The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate realizations w
ith Fourier phase correlations leading to non-detections of nonlinearities. We argue that reliable surrogates can only be generated, if one tests separately for static and dynamic nonlinearities.
We present the results from the spectral analysis of more than 7,500 RXTE spectra of 10 AGN, which have been observed by RXTE regularly over a long period of time ~ 7-11 years. These observations most probably sample most of the flux and spectral var
iations that these objects exhibit, thus, they are ideal for the study of their long term X-ray spectral variability. We modelled the 3-10 spectrum of each observation in a uniform way using a simple power-law model (with the addition of Gaussian line and/or edge to model the iron Kalpha emission/absorption features, if necessary) to consistently parametrize the shape of the observed X-ray continuum. 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 larger flux range than before. We found that this correlation is similar in almost all objects. We discuss this global spectral slope-flux trend in the light of current models for spectral variability. We consider (i) intrinsic variability, expected e.g. 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 shape. Our final conclusion is that scenario (iv) describes better our results.
We present the results from a combined study of the average X-ray spectral and timing properties of 14 nearby AGN. For 11 of the sources in the sample, we used all the available data from the RXTE archive, which were taken until the end of 2006. Ther
e are 7795 RXTE observations in total for these AGN, obtained over a period of ~7-11 years. We extracted their 3-20 keV spectra and fitted them with a simple power-law model, modified by the presence of a Gaussian line (at 6.4 keV) and cold absorption, when necessary. We used these best-fit slopes to estimate the mean spectral slope for each object, while we used results from the literature to estimate the average spectral slope of the three objects without archival, monitorin RXTE data. Our results show that the AGN average spectral slopes are not correlated either with the black hole mass or the characteristic frequencies that were detected in the power spectra.They are positively correlated, though, with the characteristic frequency when normalised to the sources black hole mass. This is similar to the spectral-timing correlation that has been observed in Cyg X-1, but not the same.The AGN spectral-timing correlation can be explained if we assume that the accretion rate determines both the average spectral slope and the characteristic time scales in AGN. The spectrum should steepen and the characteristic frequency should increase, proportionally, with increasing accretion rate. We also provide a quantitative expression between spectral slope and accretion rate. Thermal Comptonisation models are broadly consistent with our result, but only if the ratio of the soft photons luminosity to the power injected to the hot corona is proportionally related to the accretion rate.
Some recent observational results impose significant constraints on all the models that have been proposed to explain the Galactic black-hole X-ray sources in the hard state. In particular, it has been found that during the hard state of Cyg X-1 the
power-law photon number spectral index is correlated with the average time lag between hard and soft X-rays. Furthermore, the peak frequencies of the four Lorentzians that fit the observed power spectra are correlated with both the photon index and the time lag. We performed Monte Carlo simulations of Compton upscattering of soft, accretion-disk photons in the jet and computed the time lag between hard and soft photons and the power-law index of the resulting photon number spectra. We demonstrate that our jet model naturally explains the above correlations, with no additional requirements and no additional parameters.
We present the results from a detailed X-ray variability analysis of 66 AGN in the Lockman Hole, which have optical spectroscopic identifications. We compare, quantitatively, their variability properties with the properties of local AGN, and we study
the variability-luminosity relation as a function of redshift, and the variability-redshift relation in two luminosity bins. We use archival data from the last 10 XMM observations of the Lockman Hole field to extract light curves in the rest frame, 2-10 keV band. We use the normalized excess variance to quantify the variability amplitude. Using the latest results regarding the AGN power spectral shape and its dependence on black hole mass and accretion rate, we are able to compute model variability-luminosity curves, which we compare with the relations we observe. When we consider all the sources in our sample, we find that their variability amplitude decreases with increasing redshift and luminosity. These global anti-correlations are less pronounced when we split the objects in various luminosity and redshift bins. We do not find a significant correlation between variability amplitude and spectral slope. The variability-luminosity relation that we detect has a larger amplitude when compared to that of local AGN. We also find that, at a given luminosity, the variability amplitude increases with redshift up to z~1, and then stays roughly constant. Our results imply that the AGN X-ray mechanism operates in the same way at all redshifts. Among objects with the same luminosity in our sample, the black hole mass decreases and the accretion rate increases with larger redshift.
