Variability-selected low-luminosity active galactic nuclei candidates in
  the 7 Ms Chandra Deep Field-South
  In deep X-ray surveys, active galactic nuclei (AGNs) with a broad range of
luminosities have been identified. However, cosmologically distant
low-luminosity AGN (LLAGN, $L_{\mathrm{X}} \lesssim 10^{42}$ erg s$^{-1}$)
identification still poses a challenge due to significant contamination from
host galaxies. Based on the 7 Ms Chandra Deep Field-South (CDF-S) survey, the
longest timescale ($\sim 17$ years) deep X-ray survey to date, we utilize an
X-ray variability selection technique to search for LLAGNs that remain
unidentified among the CDF-S X-ray sources. We find 13 variable sources from
110 unclassified CDF-S X-ray sources. Except for one source which could be an
ultraluminous X-ray source, the variability of the remaining 12 sources is most
likely due to accreting supermassive black holes. These 12 AGN candidates have
low intrinsic X-ray luminosities, with a median value of $7 \times10^{40}$ erg
s$^{-1}$. They are generally not heavily obscured, with an average effective
power-law photon index of 1.8. The fraction of variable AGNs in the CDF-S is
independent of X-ray luminosity and is only restricted by the total number of
observed net counts, confirming previous findings that X-ray variability is a
near-ubiquitous property of AGNs over a wide range of luminosities. There is an
anti-correlation between X-ray luminosity and variability amplitude for
high-luminosity AGNs, but as the luminosity drops to $\lesssim 10^{42}$ erg
s$^{-1}$, the variability amplitude no longer appears dependent on the
luminosity. The entire observed luminosity-variability trend can be roughly
reproduced by an empirical AGN variability model based on a broken power-law
power spectral density function.
