Time-delay Measurement of Mg ii Broad-line Response for the Highly Accreting Quasar HE 0413-4031: Implications for the Mg ii–based Radius–Luminosity Relation

Abstract

We present the monitoring of the active galactic nuclei continuum and Mg ii broad-line emission for the quasar HE 0413-4031 (z = 1.38) based on the six-year monitoring by the South African Large Telescope (SALT). We manage to estimate a time-delay of days in the rest frame of the source using seven different methods: interpolated cross-correlation function, discrete correlation function (DCF), z-transformed DCF, JAVELIN, two estimators of data regularity (Von Neumann, Bartels), and χ 2 method. This time-delay is below the value expected from the standard radius–luminosity relation. However, based on the monochromatic luminosity of the source and the spectral energy distribution modeling, we interpret this departure as the shortening of the time-delay due to the higher accretion rate of the source, with the inferred Eddington ratio of ∼0.4. The Mg ii line luminosity of HE 0413-4031 responds to the continuum variability as , which is consistent with the light-travel distance of the location of Mg ii emission at R out ∼ 1018 cm. Using the data of 10 other quasars, we confirm the radius–luminosity relation for the broad Mg ii line, which was previously determined for the broad Hβ line for lower-redshift sources. In addition, we detect a general departure of higher-accreting quasars from this relation in analogy to the Hβ sample. After the accretion-rate correction of the light-travel distance, the Mg ii–based radius–luminosity relation has a small scatter of only 0.10 dex.

Standardizing reverberation-measured Mg II time-lag quasars, by using the radius-luminosity relation, and constraining cosmological model parameters

“…the higher the acrretion rate, the larger the departure. The same trend was later confirmed for the Mg II QSO 𝑅 − 𝐿 relation (Zajaček et al 2020;Martínez-Aldama et al 2020b;Zajaček et al 2021).…”

“…We refer to these reverberation-mapped sources as Mg II QSOs. We use Mg II QSOs to constrain cosmological dark energy models for the following reasons: (i) The current reasonably large number, 78, of studied Mg II QSOs at intermediate 𝑧 (Czerny et al 2019;Homayouni et al 2020;Martínez-Aldama et al 2020b;Zajaček et al 2020Zajaček et al , 2021Yu et al 2021). The current Mg II QSO redshift range 0.0033 ≤ 𝑧 ≤ 1.89 is more extended, especially towards higher redshifts, than that of 117 reverberation-mapped H𝛽 quasars (0.002 ≤ 𝑧 ≤ 0.89; Martínez-Aldama et al 2019).…”

Estimating supermassive black hole masses in active galactic nuclei using polarization of broad Mg ii, H α, and H β lines

“…We measured the FWHM = 4791 ± 552 km s −1 and line dispersion σ = 2275 ± 263 km s −1 after subtracting the Fe II contribu- The size of the BLR region in the Mg II line is estimated using the empirical BLR radius -luminosity (R-L) relation (see Czerny et al 2019;Popović 2020). We used an updated R-L relation at 3000 Å given by Zajaček et al (2020). The estimation of the quasar luminosity was obtained from (Shen et al 2016) λL 3000 = 6.1 × 10 46 erg s −1 .…”

The Sloan Digital Sky Survey Reverberation Mapping Project: Estimating Masses of Black Holes in Quasars with Single-epoch Spectroscopy

“…Of the three strong emission lines generally used to estimate central black hole masses, the R-L relationship is only well established for Hβ λ4861 (Bentz et al 2013 and references therein; but see the discussion in Section 3.3). Empirically establishing the R-L relationship for Mg II λ2798 (Clavel et al 1990(Clavel et al , 1991Reichert et al 1994;Metzroth et al 2006;Cackett et al 2015;Shen et al 2016;Lira et al 2018;Czerny et al 2019;Homayouni et al 2020;Zajaček et al 2020), as well as for C IV λ1549 (Clavel et al 1989(Clavel et al , 1990(Clavel et al , 1991Reichert et al 1994;Korista et al 1995;Rodríguez-Pascual et al 1997;Wanders et al 1997;O'Brien et al 1998;Peterson et al 2005;Metzroth et al 2006;Kaspi et al 2007;Trevese et al 2014;De Rosa et al 2015;Lira et al 2018;Grier et al 2019;Hoormann et al 2019),has been difficult because of the nature of the UV line variability and the high level of competition for suitable facilities.…”