The Black Hole-Bulge Relationship in QSOs

We use QSO emission-line widths to examine the black hole mass - sigma relationship as a function of redshift and to extend the relationship to larger masses. Supermassive black holes in galactic nuclei are closely related to the bulge of the host galaxy. The mass of the black hole, M_BH, increases with the bulge luminosity and with the velocity dispersion of the bulge stars, sigma_*. An important clue to the origin of this correlation would be an observational determination of the evolution, if any, in the M_BH - sigma_* relationship as a function of cosmic time. The high luminosity of QSOs affords the potential for studies at large redshifts. We derive black hole masses from the continuum luminosity and the width of the broad Hbeta line and sigma_* from the width of the narrow [O III] lines. We find that radio quiet QSOs conform to the established M_BH - sigma_* relationship up to values M_BH of 10 billion solar masses, with no discernible change in the relationship out to redshifts of $z \approx 3$. These results are consistent with the idea that the growth of supermassive black holes and massive bulges occurred simultaneously.