The SDSS/XMM-Newton Quasar Survey: Correlation between X-ray spectral
  slope and Eddington ratio
  We present a correlation between the 2-10 keV spectral slope Gamma 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 Gamma-L/L_{EDD} correlation is strongest in objects with black
hole (BH) masses determined from the Hbeta line, and weaker (but still present)
for those based on Mg II. An empirical non-linear correction of the Mg II-based
masses, obtained by comparing the mass estimates in SDSS quasars having both
Hbeta 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
Gamma-M_BH relation is present, though with a lower statistical significance
than between Gamma 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.
