Implications of Quasar Black Hole Masses at High Redshifts

We investigated a sample of 15 luminous high-redshift quasars (3.3 z 5.1) to measure the mass of their super-massive black holes (SMBH) and compare, for the first time, results based on C iv, Mg ii, and Hβ emission lines at high-redshifts. Assuming gravitationally bound orbits as dominant broad-line region gas motion, we determine black hole masses in the range of M bh ≃ 2 × 10 8 M ⊙ up to M bh ≃ 4 × 10 10 M ⊙. While the black hole mass estimates based on C iv and Hβ agree well, Mg ii typically indicates a factor of ∼ 5× lower SMBH masses. A flatter slope of the Hβ radius – luminosity relation, a possibly steeper slope of the Mg ii radius – luminosity relation, and a slightly larger radius of the Mg ii BLR than for Hβ could relax the discrepancy. In spite of these uncertainties, the C iv, Mg ii, and Hβ emission lines consistently indicate super-massive black hole masses of several times 10 9 M ⊙ at redshifts up to z=5.1. Assuming logarithmic growth by spherical accretion with a mass to energy conversion efficiency of ǫ = 0.1 and an Eddington ratio L bol /L edd calculated for each quasar individually, we estimate black hole growth-times of the order of several ∼ 100 Myr which are smaller than the age of the universe at the corresponding redshift. Assuming high-mass seed black holes (M seed bh = 10 3 to 10 5 M ⊙) the SMBHs in the z ≃ 3.5 quasars began to grow at redshifts z 4, while for the quasars with z 4.5 they started at z ≃ 6 to 10. These estimated time scales for forming SMBHs at high redshifts, together with previous studies indicating high quasar metallicities, suggest that the main SMBH growth phase occurs roughly contemporaneously with a period of violent and extensive star formation in proto-galactic nuclei.