Calibrating Mg II-based Black Hole Mass Estimators Using Low-to-high-luminosity Active Galactic Nuclei

Abstract

We present single-epoch black hole mass (M_BH) estimators based on the rest-frame ultraviolet (UV) Mg II 2798 Å and optical Hβ 4861 Å emission lines. To enlarge the luminosity range of active galactic nuclei (AGNs), we combine the 31 reverberation-mapped AGNs with relatively low luminosities from Bahk et al., 47 moderate-luminosity AGNs from Woo et al., and 425 high-luminosity AGNs from the Sloan Digital Sky Survey. The combined sample has a monochromatic luminosity at 5100 Å in the range $\mathrm{log}\lambda {L}_{5100}\sim 41.3\mbox{--}46.5$ erg s^-1, over the range 5.5 < log(M_BH/M_⊙) < 9.5. Based on the fiducial mass from the line dispersion or FWHM of Hβ paired with the continuum luminosity at 5100 Å, we calibrate the best-fit parameters in the black hole mass estimators using the Mg II line. We find that the differences in the line profiles between Mg II and Hβ have significant effects on calibrating the UV M_BH estimators. By exploring the systematic discrepancy between the UV and optical M_BH estimators as a function of AGN properties, we suggest adding a correction term ${\rm{\Delta }}M=-1.44\,{\rm{log}}({{\rm{FWHM}}}_{{\rm{MgII}}}/{\sigma }_{{\rm{MgII}}})+0.33$ in the equation for the UV mass estimator. We also find a ∼0.1 dex bias in the M_BH estimation due to the difference in the spectral slope in the range 2800-5200 Å. Depending on whether the selection of M_BH estimator is based on either line dispersion or FWHM and either continuum or line luminosity, the derived UV mass estimators show ≳0.1 dex intrinsic scatter with respect to the fiducial Hβ-based M_BH.