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 CIV, MgII, and Hbeta 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 times 10^8 M_sun up to M_bh = 4 times 10^10 M_sun. While the black hole mass estimates based on CIV and Hbeta agree well, MgII typically indicates a factor of $\sim 5 \times$ lower SMBH masses. A flatter slope of the Hbeta radius - luminosity relation, a possibly steeper slope of the MgII radius - luminosity relation, and a slightly larger radius of the MgII BLR than for Hbeta could relax the discrepancy. In spite of these uncertainties, the CIV, MgII, and Hbeta emission lines consistently indicate super-massive black hole masses of several times 10^9 M_sun at redshifts up to z = 5.1. Assuming logarithmic growth by spherical accretion with a mass to energy conversion efficiency of epsilon = 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_bh^seed = 10^3 to 10^5 M_sun) 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. 
Matthias Dietrich and Fred Hamann