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In deep X-ray surveys, active galactic nuclei (AGNs) with a broad range ofluminosities have been identified. However, cosmologically distantlow-luminosity AGN (LLAGN, $L_{\mathrm{X}} \lesssim 10^{42}$ erg s$^{-1}$)identification still poses a challenge due to significant contamination fromhost galaxies. Based on the 7 Ms Chandra Deep Field-South (CDF-S) survey, thelongest timescale ($\sim 17$ years) deep X-ray survey to date, we utilize anX-ray variability selection technique to search for LLAGNs that remainunidentified among the CDF-S X-ray sources. We find 13 variable sources from110 unclassified CDF-S X-ray sources. Except for one source which could be anultraluminous X-ray source, the variability of the remaining 12 sources is mostlikely due to accreting supermassive black holes. These 12 AGN candidates havelow intrinsic X-ray luminosities, with a median value of $7 \times10^{40}$ ergs$^{-1}$. They are generally not heavily obscured, with an average effectivepower-law photon index of 1.8. The fraction of variable AGNs in the CDF-S isindependent of X-ray luminosity and is only restricted by the total number ofobserved net counts, confirming previous findings that X-ray variability is anear-ubiquitous property of AGNs over a wide range of luminosities. There is ananti-correlation between X-ray luminosity and variability amplitude forhigh-luminosity AGNs, but as the luminosity drops to $\lesssim 10^{42}$ ergs$^{-1}$, the variability amplitude no longer appears dependent on theluminosity. The entire observed luminosity-variability trend can be roughlyreproduced by an empirical AGN variability model based on a broken power-lawpower spectral density function.

Variability-selected low-luminosity active galactic nuclei candidates in the 7 Ms Chandra Deep Field-South