Correcting CIV-Based Virial Black Hole Masses

The CIV broad emission line is visible in optical spectra to redshifts exceeding z~5. CIV has long been known to exhibit significant displacements to the blue and these `blueshifts' almost certainly signal the presence of strong outflows. As a consequence, single-epoch virial black hole (BH) mass estimates derived from CIV velocity-widths are known to be systematically biased compared to masses from the hydrogen Balmer lines. Using a large sample of 230 high-luminosity (log $L_{\rm Bol}$ = 45.5-48 erg/s), redshift 1.5<z<4.0 quasars with both CIV and Balmer line spectra, we have quantified the bias in CIV BH masses as a function of the CIV blueshift. CIV BH masses are shown to be a factor of five larger than the corresponding Balmer-line masses at CIV blueshifts of 3000 km/s and are over-estimated by almost an order of magnitude at the most extreme blueshifts, >5000 km/s. Using the monotonically increasing relationship between the CIV blueshift and the mass ratio BH(CIV)/BH(H$\alpha$) we derive an empirical correction to all CIV BH-masses. The scatter between the corrected CIV masses and the Balmer masses is 0.24 dex at low CIV blueshifts (~0 km/s) and just 0.10 dex at high blueshifts (~3000 km/s), compared to 0.40 dex before the correction. The correction depends only on the CIV line properties - i.e. full-width at half maximum and blueshift - and can therefore be applied to all quasars where CIV emission line properties have been measured, enabling the derivation of un-biased virial BH mass estimates for the majority of high-luminosity, high-redshift, spectroscopically confirmed quasars in the literature.