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The X-ray variability of the Active Galactic Nuclei (AGN) has been most often investigated with studies of individual, nearby, sources, and only a few ensemble analyses have been applied to large samples in wide ranges of luminosity and redshift. We want to determine the ensemble variability properties of two serendipitously selected AGN samples extracted from the catalogues of XMM-Newton and Swift, with redshift between ~0.2 and ~4.5, and X-ray luminosities, in the 0.5-4.5 keV band, between ~10^43 erg/s and ~10^46 erg/s. We use the structure function (SF), which operates in the time domain, and allows for an ensemble analysis even when only a few observations are available for individual sources and the power spectral density (PSD) cannot be derived. SF is also more appropriate than fractional variability and excess variance, because such parameters are biased by the duration of the monitoring time interval in the rest-frame, and thus by cosmological time dilation. We find statistically consistent results for the two samples, with the SF described by a power law of the time lag, approximately as SF propto tau^0.1. We do not find evidence of the break in the SF, at variance with the case of lower luminosity AGNs. We confirm a strong anti-correlation of the variability with X-ray luminosity, accompanied by a change of the slope of the SF. We find evidence in support of a weak, intrinsic, average increase of X-ray variability with redshift. The change of amplitude and slope of the SF with X-ray luminosity provides new constraints on both single oscillator models and multiple subunits models of variability.
The observed relation between the X-ray radiation from AGNs, originating in the corona, and the optical/UV radiation from the disk is usually described by the anticorrelation between the UV to X-ray slope alpha_ox and the UV luminosity. Many factors can affect this relation, including: enhanced X-ray emission associated with the jets of radio-loud AGNs; X-ray absorption associated with the UV Broad Absorption Line (BAL) outflows; other X-ray absorption not associated with BALs; intrinsic X-ray weakness; UV and X-ray variability, and non-simultaneity of UV and X-ray observations. The separation of these effects provides information about the intrinsic alpha_ox-L_UV relation and its dispersion, constraining models of disk-corona coupling. We extract simultaneous data from the second XMM-Newton serendipitous source catalogue and the XMM-Newton Optical Monitor Serendipitous UV Source Survey Catalog, and derive the single-epoch alpha_ox indices. We use ensemble structure functions to analyse multi-epoch data. We confirm the anticorrelation of alpha_ox with L_UV, and do not find any evidence of a dependence of alpha_ox on z. The dispersion in our simultaneous data (0.12) is not significantly smaller than in previous non-simultaneous studies, suggesting that artificial alpha_ox variability introduced by non-simultaneity is not the main cause of dispersion. Intrinsic alpha_ox variability, i.e., the true variability of the X-ray to optical ratio, is instead important, and accounts for ~30% of the total variance, or more. Inter-source dispersion, due to intrinsic differences in the average alpha_ox values from source to source, is also important. The dispersion introduced by variability is mostly caused by the long timescale variations, which are expected to be driven by the optical variations.
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