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

We study the X-ray variability properties of distant AGNs in the Chandra Deep Field-South region over 17 years, up to $z\sim 4$, and compare them with those predicted by models based on local samples. We use the results of Monte Carlo simulations to account for the biases introduced by the discontinuous sampling and the low-count regime. We confirm that variability is an ubiquitous property of AGNs, with no clear dependence on the density of the environment. The variability properties of high-z AGNs, over different temporal timescales, are most consistent with a Power Spectral Density (PSD) described by a broken (or bending) power-law, similar to nearby AGNs. We confirm the presence of an anti-correlation between luminosity and variability, resulting from the dependence of variability on BH mass and accretion rate. We explore different models, finding that our acceptable solutions predict that BH mass influences the value of the PSD break frequency, while the Eddington ratio $\lambda_{Edd}$ affects the PSD break frequency and, possibly, the PSD amplitude as well. We derive 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 constant Eddington ratio, although one of our models suggest a possible increase of $\lambda_{Edd}$ with lookback time up to $z\sim 2-3$. We conclude that variability is a viable mean to trace the accretion history of supermassive BHs, whose usefulness will increase with future, wide-field/large effective area X-ray missions.