Time series analysis in astronomy - an application to quasar variability studies

Vio, R.; Cristiani, S.; Lessi, O.; Provenzale, A.

doi:10.1086/171367

Cited by 54 publications

(49 citation statements)

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“…We derived analytical formulae for the PSD, Eqs. (14) and (33) It is worth noting that the PSD does not maintain all information about the light curves that can be studied by Fourier methods (Vio et al 1992). Extensions have been discussed and compared with real data (Krolik et al 1993;Karas 1997;Nowak et al 1999;Vaughan & Uttley 2008), but this would go beyond the scope of our present work.…”

Section: Discussionmentioning

confidence: 97%

Hot-spot model for accretion disc variability as random process

Pecháček

Karas

2008

A&A

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Aims. Theory of random processes provides an attractive mathematical tool to describe the fluctuating signal from accreting sources, such as active galactic nuclei and Galactic black holes observed in X-rays. These objects exhibit featureless variability on different timescales, probably originating from an accretion disc. Methods. We study the basic features of the power spectra in terms of a general framework, which permits semi-analytical determination of the power spectral density (PSD) of the resulting light curve. We consider the expected signal generated by an ensemble of spots randomly created on the accretion disc surface. Spot generation is governed by Poisson or by Hawkes processes. The latter one represents an avalanche mechanism and seems to be suggested by the observed form of the power spectrum. We include general relativity effects shaping the signal on its propagation to a distant observer. Results. We analyse the PSD of a spotted disc light curve and show the accuracy of our semi-analytical approach by comparing the obtained PSD with the results of Monte Carlo simulations. The asymptotic slopes of PSD are 0 at low frequencies and they drop to −2 at high frequencies, usually with a single frequency break. More complex two-peak solutions also occur. The amplitude of the peaks and their frequency difference depend on the inherent timescales of the model, i.e., the intrinsic lifetime of the spots and the typical duration of avalanches. Conclusions. At intermediate frequencies, the intrinsic PSD is influenced by the individual light curve profile as well as by the type of the underlying process. However, even in cases when two Lorentzians seem to dominate the PSD, it does not necessarily imply that two single oscillation mechanisms operate simultaneously. Instead, it may well be the manifestation of the avalanche mechanism. The main advantage of our approach is an insight in the model functioning and the fast evaluation of the PSD.

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Section: Discussionmentioning

confidence: 97%

Hot-spot model for accretion disc variability as random process

Pecháček

Karas

2008

A&A

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“…It has been pointed out by Vio et al (1992) that a naive application of the correlation integral method may lead to conceptual errors (as the detection of low-dimensional dynamics from signals produced by stochastic processes) and that this method must not be used in isolation, but as one of a collection of tests to discriminate chaos from stochasticity. Here we stress once more that the nonlinear statistics based on the scaling index is used only as a statistical test to discriminate between two states of the system, not to determine any kind of dimension, which would be meaningless for non-deterministic systems.…”

Section: Nonlinear Analysismentioning

confidence: 99%

On the nature of X-ray variability in Ark 564

Gliozzi

Brinkmann

Räth

et al. 2002

A&A

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Abstract.We use data from a recent long ASCA observation of the Narrow Line Seyfert 1 galaxy Ark 564 to investigate in detail its timing properties. We show that a thorough analysis of the time series, employing techniques not generally applied to AGN light curves, can provide useful information to characterize the engines of these powerful sources. We searched for signs of non-stationarity in the data, but did not find strong evidences for it. We find that the process causing the variability is very likely nonlinear, suggesting that variability models based on many active regions, as the shot noise model, may not be applicable to Ark 564. The complex light curve can be viewed, for a limited range of time scales (as indicated by the breaks in the structure and power density spectrum), as a fractal object with non-trivial fractal dimension and statistical self-similarity. Finally, using a nonlinear statistic based on the scaling index as a tool to discriminate time series, we demonstrate that the high and low count rate states, which are indistinguishable on the basis of their autocorrelation, structure and probability density functions, are intrinsically different, with the high state characterized by higher complexity.

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“…In order to develop a more general approach, we start with the observation that signals x(t), characteristic of many physical systems with unpredictable time evolution, can be described in terms of the following stochastic model (Vio et al 1992) :…”

Section: A General Approachmentioning

confidence: 99%

On the Reconstruction of Irregularly Sampled Time Series

Vio

Strohmer

Wamsteker

2000

PUBL ASTRON SOC PAC

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ABSTRACT. We consider the question of numerical treatment of irregularly sampled time series. This problem is quite common in astronomy because of factors such as the day-night alternation, weather conditions, nonobservability of the objects under study, etc. For this reason an extensive literature is available on this subject. Most of the proposed techniques, however, are based on heuristic arguments, and their usefulness is essentially in the estimation of power spectra and/or autocovariance functions. Here we propose an approach, based on the reasonable assumption that many signals of astronomical interest are the realization of band-limited processes, which can be used to Ðll gaps in experimental time series. By using this approach we propose several reconstruction algorithms that, because of their regularization properties, yield reliable signal reconstructions even in case of noisy data and large gaps. A detailed description of these algorithms is provided, their theoretical implications are considered, and their practical performances are tested via numerical experiments. MATLAB software implementing the methods described in this work is obtainable by request from the authors.

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Time series analysis in astronomy - an application to quasar variability studies

Cited by 54 publications

References 0 publications

Hot-spot model for accretion disc variability as random process

Hot-spot model for accretion disc variability as random process

On the nature of X-ray variability in Ark 564

On the Reconstruction of Irregularly Sampled Time Series

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