2020ApJ...896..146Z

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 302.6_–33.1^+28.7 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 χ² 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 L_line∝L_cont^0.43±0.10^, 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.