Comparing single-epoch virial black hole mass estimators for luminous quasars

Single-epoch virial black hole (BH) mass estimators utilizing broad emission lines have been routinely applied to high-redshift quasars to estimate their BH masses. Depending on the redshift, different line estimators (Hα, Hβ, Mg IIλ2798, C IVλ1549) are often used with optical/near-infrared spectroscopy. Here, we use a homogeneous sample of 60 intermediate-redshift (z 1.5-2.2) Sloan Digital Sky Survey quasars with optical and near-infrared spectra covering C IV through Hα to investigate the consistency between different single-epoch virial BH mass estimators. We critically compare rest-frame UV line estimators (C IVλ1549, C III]λ1908, and Mg IIλ2798) with optical estimators (Hβ and Hα) in terms of correlations between line widths and between continuum/line luminosities, for the high-luminosity regime (L ₅₁₀₀ > 10^45.4 erg s^-1) probed by our sample. The continuum luminosities of L ₁₃₅₀ and L ₃₀₀₀, and the broad-line luminosities are well correlated with L ₅₁₀₀, reflecting the homogeneity of quasar spectra in the rest-frame UV-optical, among which L ₁₃₅₀ and the line luminosities for C IV and C III] have the largest scatter in the correlation with L ₅₁₀₀. We found that the Mg II FWHM correlates well with the FWHMs of the Balmer lines and that the Mg II line estimator can be calibrated to yield consistent virial mass estimates with those based on the Hβ/Hα estimators, thus extending earlier results on less luminous objects. The C IV FWHM is poorly correlated with the Balmer line FWHMs, and the scatter between the C IV and Hβ FWHMs consists of an irreducible part (0.12dex), and a part that correlates with the blueshift of the C IV centroid relative to that of Hβ, similar to earlier studies comparing C IV with Mg II. The C III] FWHM is found to correlate with the C IV FWHM, and hence is also poorly correlated with the Hβ FWHM. While the C IV and C III] lines can be calibrated to yield consistent virial mass estimates as Hβ on average, the scatter is substantially larger than Mg II, and the usage of C IV/C III] FWHM in the mass estimators does not improve the agreement with the Hβ estimator. We discuss controversial claims in the literature on the correlation between C IV and Hβ FWHMs, and suggest that the reported correlation is either a result based on small samples or only valid for low-luminosity objects.