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We study the X-ray variability properties of distant AGNs in the Chandra DeepField-South region over 17 years, up to $z\sim 4$, and compare them with thosepredicted by models based on local samples. We use the results of Monte Carlosimulations to account for the biases introduced by the discontinuous samplingand the low-count regime. We confirm that variability is an ubiquitous propertyof AGNs, with no clear dependence on the density of the environment. Thevariability properties of high-z AGNs, over different temporal timescales, aremost consistent with a Power Spectral Density (PSD) described by a broken (orbending) power-law, similar to nearby AGNs. We confirm the presence of ananti-correlation between luminosity and variability, resulting from thedependence of variability on BH mass and accretion rate. We explore differentmodels, finding that our acceptable solutions predict that BH mass influencesthe value of the PSD break frequency, while the Eddington ratio $\lambda_{Edd}$affects the PSD break frequency and, possibly, the PSD amplitude as well. Wederive the evolution of the average $\lambda_{Edd}$ as a function of redshift,finding results in agreement with measurements based on different estimators.The large statistical uncertainties make our results consistent with a constantEddington ratio, although one of our models suggest a possible increase of$\lambda_{Edd}$ with lookback time up to $z\sim 2-3$. We conclude thatvariability is a viable mean to trace the accretion history of supermassiveBHs, whose usefulness will increase with future, wide-field/large effectivearea X-ray missions.

Tracing the accretion history of supermassive Black Holes through X-ray variability: results from the Chandra Deep Field-South