of the Comptonized continuum accompanied by a complex absorption and a Compton reflection. Both the large data set used and the model space explored allowed us to accurately determine a mean temperature kT
e of the electron plasma, the Compton parameter y and the Compton reflection strength R for the majority of objects in the sample. Our main finding is that a vast majority of the sample (20 objects) is characterized by kT
e < 100 keV, and only for two objects we found kT
e > 200 keV. The median kT
e for entire sample is 48
$_{-14}^{+57}$
keV. The distribution of the y parameter is bimodal, with a broad component centred at ≈0.8 and a narrow peak at ≈1.1. A complex, dual absorber model improved the fit for all data sets, compared to a simple absorption model, reducing the fitted strength of Compton reflection by a factor of about 2. Modest reflection (median R ≈ 0.32) together with a high ratio of Comptonized to seed photon fluxes point towards a geometry with a compact hard X-ray emitting region well separated from the accretion disc. Our results imply that the template Seyferts spectra used in the population synthesis models of active galactic nuclei (AGN) should be revised.
We present measurements of rotations of the optical polarization of blazars during the second year of operation of RoboPol, a monitoring programme of an unbiased sample of gamma-ray bright blazars ...specially designed for effective detection of such events, and we analyse the large set of rotation events discovered in two years of observation. We investigate patterns of variability in the polarization parameters and total flux density during the rotation events and compare them to the behaviour in a non-rotating state. We have searched for possible correlations between average parameters of the polarization-plane rotations and average parameters of polarization, with the following results: (1) there is no statistical association of the rotations with contemporaneous optical flares; (2) the average fractional polarization during the rotations tends to be lower than that in a non-rotating state; (3) the average fractional polarization during rotations is correlated with the rotation rate of the polarization plane in the jet rest frame; (4) it is likely that distributions of amplitudes and durations of the rotations have physical upper bounds, so arbitrarily long rotations are not realized in nature.
We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of ...12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above 10−4 Hz), i.e. soft-band variations lag the hard-band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral Fe Kα line at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly used, but erroneous, top-hat models. Additionally, we parametrize the positive part of the time-lag spectra (typically seen below 10−4 Hz) by a power law. We find that the best-fitting black hole (BH) masses, M, agree quite well with those derived by other methods, thus providing us with a new tool for BH mass determination. We find no evidence for any correlation between M and the BH spin parameter, α, the viewing angle, θ, or the height of the X-ray source above the disc, h. Also on average, the X-ray source lies only around 3.7 gravitational radii above the accretion disc and θ is distributed uniformly between 20° and 60°. Finally, there is a tentative indication that the distribution of α may be bimodal above and below 0.62.
Context. The study of X-ray time-lag spectra in active galactic nuclei (AGN) is currently an active research area, since it has the potential to illuminate the physics and geometry of the innermost ...region (i.e. close to the putative super-massive black hole) in these objects. To obtain reliable information from these studies, the statistical properties of time-lags estimated from data must be known as accurately as possible. Aims. We investigated the statistical properties of Fourier-based time-lag estimates (i.e. based on the cross-periodogram), using evenly sampled time series with no missing points. Our aim is to provide practical “guidelines” on estimating time-lags that are minimally biased (i.e. whose mean is close to their intrinsic value) and have known errors. Methods. Our investigation is based on both analytical work and extensive numerical simulations. The latter consisted of generating artificial time series with various signal-to-noise ratios and sampling patterns/durations similar to those offered by AGN observations with present and past X-ray satellites. We also considered a range of different model time-lag spectra commonly assumed in X-ray analyses of compact accreting systems. Results. Discrete sampling, binning and finite light curve duration cause the mean of the time-lag estimates to have a smaller magnitude than their intrinsic values. Smoothing (i.e. binning over consecutive frequencies) of the cross-periodogram can add extra bias at low frequencies. The use of light curves with low signal-to-noise ratio reduces the intrinsic coherence, and can introduce a bias to the sample coherence, time-lag estimates, and their predicted error. Conclusions. Our results have direct implications for X-ray time-lag studies in AGN, but can also be applied to similar studies in other research fields. We find that: a) time-lags should be estimated at frequencies lower than ≈ 1/2 the Nyquist frequency to minimise the effects of discrete binning of the observed time series; b) smoothing of the cross-periodogram should be avoided, as this may introduce significant bias to the time-lag estimates, which can be taken into account by assuming a model cross-spectrum (and not just a model time-lag spectrum); c) time-lags should be estimated by dividing observed time series into a number, say m, of shorter data segments and averaging the resulting cross-periodograms; d) if the data segments have a duration ≳ 20 ks, the time-lag bias is ≲15% of its intrinsic value for the model cross-spectra and power-spectra considered in this work. This bias should be estimated in practise (by considering possible intrinsic cross-spectra that may be applicable to the time-lag spectra at hand) to assess the reliability of any time-lag analysis; e) the effects of experimental noise can be minimised by only estimating time-lags in the frequency range where the sample coherence is larger than 1.2/(1 + 0.2m). In this range, the amplitude of noise variations caused by measurement errors is smaller than the amplitude of the signal’s intrinsic variations. As long as m ≳ 20, time-lags estimated by averaging over individual data segments have analytical error estimates that are within 95% of the true scatter around their mean, and their distribution is similar, albeit not identical, to a Gaussian.
