On characterising the variability properties of X-ray light curves from active galaxies

We review some practical aspects of measuring the amplitude of variability in `red noise' light curves typical of those from Active Galactic Nuclei (AGN). The quantities commonly used to estimate the variability amplitude in AGN light curves, such as the fractional rms variability amplitude, F_var, and excess variance, sigma_XS^2, are examined. Their statistical properties, relationship to the power spectrum, and uses for investigating the nature of the variability processes are discussed. We demonstrate that sigma_XS^2 (or similarly F_var) shows large changes from one part of the light curve to the next, even when the variability is produced by a stationary process. This limits the usefulness of these estimators for quantifying differences in variability amplitude between different sources or from epoch to epoch in one source. Some examples of the expected scatter in the variance are tabulated for various typical power spectral shapes, based on Monte Carlo simulations. The excess variance can be useful for comparing the variability amplitudes of light curves in different energy bands from the same observation. Monte Carlo simulations are used to derive a description of the uncertainty in the amplitude expected between different energy bands (due to measurement errors). Finally, these estimators are used to demonstrate some variability properties of the bright Seyfert 1 galaxy Markarian 766. The source is found to show a strong, linear correlation between rms amplitude and flux, and to show significant spectral variability.Comment: 14 pages. 12 figures. Accepted for publication in MNRA

A non-separable stochastic model for pulse-like ground motions

A phenomenological non-separable non-stationary stochastic model is proposed to represent near-fault pulse-like ground motions (PLGMs) by means of a parametrically defined evolutionary power spectrum (EPSD). Numerical data pertaining to ensembles of EPSD compatible realizations and considering statistical analysis of peak elastic and inelastic spectral ordinates demonstrate the applicability of the model to capture the salient effects of PLGMs to structural responses. To this aim, the model parameters are calibrated against a field recorded PLGM. Further numerical data considering stochastic processes compatible with the response spectrum of the European aseismic code (EC8) are furnished to demonstrate the potential of the proposed model for including near-fault effects to spectrum compatible representations of the seismic action. It is foreseen that this model can be a useful tool in accounting for the low-frequency content of PLGMs in both Monte Carlo simulation-based analyses and in statistical linearization based studies

XMM-Newton View of PKS 2155-304: Characterizing the X-ray Variability Properties with EPIC-PN

Starting from XMM-Newton EPIC-PN data, we present the X-ray variability characteristics of PKS 2155-304 using a simple analysis of the excess variance, \xs, and of the fractional rms variability amplitude, fvar. The scatter in \xs\ and \fvar, calculated using 500 s long segments of the light curves, is smaller than the scatter expected for red noise variability. This alone does not imply that the underlying process responsible for the variability of the source is stationary, since the real changes of the individual variance estimates are possibly smaller than the large scatters expected for a red noise process. In fact the averaged \xs and \fvar, reducing the fluctuations of the individual variances, chang e with time, indicating non-stationary variability. Moreover, both the averaged \sqxs (absolute rms variability amplitude) and \fvar show linear correlation with source flux but in an opposite sense: \sqxs correlates with flux, but \fvar anti-correlates with flux. These correlations suggest that the variability process of the source is strongly non-stationary as random scatters of variances should not yield any correlation. \fvar spectra were constructed to compare variability amplitudes in different energy bands. We found that the fractional rms variability amplitude of the source, when significant variability is observed, increases logarithmically with the photon energy, indicating significant spectral variability. The point-to-point variability amplitude may also track this trend, suggesting that the slopes of the power spectral density of the source are energy-independent. Using the normalized excess variance the black hole mass of \pks was estimated to be about $1.45 \times 10^8 M_{\bigodot}$. This is compared and contrasted with the estimates derived from measurements of the host galaxies.Comment: Accepted for publication in The Astrophysical Journa

Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain

Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain, Research Methods/ Statistical Methods,

Spectral Analysis Of Business Cycles In The Visegrad Group Countries

This paper examines the business cycle properties of Visegrad group countries. The main objective is to identify business cycles in these countries and to study the relationships between them. The author applies a modification of the Fourier analysis to estimate cycle amplitudes and frequencies. This allows for a more precise estimation of cycle characteristics than the traditional approach. The cross-spectral analysis of GDP cyclical components for the Czech Republic, Hungary, Poland and Slovakia makes it possible to assess the degree of business cycle synchronization between the countries

The human ECG - nonlinear deterministic versus stochastic aspects

We discuss aspects of randomness and of determinism in electrocardiographic signals. In particular, we take a critical look at attempts to apply methods of nonlinear time series analysis derived from the theory of deterministic dynamical systems. We will argue that deterministic chaos is not a likely explanation for the short time variablity of the inter-beat interval times, except for certain pathologies. Conversely, densely sampled full ECG recordings possess properties typical of deterministic signals. In the latter case, methods of deterministic nonlinear time series analysis can yield new insights.Comment: 6 pages, 9 PS figure

Intrinsic electromagnetic variability in celestial objects containing rapidly spinning black holes

Analytical studies have raised the concern that a mysterious expulsion of magnetic field lines by a rapidly-spinning black hole (dubbed the black hole Meissner effect) would shut down the Blandford-Znajek process and quench the jets of active galactic nuclei and microquasars. This effect is however not seen observationally or in numerical simulations. Previous attempts at reconciling the predictions with observations have proposed several mechanisms to evade the Meissner effect. In this paper, we identify a new evasion mechanism and discuss its observational significance. Specifically, we show that the breakdown of stationarity is sufficient to remove the expulsion of the magnetic field at all multipole orders, and that the associated temporal variation is likely turbulent due to the existence of efficient mechanisms for sharing energy across different modes. Such an intrinsic (as opposed to being driven externally by, e.g., changes in the accretion rate) variability of the electromagnetic field can produce the recorded linear correlation between microvariability amplitudes and mean fluxes, help create magnetic randomness and seed sheared magnetic loops in jets, and lead to a better theoretical fit to the X-ray microvariability power spectral density.Comment: 16 pages, 9 figure