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

By S. Vaughan, R. Edelson, R. Warwick, P. U. IoA, Cambridge, U. Leicester, Ucla, U. Southampton. 2003

809 citations recorded by the source corpus.

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 v a r , and excess variance, σ 2 XS, 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 σ 2 XS (or similarly F v a r ) 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d0689e75d4e4769ae9647fd7c488ffc1e8ec6422

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Citations in the corpus

Variability in red supergiant stars: pulsations, long secondary periods and convection noise (2006, background): “In astrophysics, X-ray light curves of active galaxies and interacting binaries have been a major inspiration of such tudies (e.g. Vaughan et al. 2003 and references therein).”
Second ROSAT all-sky survey (2RXS) source catalogue (2016, methodology): “The normalised excess variance is a powerful and commonly used method to determine the probability that a time series shows variability above a certain threshold (e.g. Nandra et al. 1997; Vaughan et al. 2003; Ponti et al. 2004).”
Accretion disc variability in the hard state of black hole X-ray binaries (2009, methodology): “By comparison with equation B2 of Vaughan et al. 2003, using the relation: σ2err,y σ2xs,y << σ2err,x σ2xs,x (which is true because the reference band has good signal to noise) it can be shown that the errors on the covariance are smaller than corresponding errors on the rms values.”
A Bayesian test for periodic signals in red noise (2009, methodology): “The results of the present analysis of the Mrk766 data agree reasonably well with those previously reported by Vaughan et al. (2003) which were obtained using standard frequentist methods (e.g. binning the data and estimating parameters by minimising the χ2 statistic).”
The ultraluminous state revisited: fractional variability and spectral shape as diagnostics of super-Eddington accretion (2013, neutral): “Fractional variability and the associated errors were calculated following the prescription of Vaughan et al. (2003); it should be noted that this does not account for the effects of intrinsic scattering in the red noise, although Vaughan et al. state that differences in a fractional variability…”
Generating artificial light curves: revisited and updated (2013, methodology): “There is a plethora of normalisation factors that can be applied to the periodogram (e.g. Vaughan et al. 2003).”
X-ray reverberation around accreting black holes (2014, background): “The errors on the rms spectrum must be calculated based on the errors expected due to Poisson noise (e.g. see Vaughan et al. 2003a), since they are independent between different energy bins in the rms spectrum, whereas the errors in the rms due to intrinsic stochastic variability (i.e. the…”
Non‐linear X‐ray variability in X‐ray binaries and active galaxies (2005, background): “The X-ray light curves of active galactic nuclei (AGN) and X-ray binary systems (XRBs) are often dominated by strong flickering type variability, which is aperiodic (noise-like), e.g. McHardy (1988); Vaughan et al. (2003); van der Klis (1995).”
Measurement of the extragalactic background light imprint on the spectra of the brightest blazars observed with H.E.S.S. (2012, methodology): “The estimate chosen is similar to the excess variance estimator developed by Vaughan et al. (2003) for variability.”
An Exceptional Very High Energy Gamma-Ray Flare of PKS 2155–304 (2007, background): “The average power expected when the measurement error dominates is shown as a dashed line (see the Appendix in Vaughan et al. 2003).”
X-ray variability of 104 active galactic nuclei - XMM-Newton power-spectrum density profiles (2012, methodology): “The expected Poisson noise level was calculated assuming the standard formula (e.g. Uttley et al., 2002; Vaughan et al., 2003A) and this value was used in cases where the parameterC was poorly constrained in the periodogram fitting (these observations are indicated by an asterisk in tables 2 and 3).”
Active galactic nuclei: what’s in a name? (2017, methodology): “…1989) had difficulties in explaining other X-ray timing properties of both AGN and BHXRBs, such as the observed “rms-flux” relation, whose existence was first shown by Uttley and McHardy (2001) and later confirmed by several studies (e.g. Vaughan et al. 2003; Gaskell 2004; McHardy et al. 2004).”
Rapid optical and X-ray timing observations of GX 339-4: multi-component optical variability in the low/hard state (2010, background): “…as PSD(f) = A ∣ ∣ ∣ ∣ ∣ N ∑ i=1 (li − l̄)e2πifti ∣ ∣ ∣ ∣ ∣ 2 , (2) c© 2010 RAS, MNRAS000, 1–27 c© 2010 RAS, MNRAS000, 1–27 with the frequencies themselves being discretised atN/2 evenlyspaced values from 1/N∆T to the Nyquist frequency 1/2∆T , where∆T is the time bin (cf. Vaughan et al. 2003).”
KEPLER OBSERVATIONS OF RAPID OPTICAL VARIABILITY IN ACTIVE GALACTIC NUCLEI (2011, methodology): “An independent method of determining the error from the PSD uses the formula of Vaughan et al. (2003): errind = √ 〈err2〉/〈 f lux〉2, and is given in Col- umn 5.”
A long hard look at MCG–6-30-15 with XMM-Newton (2002, methodology): “The continuum variations are energy dependent and show the PSD is a function of energy and that the hard variations are delayed with respect to the soft variations.”
What drives the growth of black holes (2011, background): “…in response to changes to the BH 3The X-ray variability of AGN seen on intra-day timescales is related to the mass accretion but is unrelated to the accretion-disc state (e.g., Ulrich et al., 1997; Vaughan et al., 2003; Uttley et al., 2005). accretion rate (e.g., Nowak, 1995; Done et al., 2007).”