2008A&A...487..475P

We present the results from a detailed X-ray variability analysis of 66 AGN in the Lockman Hole, which have optical spectroscopic identifications. We compare, quantitatively, their variability properties with the properties of local AGN, and we study the ``variability - luminosity'' relation as a function of redshift, and the ``variability - redshift'' relation in two luminosity bins. We use archival data from the last 10 XMM-Newton observations of the Lockman Hole field to extract light curves for the rest frame 2-10keV band. We use the ``normalized excess variance'' to quantify the variability amplitude. Using the results about the AGN power spectral shape and its dependence on black hole mass and accretion rate, we are able to compute model ``variability - luminosity'' curves, which we compare with the relations that we observe. When we consider all the sources in our sample, we find that their variability amplitude decreases with increasing redshift and luminosity. These global anti-correlations become weaker when we split the objects into various luminosity and redshift bins. We do not find a significant correlation between variability amplitude and spectral slope, Γ. We measure a ``variability - luminosity'' relation that has a larger amplitude that for local AGN. At a given luminosity we also find that the variability amplitude increases with redshift up to z∼1, and then remains approximately constant. Our results imply that the AGN X-ray mechanism operates in the same way at all redshifts. The accretion rate (in units of the Eddington limit) for the objects in our sample increases from ∼0.25, at z∼0.5, to 0.5 at z∼3. It does not exceed unity even in the case of the most luminous AGN. Their black hole mass also increases with redshift. The upper limit we find is consistent with the largest black hole masses found to date in the local Universe. The increase in the black hole mass, and the decrease in the rest frame light curve duration with increasing redshift, can explain the global variability amplitude - redshift/luminosity anti-correlations that we observe. For objects of similar luminosity, the black hole mass decreases and the accretion rate increases as the redshift becomes higher. This effect explains the increase in the variability amplitude up to redshift∼1 (at fixed luminosity bins). At higher redshifts, the decrease in the light curves duration affects the variability amplitude significantly, forcing it to remain essentially constant.