Context. Recently, nearby bright galaxies have been the subject of long monitoring surveys in the X-rays, UV, and optical. All of these campaigns revealed a strong correlation between the various UV ...and optical bands, with time lags that increase with wavelength. In a series of papers, we have demonstrated that a scenario in which an X-ray source located on the rotation axis of the central black hole illuminating the accretion disc is a viable explanation for the observed correlations. However, some of the monitored sources showed low or moderate correlation between the X-rays and the UV, which could challenge this scenario. Aims. In this paper, we analyse the time-averaged and the variable broadband X-ray/UV/optical spectral energy distributions (SEDs) of NGC 5548, one of the most intensely monitored Seyfert 1 galaxies, using Swift , HST, and ground-based telescopes. The aim of this paper is to test whether the broadband spectral behaviour of the source could be explained with the X-ray illumination hypothesis, despite the apparently moderate correlation between the X-rays and longer wavelength. Methods. We modelled the broadband time-averaged SED, from the Space Telescope and Optical Reverberation Mapping (STORM) monitoring campaign of the source performed using the KYNSED model, which assumes X-ray illumination of the disc. We also modelled 15 time-resolved SEDs extracted from the same campaign to check whether this model can account for the spectral variability seen in the various wavebands during the monitoring. We assumed in our modelling that the X-ray corona is powered via the accretion process. Results. Our results show that the proposed scenario could describe the time-averaged and the time-resolved SEDs of NGC 5548 perfectly well. In this scenario, the height of the corona, the X-ray photon index, and the power that is transferred to the corona all vary. This would explain the variability behaviour at the various wavelengths. The best-fit model is obtained for a non-spinning black hole accreting at a constant rate of 5% of its Eddington limit. Since each of the variable parameters will affect the observed flux in a particular way, the combined variability of all of these parameters will then account for the moderate correlation between the X-rays and UV/optical. Conclusions. We demonstrate in this paper that X-ray illumination of the accretion disc can actually explain the observed properties of NGC 5548. In fact, this model not only fits the broadband spectra of the source well, but it also explains the time-lag behaviour as a function of wavelength as well as the power spectral distribution, providing a complete description of the behaviour of this source.
Aims. We study the X-ray power spectrum of active galactic nuclei (AGN) in order to investigate whether Seyfert I and II power spectra are similar or not and whether AGN variability depends on the ...mass and accretion rate of black holes as well as to compare the power spectra of AGN with the power spectra of Galactic X-ray black hole binaries. Method. We used 14–195 keV band light curves from the 157-month Swift /BAT hard X-ray survey, and we computed the mean power spectrum and excess variance of AGN in narrow black hole mass and AGN luminosity bins. We fitted a power-law model to the AGN power spectra, and we investigated whether the power spectrum parameters and the excess variance depend on the black hole mass, luminosity, and accretion rate of AGN. Results. We found the Seyfert I and Seyfert II power spectra to be identical, in agreement with AGN unification models. The mean AGN X-ray power spectrum has the same power-law like shape, with a slope of −1 in all AGN irrespective of their luminosity and black hole mass. We did not detect any flattening to a slope of zero at frequencies as low as 10 −9 Hz. We detected an anti-correlation between the power spectral density function (PSD) amplitude and the accretion rate, similar to what has been seen in the past in the 2–10 keV band. This implies that the variability amplitude in AGN decreases with an increasing accretion rate. The universal AGN power spectrum is consistent with the mean 2–9 keV band Cyg X-1 power spectrum in its soft state. We detected a small difference in amplitude, but this is probably due to the difference in energy. Conclusions. The mean low-frequency AGN X-ray power spectrum is consistent with the extension of the mean 0.01–25 Hz Cyg X-1 power spectrum in its soft state to lower frequencies. We cannot prove that the mean AGN PSD is analogous to the mean Cyg X-1 PSD in its soft state, as we do not know the location of the high-frequency break in the hard X-ray AGN PSDs. However, if this is the case, then the accretion disc in AGN probably extends to the radius of the innermost circular stable orbit (as is probably the case with the black hole binaries in their soft state). The X-ray corona will then be located on top, illuminating the disc and producing the X-ray reflection and disc reverberation phenomena commonly observed in these objects. Furthermore, the agreement between the PSD amplitude in AGN and the Cyg X-1 (either in the soft or the hard state) over many decades in frequency indicates that the X-ray variability process is probably the same in all accreting objects, irrespective of the mass of the compact object. We plan to investigate this issue further in the near future.
Revisiting UV/optical continuum time lags in AGN Kammoun, E S; Robin, L; Papadakis, I E ...
Monthly notices of the Royal Astronomical Society,
11/2023, Letnik:
526, Številka:
1
Journal Article
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ABSTRACT
In this paper, we present an updated version of our model (KYNXiltr) which considers thermal reverberation of a standard Novikov–Thorne accretion disc illuminated by an X-ray point-like ...source. Previously, the model considered only two cases of black hole spins, and assumed a colour correction factor fcol = 2.4. Now, we extend the model to any spin value and fcol. In addition, we consider two scenarios of powering the X-ray corona, either via accretion, or external to the accretion disc. We use KYNXiltr to fit the observed time lags obtained from intense monitoring of four local Seyfert galaxies (NGC 5548, NGC 4593, Mrk 817, and Fairall 9). We consider various combinations of black hole spin, colour correction, corona height, and fraction of accretion power transferred to the corona. The model fits well the overall time-lag spectrum in these sources (for a large parameter space). For NGC 4593 only, we detect a significant excess of delays in the U band. The contribution of the diffuse BLR emission in the time-lag spectrum of this source is significant. It is possible to reduce the large best-fitting parameter space by combining the results with additional information, such as the observed Eddington ratio and average X-ray luminosity. We also provide an update to the analytic expression provided by Kammoun et al., for an X-ray source that is not powered by the accretion process, which can be used for any value of fcol, and for two values of the black hole spin (0 and 0.998).
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