The X-ray Energy Dependence of the Relation between Optical and X-ray
  Emission in Quasars
  We develop a new approach to the well-studied anti-correlation between the
optical-to-X-ray spectral index, alpha_ox, and the monochromatic optical
luminosity, l_opt. By cross-correlating the SDSS DR5 quasar catalog with the
XMM-Newton archive, we create a sample of 327 quasars with X-ray S/N > 6, where
both optical and X-ray spectra are available. This allows alpha_ox to be
defined at arbitrary frequencies, rather than the standard 2500 Angstroms and 2
keV. We find that while the choice of optical wavelength does not strongly
influence the alpha_ox-l_opt relation, the slope of the relation does depend on
the choice of X-ray energy. The slope of the relation becomes steeper when
alpha_ox is defined at low (~ 1 keV) X-ray energies. This change is significant
when compared to the slope predicted by a decrease in the baseline over which
alpha_ox is defined. The slopes are also marginally flatter than predicted at
high (~ 10 keV) X-ray energies. Partial correlation tests show that while the
primary driver of alpha_ox is l_opt, the Eddington ratio correlates strongly
with alpha_ox when l_opt is taken into account, so accretion rate may help
explain these results. We combine the alpha_ox-l_opt and Gamma -L_bol/L_Edd
relations to naturally explain two results: 1) the existence of the Gamma-l_x
relation as reported in Young et al. (2009) and 2) the lack of a Gamma-l_opt
relation. The consistency of the optical/X-ray correlations establishes a more
complete framework for understanding the relation between quasar emission
mechanisms. We also discuss two correlations with the hard X-ray bolometric
correction, which we show correlates with both alpha_ox and Eddington ratio.
This confirms that an increase in accretion rate correlates with a decrease in
the fraction of up-scattered disk photons.
