Generating artificial light curves: Revisited and updated

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 randomisation 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 distribution 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. same PDF and PSD, respectively. Within the framework of Reproducible Research, the code, together with the illustrative example used in this manuscript, are both made publicly available in the form of an interactive Mathematica notebook.Comment: Accepted for publication in MNRAS. The paper is 23 pages long and contains 21 figures and 2 tables. The Mathematica notebook can be found in the web as part of this paper (Online Material) or at http://www.astro.soton.ac.uk/~de1e08/ArtificialLightCurves

General relativistic modelling of the negative reverberation X-ray time delays in AGN

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 iron line (Fe k$\alpha$) 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 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, $\alpha$, the viewing angle, $\theta$, 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 the viewing angles are distributed uniformly between 20 and 60 degrees. Finally, there is a tentative indication that the distribution of spin parameters may be bimodal above and below 0.62.Comment: Accepted for publication in MNRAS. The paper is 22 pages long and contains 19 figures and 2 table

Extensive X-ray variability studies of NGC 7314 using long XMM-Newton observations

We present a detailed X-ray variability study of the low mass Active Galactic Nuclei (AGN) NGC 7314 using the two newly obtained XMM-Newton observations ($140$ and $130$ ks), together with two archival data sets of shorter duration ($45$ and $84$ ks). The relationship between the X-ray variability characteristics and other physical source properties (such as the black hole mass) are still relatively poorly defined, especially for low-mass AGN. We perform a new, fully analytical, power spectral density (PSD) model analysis method, which will be described in detail in a forthcoming paper, that takes into consideration the spectral distortions, caused by red-noise leak. We find that the PSD in the $0.5-10$ keV energy range, can be represented by a bending power-law with a bend around $6.7\times10^{-5}$ Hz, having a slope of $0.51$ and $1.99$ below and above the bend, respectively. Adding our bend time-scale estimate, to an already published ensemble of estimates from several AGN, supports the idea that the bend time-scale depends linearly only on the black hole mass and not on the bolometric luminosity. Moreover, we find that as the energy range increases, the PSD normalization increases and there is a hint that simultaneously the high frequency slope becomes steeper. Finally, the X-ray time-lag spectrum of NGC 7314 shows some very weak signatures of relativistic reflection, and the energy resolved time-lag spectrum, for frequencies around $3\times10^{-4}$ Hz, shows no signatures of X-ray reverberation. We show that the previous claim about ks time-delays in this source, is simply an artefact induced by the minuscule number of points entering during the time-lag estimation in the low frequency part of the time-lag spectrum (i.e. below $10^{-4}$ Hz).Comment: Accepted for publication in MNRAS. The paper is 21 pages long and contains 15 figures and 3 table

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

We compute fully relativistic disc response functions in the case of the "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. 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. 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.Comment: Astronomy and Astrophysics accepte

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

Long-term X-ray spectral variability in AGN from the Palomar sample observed by Swift

We present X-ray spectral variability of 24 local active galactic nuclei (AGN) from the Palomar sample of nearby galaxies, as observed mainly by Swift. From hardness ratio measurements, we find that 18 AGN with low accretion rates show hardening with increasing count rate, converse to the softer-when-brighter behaviour normally observed in AGN with higher accretion rates. Two AGN show softening with increasing count rate, two show more complex behaviour, and two do not show any simple relationship. Sufficient data were available for the spectra of 13 AGN to be summed in flux-bins. In nine of these sources, correlated luminosity-dependent changes in the photon index (?) of a power-law component are found to be the main cause of hardness variability. For six objects, with a low accretion rate as a fraction of the Eddington rate (m?Edd), ? is anticorrelated with m?Edd, i.e. ‘harder-when-brighter’ behaviour is observed. The three higher m?Edd-rate objects show a positive correlation between ? and m?Edd. This transition from harder-when-brighter at low m?Eddto softer-when-brighter at high m?Edd can be explained by a change in the dominant source of seed-photons for X-ray emission from cyclo-synchrotron emission from the Comptonizing corona itself to thermal seed-photons from the accretion disc. This transition is also seen in the ‘hard state’ of black hole X-ray binaries (BHXRBs). The results support the idea that low-ionization nuclear emission-line regions are analogues of BHXRBs in the hard state and that Seyferts are analogues of BHXRBs in either the high-accretion rate end of the hard state or in the hard-intermediate state

X-ray spectral analysis of the low-luminosity active galactic nucleus NGC 7213 using long XMM-Newton observations

We present the X-ray spectral results from the longest X-ray Multi-mirror Mission–Newton observation, 133 ks, of the low-luminosity active galactic nucleus NGC 7213. The hardness-ratio analysis of the X-ray light curves discloses a rather constant X-ray spectral shape, at least for the observed exposure time, enabling us to perform X-ray spectral studies using the total observed spectrum. Apart from a neutral Fe K? emission line, we also detect narrow emission lines from the ionized iron species, Fe?xxv and Fe?xxvi. Our analysis suggests that the neutral Fe K? originates from a Compton-thin reflector, while the gas responsible for the high-ionization lines is collisionally excited. The overall spectrum, in the 0.3–10?keV energy band, registered by the European Photon Imaging Camera can be modelled by a power-law component (with a slope of ? ? 1.9) plus two thermal components at 0.36 and 8.84?keV. The low-energy thermal component is entirely consistent with the X-ray spectral data obtained by the Reflection Grating Spectrometer between 0.35–1.8?keV