Implications of quasar black hole masses at high redshifts

We investigated a sample of 15 luminous high-redshift quasars (3.3less than or similar tozless than or similar to5.1) to measure the mass of their supermassive black holes (SMBH) and compare, for the first time, results based on C IV, Mg II, 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)similar or equal to2x10(8) up to M(bh)similar or equal to4x10(10) M-circle dot. While the black hole mass estimates based on C IV and Hbeta agree well, Mg II typically indicates a factor of similar to5 times lower SMBH masses. A flatter slope of the Hbeta radius-luminosity relation, a possibly steeper slope of the Mg II radius-luminosity relation, and a slightly larger radius of the Mg ii broad-line region than for Hbeta could relax the discrepancy. In spite of these uncertainties, the C IV, Mg II, and Hbeta emission lines consistently indicate supermassive black hole masses of several times 10(9) M-circle dot 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 similar to100 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)-10(5) M-circle dot) the SMBHs in the zsimilar or equal to3.5 quasars began to grow at redshifts zgreater than or similar to4, while for the quasars with zgreater than or similar to4.5 they started at zsimilar or equal to6 to 10. These estimated timescales 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 protogalactic nuclei.