  The 4 Ms Chandra Deep Field-South (CDF-S) and other deep X-ray surveys have
been highly effective at selecting active galactic nuclei (AGN). However,
cosmologically distant low-luminosity AGN (LLAGN) have remained a challenge to
identify due to significant contribution from the host galaxy. We identify
long-term X-ray variability (~month-years, observed frame) in 20 of 92 CDF-S
galaxies spanning redshifts z~0.08-1.02 that do not meet other AGN selection
criteria. We show that the observed variability cannot be explained by X-ray
binary populations or ultraluminous X-ray sources, so the variability is most
likely caused by accretion onto a supermassive black hole. The variable
galaxies are not heavily obscured in general, with a stacked effective
power-law photon index of Gamma_stack~1.93+/-0.13, and are therefore likely
LLAGN. The LLAGN tend to lie a factor of ~6-80 below the extrapolated linear
variability-luminosity relation measured for luminous AGN. This may be
explained by their lower accretion rates. Variability-independent black-hole
mass and accretion-rate estimates for variable galaxies show that they sample a
significantly different black-hole mass-accretion rate space, with masses a
factor of 2.4 lower and accretion rates a factor of 22.5 lower than variable
luminous AGN at the same redshift. We find that an empirical model based on a
universal broken power-law PSD function, where the break frequency depends on
SMBH mass and accretion rate, roughly reproduces the shape, but not the
normalization, of the variability-luminosity trends measured for variable
galaxies and more luminous AGN.
