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 Å and Hβ 4861 Å 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 Å, 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 + α_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. [ABSTRACT FROM AUTHOR]