Measuring the black hole masses of high redshift quasars

A new technique is presented for determining the black-hole masses of high-redshift quasars from optical spectroscopy. The new method utilizes the full-width half maximum (FWHM) of the low-ionization MgII emission line and the correlation between broad-line region (BLR) radius and continuum luminosity at 3000 Angstroms. Using archival UV spectra it is found that the correlation between BLR radius and 3000 Angstrom luminosity is tighter than the established correlation with 5100 Angstrom luminosity. Furthermore, it is shown that, when considered together, both correlations are most consistent with a relation of the form $R_{BLR}\propto \lambda L_{\lambda}^{0.5}$, as expected for a constant ionization parameter. Using a sample of objects with broad-line radii determined from reverberation mapping it is shown that the FWHM of MgII and H$\beta$ are consistent with following an exact one-to-one relation, as expected if both H$\beta$ and MgII are emitted at the same radius from the central ionizing source. The resulting virial black-hole mass estimator based on rest-frame UV observables is shown to reproduce black-hole mass measurements based on reverberation mapping to within a factor of 2.5 ($1\sigma$). Finally, the new UV black-hole mass estimator is shown to produce identical results to the established optical (H$\beta$) estimator when applied to 128 intermediate-redshift (0.3<z<0.9) quasars drawn from the Large Bright Quasar Survey and the radio-selected Molonglo quasar sample. We therefore conclude that the new UV virial black-hole mass estimator can be reliably used to estimate the black-hole masses of quasars from z~0.25 through to the peak epoch of quasar activity at z~2.5 via optical spectroscopy alone.