Correcting C $\small \text{IV}$-Based Virial Black Hole Masses

Abstract

The C $\small \text{IV}$λλ1498,1501 broad emission line is visible in optical spectra to redshifts exceeding $z$ ∼ 5. C $\small \text{IV}$ 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 $\small \text{IV}$ velocity widths are known to be systematically biased compared to masses from the hydrogen Balmer lines. Using a large sample of 230 high-luminosity ($L_\text{Bol}$ = 10$^{45.5}$–10$^{48}$ erg s$^{-1}$), redshift 1.5 < $z$ < 4.0 quasars with both C $\small \text{IV}$ and Balmer line spectra, we have quantified the bias in C $\small \text{IV}$ BH masses as a function of the C $\small \text{IV}$ blueshift. C $\small \text{IV}$ BH masses are shown to be a factor of 5 larger than the corresponding Balmer-line masses at C $\small \text{IV}$ blueshifts of 3000 km s$^{-1}$ and 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 $\small \text{IV}$ blueshift and the mass ratio BH(C $\small \text{IV}$)/BH(H$\alpha$), we derive an empirical correction to all C $\small \text{IV}$ BH masses. The scatter between the corrected C $\small \text{IV}$ masses and the Balmer masses is 0.24 dex at low C $\small \text{IV}$ 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 $\small \text{IV}$ line properties – i.e. full width at half-maximum and blueshift – and can therefore be applied to all quasars where C $\small \text{IV}$ 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.