
 We examine the long-term (rest-frame time scales from a few months to ∼20 years) X-ray variability of a sample of 2344 X-ray bright quasars from the SDSS DR14Q Catalogue, based on the data of the SRG/eROSITA All-Sky Survey complemented for ∼7% of the sample by archival data from the XMM-Newton Serendipitous Source Catalogue. We characterise variability by a structure function, SF2(Δt). We confirm the previously known anti-correlation of the X-ray variability amplitude with luminosity. We also study the dependence of X-ray variability on black hole mass, MBH, and on an X-ray based proxy of the Eddington ratio, λX. Less massive black holes prove to be more variable for given Eddington ratio and time scale. X-ray variability also grows with decreasing Eddington ratio and becomes particularly strong at λX of less than a few per cent. We confirm that the X-ray variability amplitude increases with increasing time scale. The SF2(Δt) dependence can be satisfactorily described by a power law, with the slope ranging from ∼0 to ∼0.4 for different (MBH, λX) subsamples (except for the subsample with the lowest black hole mass and lowest Eddington ratio, where it is equal to 1.1 ± 0.4).

X-ray variability of SDSS quasars based on the SRG/eROSITA all-sky survey

We study the X-ray power spectrum of active galactic nuclei (AGN) in order to investigate whether Seyfert I and II power spectra are similar or not and whether AGN variability depends on the mass and accretion rate of black holes as well as to compare the power spectra of AGN with the power spectra of Galactic X-ray black hole binaries. We used 14-195 keV band light curves from the 157-month hard X-ray survey, and we computed the mean power spectrum and excess variance of AGN in narrow black hole mass and AGN luminosity bins. We fitted a power-law model to the AGN power spectra, and we investigated whether the power spectrum parameters and the excess variance depend on the black hole mass, luminosity, and accretion rate of AGN. We found the Seyfert I and Seyfert II power spectra to be identical, in agreement with AGN unification models. The mean AGN X-ray power spectrum has the same power-law like shape, with a slope of $-1$ in all AGN irrespective of their luminosity and black hole mass. We did not detect any flattening to a slope of zero at frequencies as low as $10^ $ Hz. We detected an anti-correlation between the power spectral density function (PSD) amplitude and the accretion rate, similar to what has been seen in the past in the 2-10 keV band. This implies that the variability amplitude in AGN decreases with an increasing accretion rate. The universal AGN power spectrum is consistent with the mean 2-9 keV band Cyg X-1 power spectrum in its soft state. We detected a small difference in amplitude, but this is probably due to the difference in energy. The mean low-frequency AGN X-ray power spectrum is consistent with the extension of the mean 0.01-25 Hz Cyg X-1 power spectrum in its soft state to lower frequencies. We cannot prove that the mean AGN PSD is analogous to the mean Cyg X-1 PSD in its soft state, as we do not know the location of the high-frequency break in the hard X-ray AGN PSDs. However, if this is the case, then the accretion disc in AGN probably extends to the radius of the innermost circular stable orbit (as is probably the case with the black hole binaries in their soft sate). The X-ray corona will then be located on top, illuminating the disc and producing the X-ray reflection and disc reverberation phenomena commonly observed in these objects. Furthermore, the agreement between the PSD amplitude in AGN and the Cyg X-1 (either in the soft or the hard state) over many decades in frequency indicates that the X-ray variability process is probably the same in all accreting objects, irrespective of the mass of the compact object. We plan to investigate this issue further in the near future.

https://www.aanda.org/articles/aa/pdf/2024/05/aa47995-23.pdf

The X-ray variability of active galactic nuclei: Power spectrum and variance analysis of the light curves

ABSTRACT Although flux variability is one of the defining properties of accretion flows on to supermassive black holes, its dependence on physical parameters such as the mass of the compact object and the Eddington ratio remains under discussion. In this paper, we address this issue using the structure function statistic to measure the variability at X-ray wavelengths of a sample of optically selected QSOs with available black hole masses and Eddington ratios. We present a new Bayesian methodology for estimating the structure function tailored to the Poisson nature of the X-ray data. This is applied to 15 548 SDSS DRQ16 QSOs with repeat observations in the XMM–Newton archive and/or the SRG/eROSITA All Sky Survey. The X-ray structure function monotonically increases to time intervals of about 10–15 yrs, consistent with scenarios in which instabilities of the accretion disc contribute to the X-ray variability on long time-scales. Additionally, there is evidence that the amplitude of the stochastic X-ray flux variations rises with decreasing black hole mass and Eddington ratio. This finding imposes stringent constraints on empirical models of Active Galactic Nuclei variability derived from local samples, emphasizing the significance of high-redshift population studies for comprehending the stochastic flux variations in active black holes. 

