Indicators of Black Hole Mass and Eddington Accretion Ratio from QSO X-ray and UV Spectra

The evolution of luminous QSOs is linked to the evolution of massive galaxies. We know this because the relic black-holes found locally have masses dependent on the properties of the host galaxy's bulge. An important way to explore this evolution would be to measure dependences of black hole masses and Eddington accretion ratios over a range of redshifts, i.e., with cosmological age. For low redshift QSOs (and their lower luminosity Seyfert galaxy counterparts) it has been possible to infer black hole masses from the luminosities and velocity dispersions of their host-galaxy bulges. These masses agree with those virial black hole masses calculated from the Doppler widths of the broad Hbeta emission lines. The latter method can then be extended to more distant and luminous QSOs, up to redshifts of 0.6 with ground-based optical observations. We discuss ways to extend these explorations to higher redshifts -- up to about 3 using the widths of QSOs' broad UV emission lines, and in principle, and to redshifts near 4 from ground-based infrared observations of rest-frame Hbeta at 2.5 micron. We discuss the possibility of investigating the accretion history of the higher redshift QSOs using measures of Eddington accretion ratio -- the soft X-ray spectral index and the eigenvectors of Principal Components Analyses of QSOs' UV emission-line spectra.