Deepest view of AGN X-ray variability with the 7 Ms Chandra Deep Field-South survey

We systematically analyze X-ray variability of active galactic nuclei (AGNs) in the 7~Ms \textit{Chandra} Deep Field-South survey. On the longest timescale ($\approx~17$ years), we find only weak (if any) dependence of X-ray variability amplitudes on energy bands or obscuration. We use four different power spectral density (PSD) models to fit the anti-correlation between normalized excess variance ($\sigma^2_{\rm nxv}$) and luminosity, and obtain a best-fit power law index $\beta=1.16^{+0.05}_{-0.05}$ for the low-frequency part of AGN PSD. We also divide the whole light curves into 4 epochs in order to inspect the dependence of $\sigma^2_{\rm nxv}$ on these timescales, finding an overall increasing trend. The analysis of these shorter light curves also infers a $\beta$ of $\sim 1.3$ that is consistent with the above-derived $\beta$, which is larger than the frequently-assumed value of $\beta=1$. We then investigate the evolution of $\sigma^2_{\rm nxv}$. No definitive conclusion is reached due to limited source statistics but, if present, the observed trend goes in the direction of decreasing AGN variability at fixed luminosity toward large redshifts. We also search for transient events and find 6 notable candidate events with our considered criteria. Two of them may be a new type of fast transient events, one of which is reported here for the first time. We therefore estimate a rate of fast outbursts $\langle\dot{N}\rangle = 1.0^{+1.1}_{-0.7}\times 10^{-3}~\rm galaxy^{-1}~yr^{-1}$ and a tidal disruption event~(TDE) rate $\langle\dot{N}_{\rm TDE}\rangle=8.6^{+8.5}_{-4.9}\times 10^{-5}~\rm galaxy^{-1}~yr^{-1}$ assuming the other four long outbursts to be TDEs.