The universal shape of the X-ray variability power spectrum of AGN up to $z\sim 3$

We study the ensemble X-ray variability properties of Active Galactic Nuclei (AGN) over a large range of timescales (20 ks $\le T\le$ 14 yrs), redshift ($0\le z\lesssim 3$), luminosities (${10}^{40}$ erg s${}^{-1}\le L_X\le {10}^{46}$ erg s${}^{-1}$) and black hole (BH) masses (${10}^6\le$M${}_{\odot }\le {10}^9$). We propose the use of the variance-frequency diagram, as a viable alternative to the study of the power spectral density (PSD), which is not yet accessible for distant, faint and/or sparsely sampled AGN. We show that the data collected from archival observations and previous literature studies are fully consistent with a universal PSD form which does not show any evidence for systematic evolution of shape or amplitude with redshift or luminosity, even if there may be differences between individual AGN at a given redshift or luminosity. We find new evidence that the PSD bend frequency depends on BH mass and, possibly, on accretion rate. We finally discuss the implications for current and future AGN population and cosmological studies.