Abstract
In the present-day universe, supermassive black hole masses (MBH) appear to be strongly correlated with their galaxy's bulge luminosity, among other properties. In this study, we explore the analogous relationship between MBH, derived using the virial method, and the stellar R-band bulge luminosity (Lr) or stellar bulge mass (M*) at epochs of 1 < z < 4.5 using a sample of 31 gravitationally lensed AGNs and 20 non-lensed AGNs. At redshifts z > 1.7 (10--12 Gyrs ago), we find that the observed MBH--Lr relation is nearly the same (to within ~0.3 mag) as it is today. When the observed Lr are corrected for luminosity evolution, this means that the black holes grew in mass faster than their hosts, with the MBH/M* mass ratio being a factor of > 4(+2)(-1) times larger at z > 1.7 than it is today. By the redshift range 1<z<1.7 (8-10 Gyrs ago), the MBH/M* ratio is at most two times higher than today, but it may be consistent with no evolution. Combining the results, we conclude that the ratio MBH/M* rises with look-back time, although it may saturate at ~6 times the local value. Scenarios in which moderately luminous quasar hosts at z>1.7 were fully formed bulges that passively faded to the present epoch are ruled out.
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