Correcting C iv-based virial black hole masses

The C ivλλ1498,1501 broad emission line is visible in optical spectra to redshifts exceeding z ∼ 5. C iv 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 C iv velocity widths are known to be systematically biased compared to masses from the hydrogen Balmer lines. Using a large sample of 230 high-luminosity (LBol = 1045.5–1048 erg s−1), redshift 1.5 z iv and Balmer line spectra, we have quantified the bias in C iv BH masses as a function of the C iv blueshift. C iv BH masses are shown to be a factor of 5 larger than the corresponding Balmer-line masses at C iv blueshifts of 3000 km s−1and are overestimated by almost an order of magnitude at the most extreme blueshifts, 5000 km s−1. Using the monotonically increasing relationship between the C iv blueshift and the mass ratio BH(C iv)/BH(Hα), we derive an empirical correction to all C iv BH masses. The scatter between the corrected C iv masses and the Balmer masses is 0.24 dex at low C iv blueshifts (∼0 km s−1) and just 0.10 dex at high blueshifts (∼3000 km s−1), compared to 0.40 dex before the correction. The correction depends only on the C iv line properties – i.e. full width at half-maximum and blueshift – and can therefore be applied to all quasars where C iv emission line properties have been measured, enabling the derivation of unbiased virial BH-mass estimates for the majority of high-luminosity, high-redshift, spectroscopically confirmed quasars in the literature.