Ensemble X-ray variability of active galactic nuclei II. Excess variance and updated structure function

Context. Most investigations of the X-ray variability of active galactic nuclei (AGN) have been concentrated on the detailed analyses of individual, nearby sources. A relatively small number of studies have treated the ensemble behaviour of the more general AGN population in wider regions of the luminosity-redshift plane. Aims. We want to determine the ensemble variability properties of a rich AGN sample, called Multi-Epoch XMM Serendipitous AGN Sample (MEXSAS), extracted from the fifth release of the XMM-Newton Serendipitous Source Catalogue (XMMSSC-DR5), with redshift between similar to 0.1 and similar to 5, and X-ray luminosities in the 0.5-4.5 keV band between similar to 10(42) erg/s and similar to 10(47) erg/s. Methods. We urge caution on the use of the normalised excess variance (NXS), noting that it may lead to underestimate variability if used improperly. We use the structure function (SF), updating our previous analysis for a smaller sample. We propose a correction to the NXS variability estimator, taking account of the light curve duration in the rest frame on the basis of the knowledge of the variability behaviour gained by SF studies. Results. We find an ensemble increase of the X-ray variability with the rest-frame time lag tau, given by SF proportional to tau(0.12). We confirm an inverse dependence on the X-ray luminosity, approximately as SF proportional to L-X(-0.19). We analyse the SF in different X-ray bands, finding a dependence of the variability on the frequency as SF proportional to nu(-0.15), corresponding to a so-called softer when brighter trend. In turn, this dependence allows us to parametrically correct the variability estimated in observer-frame bands to that in the rest frame, resulting in a moderate (less than or similar to 15%) shift upwards (V-correction). Conclusions. Ensemble X-ray variability of AGNs is best described by the structure function. An improper use of the normalised excess variance may lead to an underestimate of the intrinsic variability, so that appropriate corrections to the data or the models must be applied to prevent these effects.