We present a correlation between the 2-10 keV spectral slope Γ X and the Eddington ratio L/L EDD in a sample of ∼ 400 Sloan Digital Sky Survey quasars with available hard X-ray spectra from XMM-Newton serendipitous observations. We find that the Γ X -L/L EDD correlation is strongest in objects with black hole (BH) masses determined from the Hβ line, and weaker (but still present) for those based on Mg II. An empirical nonlinear correction of the Mg II-based masses, obtained by comparing the mass estimates in SDSS quasars having both Hβ and Mg II measurements, significantly increases the strength of the correlation. No correlation is found among objects with BH masses derived from C IV, confirming that this line is not a reliable indicator of the BH mass. No significant correlation is found with the bolometric luminosity, while a Γ X -M BH relation is present, though with a lower statistical significance than between Γ X and L/L EDD . Our results imply a physical link between the accretion efficiency in the (cold) accretion disc of AGNs and the physical status of the (hot) corona responsible for the X-ray emission.

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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 Γ 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 blackhole 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.