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.

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 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 , 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. [ABSTRACT FROM AUTHOR]