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

Abstract

We present the single-epoch black hole mass (M BH ) calibrations based on the rest-frame UV and optical measurements of Mg II 2798Å and Hβ 4861Å lines and AGN continuum, using a sample of 52 moderateluminosity 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 M BH based on the line dispersion of Hβ and continuum luminosity at 5100Å, 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 systematic trend with Eddington ratio, FWHM of Hβ, the Fe II strength, and the UV/optical slope, we find no significant bias except for the slope. By fitting the systematic difference of Mg IIbased and Hβ-based masses with the L 3000 /L 5100 ratio, we provide a correction term as a function of the spectral index as ∆C = 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 Hβ-based M BH , suggesting that the UV-based mass has an additional uncertainty of ∼0.2 dex, even if high quality rest-frame UV spectra are available.

Time Delay Measurement of Mg ii Line in CTS C30.10 with SALT

“…Wang et al (2009) found that on average Mg II lines are narrower by some 15% than Hβ lines, which would imply an expected shift in the R-L by ∼ 25 %, consistent with our finding. Similar shifts in black hole mass determination from Hβ and Mg II lines were found by Woo et al (2018).…”

“…There were attempts to bridge the use of Hβ and other lines by taking into account the system-atic differences in the line widths as well as due to the fact of using also a different part of the continuum as a reference (see e.g. Woo et al 2018). Statistical scaling have, however, some limitations, particularly that higher redshift sources have frequently higher masses and/or Eddington ratios, so the direct confirmation of the scaling laws from reverberation mapping in lines other than Hβ is important.…”

The mass of NLS1 black holes: reconciling accretion disk and virial estimates

“…2 shows the relation between M disc and the radiative Eddington ratio (i.e., the bolometric disk luminosity divided by 1.3 × 10 38 M disc ). As expected, all virial estimates cluster in The mass of RL-NLS1 black holes Giorgio Calderone respect to M/M vir,QSfit ∼ 1 is due to the updated calibration in [38] and references therein, which results in a factor ∼ 2 higher mass estimates with respect to previous works. 2 On the other hand, all disk modeling mass estimates are significantly larger than the virial masses by a factor of ∼ 10 on average, and the Eddington ratios are correspondingly lower.…”

“…The synchrotron contribution (when non-negligible) is extrapolated from the IR photometry and subtracted from the optical/UV data before the fitting process. Beyond the black hole mass estimates obtained with the disk modeling method (M disc , to which we associated a very cautious uncertainty of 0.7 dex) we also calculated the single epoch virial mass (M vir,QSFit ) using the FWHM of the Hβ and Mg II lines and the continuum luminosity at 5100Å and 3000Å as estimated by QSFIT, and the calibration from [38]. Also, we collected the virial mass estimates from the literature ( [15], [16], [39], [40], [8]).…”

H0LiCOW – IX. Cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 and a new measurement of the Hubble constant

“…For our study, the black hole mass estimate comes from Sloan Digital Sky Survey (SDSS) spectra (Shen et al 2011) based on Mg ii and results in a black hole mass of log(M bh, Mg ii /M ) = 8.93. Based on the limitations of the Mg ii technique, we assign a ±0.25 dex uncertainty to this measurement (Woo et al 2018). As this measurement was based on the magnified image, we apply a magnification correction…”