https://academic.oup.com/mnras/article-pdf/531/4/4524/58278644/stae1383.pdf

Ensemble X-ray variability of optically selected QSOs: dependence on black hole mass and Eddington ratio

Abstract We present a comprehensive X-ray analysis and spectral energy distribution (SED) fitting of WISEA J171419.96+602724.6, an extremely luminous type 2 quasar at z = 2.99. The source was suggested as a candidate Compton-thick (column density N H &gt; 1.5×10 24 cm −2 ) quasar by a short XMM-Newton observation in 2011. We recently observed the source with deep NuSTAR and XMM-Newton exposures in 2021 and found that the source has a lower obscuration of N H ∼ 5×10 22 cm −2 with an about four times lower flux. The two epochs of observations suggested that the source was significantly variable in X-ray obscuration, flux, and intrinsic luminosity at 2 σ –3 σ in less than 2.5 yr (in the source rest frame). We performed SED fitting of this source using Code Investigating GALaxy Emission thanks to its great availability of multiwavelength data (from hard X-rays to radio). The source is very luminous, with a bolometric luminosity of L BOL ∼ 2.5 × 10 47 erg s −1 . Its host galaxy has a huge star formation rate (SFR) of ∼1280 M ☉ yr −1 and a huge stellar mass of ∼1.1 × 10 12 M ☉ . The correlation between the SFR and stellar mass of this source is consistent with what was measured in the high- z quasars. It is also consistent with what was measured in the main-sequence star-forming galaxies, suggesting that the presence of the active nucleus in our target does not enhance or suppress the SFR of its host galaxy. The source is an infrared hyperluminous, obscured galaxy with a significant amount of hot dust in its torus and shares many similar properties with hot, dust-obscured galaxies. 

An X-Ray Significantly Variable, Luminous, Type 2 Quasar at z = 2.99 with a Massive Host Galaxy

Aims : During its all-sky survey phase, the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) X-ray telescope on board the Spectrum-Roentgen-Gamma (SRG) spacecraft scans through the ecliptic poles every 4 hours. This extensive data set of long-duration, frequent, and consistent observations of thousands of X-ray sources is ideal for a detailed long-term X-ray-variability analysis. However, individual observations are short, are separated by long but consistent gaps, and have varying exposure times. Therefore, the identification of variable sources and the characterisation and quantification of their variability requires a unique methodology. We aim to develop and evaluate variability analysis methods for eROSITA observations, focusing on sources close to the survey poles. We also aim to detect intrinsically variable sources at any count rate and quantify the variability of low-count-rate sources. Methods : We simulate eROSITA-like light curves to evaluate and quantify the effect of survey mode observations on the measured periodogram and normalised excess variance. We introduce a new method for estimating the normalised intrinsic variance of a source based on the Bayesian excess variance (bexvar) method. Results : We determine thresholds for identifying likely variable sources while minimising the false-positive rate, as a function of the number of bins, and the average count rate in the light curve. The bexvar normalised intrinsic variance estimate is significantly more accurate than the normalised excess variance method in the Poisson regime. At high count rates, the two methods are comparable. We quantify the scatter in the intrinsic variance of a stationary pink-noise process, and investigate how to reduce it. Finally, we determine a description of the excess noise in a periodogram caused by varying exposure times throughout a light curve. Although most of these methods were developed specifically for analysing variable active galactic nuclei in the eROSITA all-sky survey, they can also be used for the variability analysis of other datasets from other telescopes, with slight modifications.

Characterising X-ray variability in light curves with complex sampling patterns: Application to the eROSITA south ecliptic pole survey

We study the ensemble X-ray variability properties of Active Galactic Nuclei (AGN) over a large range of timescales (20 ks $\leq T\leq$ 14 yrs), redshift ($0\leq z \lesssim 3$), luminosities ($10^{40}$ erg s$^{-1}\leq L_X\leq 10^{46}$ erg s$^{-1}$) and black hole (BH) masses ($10^6 \leq $M$_\odot \leq 10^9$). We propose the use of the variance-frequency diagram, as a viable alternative to the study of the power spectral density (PSD), which is not yet accessible for distant, faint and/or sparsely sampled AGN. We show that the data collected from archival observations and previous literature studies are fully consistent with a universal PSD form which does not show any evidence for systematic evolution of shape or amplitude with redshift or luminosity, even if there may be differences between individual AGN at a given redshift or luminosity. We find new evidence that the PSD bend frequency depends on BH mass and, possibly, on accretion rate. We finally discuss the implications for current and future AGN population and cosmological studies.

pdf/the-universal-shape-of-the-x-ray-variability-power-spectrum-1wl9c8q3.pdf

The universal shape of the X-ray variability power spectrum of AGN up to z~3

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The universal shape of the X-ray variability power spectrum of AGN up to z~3