Calibration and Limitations of the Mg ii Line-based Black Hole Masses

We present single-epoch black hole mass ( ) calibrations based on the rest-frame ultraviolet (UV) and optical measurements of Mg ii 2798 and Hβ 4861 lines and the active galactic nucleus (AGN) continuum, using a sample of 52 moderate-luminosity AGNs at z ∼ 0.4 and z ∼ 0.6 with high-quality Keck spectra. We combine this sample with a large number of luminous AGNs from the Sloan Digital Sky Survey to increase the dynamic range for a better comparison of UV and optical velocity and luminosity measurements. With respect to the reference based on the line dispersion of Hβ and continuum luminosity at 5100 , we calibrate the UV and optical mass estimators by determining the best-fit values of the coefficients in the mass equation. By investigating whether the UV estimators show a systematic trend with Eddington ratio, FWHM of Hβ, Fe ii strength, or UV/optical slope, we find no significant bias except for the slope. By fitting the systematic difference of Mg ii-based and Hβ-based masses with the L3000/L5100 ratio, we provide a correction term as a function of the spectral index as ΔC = 0.24 (1 + λ) + 0.17, which can be added to the Mg ii-based mass estimators if the spectral slope can be well determined. The derived UV mass estimators typically show >∼0.2 dex intrinsic scatter with respect to the Hβ-based , suggesting that the UV-based mass has an additional uncertainty of ∼0.2 dex, even if high-quality rest-frame UV spectra are available.