Aperiodic variability of low-mass X-ray binaries at very low frequencies

We have obtained discrete Fourier power spectra of a sample of persistent low-mass neutron-star X-ray binaries using long-term light curves from the All Sky Monitor on board the Rossi X-ray Timing Explorer. Our aim is to investigate their aperiodic variability at frequencies in the range 1 x 10^{-7}-5 x 10^{-6} Hz and compare their properties with those of the black-hole source Cyg X-1. We find that the classification scheme that divides LMXBs into Z and atoll sources blurs at very low frequencies. Based on the long-term (~ years) pattern of variability and the results of power-law fits (P ~ v^{-a}) to the 1 x 10^{-7}-5 x 10^{-6} Hz power density spectra, low-mass neutron-star binaries fall into three categories. Type I includes all Z sources, except Cyg X-2, and the atoll sources GX9+1 and GX13+1. They show relatively flat power spectra (a < 0.9) and low variability (rms < 20%). Type II systems comprise 4U 1636-53, 4U 1735-44 and GX3+1. They are more variable (20% < rms < 30%) and display steeper power spectra (0.9 < a < 1.2) than Type I sources. Type III systems are the most variable (rms > 30%) and exhibit the steepest power spectra (a > 1.2). The sources 4U 1705-44, GX354-0 and 4U 1820-30 belong to this group. GX9+9 and Cyg X-2 appear as intermediate systems in between Type I and II and Type II and III sources, respectively. We speculate that the differences in these systems may be caused by the presence of different types of mass-donor companions. Other factors, like the size of the accretion disc and/or the presence of weak magnetic fields, are also expected to affect their low-frequency X-ray aperiodic varibility.Comment: 9 pages, 6 figures. To be published in A&

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

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

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

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

Discovery of multiple Lorentzian components in the X-ray timing properties of the Narrow Line Seyfert 1 Ark 564

We present a power spectral analysis of a 100 ksec XMM-Newton observation of the narrow line Seyfert 1 galaxy Ark~564. When combined with earlier RXTE and ASCA observations, these data produce a power spectrum covering seven decades of frequency which is well described by a power law with two very clear breaks. This shape is unlike the power spectra of almost all other AGN observed so far, which have only one detected break, and resemble Galactic binary systems in a soft state. The power spectrum can also be well described by the sum of two Lorentzian-shaped components, the one at higher frequencies having a hard spectrum, similar to those seen in Galactic binary systems. Previously we have demonstrated that the lag of the hard band variations relative to the soft band in Ark 564 is dependent on variability time-scale, as seen in Galactic binary sources. Here we show that the time-scale dependence of the lags can be described well using the same two-Lorentzian model which describes the power spectrum, assuming that each Lorentzian component has a distinct time lag. Thus all X-ray timing evidence points strongly to two discrete, localised, regions as the origin of most of the variability. Similar behaviour is seen in Galactic X-ray binary systems in most states other than the soft state, i.e. in the low-hard and intermediate/very high states. Given the very high accretion rate of Ark 564 the closest analogy is with the very high (intermediate) state rather than the low-hard state. We therefore strengthen the comparison between AGN and Galactic binary sources beyond previous studies by extending it to the previously poorly studied very high accretion rate regime.Comment: 11 pages, 11 figures, accepted for publication in MNRA