2009ApJ...696.1998D

We present near-infrared spectra of 10 luminous, intermediate-redshift quasars (z ≃2; L_bol≃ 10⁴⁷ erg/s), observed with SofI at the NTT of ESO/La Silla. With these rest-frame optical spectra we probe the Hβ-[O III] emission line region. Using the standard scaling relation involving the width of the Hβ line and the continuum luminosity, we measure black hole (BH) masses in the range of ∼2x10⁹≲ M_bh≲ 10¹⁰ M_☉ for these sources. We also used Sloan Digital Sky Survey spectra to probe Mg II λ2798 and C IV λ1549 emission lines and used these for BH mass measurements as well. The BH mass estimates using C IV λ1549 are on average smaller by about 60% than those based on Hβ. The massive BHs we observe could not have grown by simple radiatively efficient accretion at the observed accretion rate starting from seeds of up to a thousand solar masses. About 10% of the observed BH mass must have been accumulated by earlier merger events and radiatively inefficient accretion. Radiatively efficient accretion would further grow these BHs to masses of several 10⁹ M_☉ in 2-3 e-folding times, i.e., in several 10⁸ yr. This scenario is consistent with recent models of BH growth. The Hβ-based Eddington luminosity ratios are in the range of ∼0.2-0.7, with an average of bol/L_edd> = 0.39±0.05. The L_bol/L_edd ratio distribution follows a lognormal distribution which is consistent with prior studies of quasars with comparable luminosity. We also find that the gas metallicity of the broad-line region is super-solar with ∼3 Z/Z_☉, based on N III]λ1750/O III]λ1663 and N V λ1240/C IV λ1549 emission line ratios. We find no correlation of the gas metallicity with the optical Fe II emission line strength in our small sample, contrary to a recent suggestion.