Ensemble X-ray variability of active galactic nuclei from serendipitous source catalogues

Context. 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. Aims. We aim to determine the ensemble variability properties of two serendipitously selected AGN samples extracted from the catalogues of XMM-Newton and Swift, with redshift between similar to 0.2 and similar to 4.5, and X-ray luminosities, in the 0.5-4.5 keV band, between similar to 10(43) erg/s and similar to 10(46) erg/s. Methods. We used 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. The SF is also more appropriate than fractional variability and excess variance, because these parameters are biased by the duration of the monitoring time interval in the rest-frame, and therefore by cosmological time dilation. Results. We find statistically consistent results for the two samples, with the SF described by a power law of the time lag, approximately as SF alpha 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. Conclusions. The change of amplitude and slope of the SF with X-ray luminosity provides new constraints on both single oscillator models and multiple subunit models of variability.