2006ApJ...640..114P

At low redshift, there are fundamental correlations between the mass of supermassive black holes (M_BH) and the mass (M_bulge) and luminosity of the host galaxy bulge. We investigate the same relation at z≳1. Using virial mass estimates for 11 quasars at z≳2 to measure their black hole mass, we find that black holes at high z fall nearly on the same M_BHversus R-band magnitude (M_R) relation (to ∼0.3 mag) as low-redshift active and inactive galaxies, without making any correction for luminosity evolution. Using a set of conservative assumptions about the host galaxy stellar population, we show that at z≳2 (10 Gyr ago), the ratio of M_BH/M_bulgewas 3-6 times larger than today. Barring unknown systematic errors on the measurement of M_BH, we also rule out scenarios in which moderately luminous quasar hosts at z≳2 were fully formed bulges that passively faded to the present epoch. On the other hand, five quasar hosts at z~1 are consistent with the current-day M_BH-M_Rrelationship after taking into account evolution that is appropriate for E/S0 galaxies. Therefore, z~1 host galaxies appear to fit the hypothesis that they are fully formed early-type galaxies. We also find that most quasar hosts with absolute magnitudes brighter than M_R=-23 cannot fade below L_*galaxies today, regardless of their stellar population makeup, because their black hole masses are too high and they must arrive at the local M_BH-M_Rrelationship by z=0.