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 ( \sim month–years , observed frame ) in 20 of 92 CDF-S galaxies spanning redshifts z \approx 0.08 - 1.02 that do not meet other AGN selection criteria .
We show that the observed variability can not 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 _ { \mathrm { stack } } \approx 1.93 \pm 0.13 , and are therefore likely LLAGN .
The LLAGN tend to lie a factor of \approx 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 .