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 Mgiibroad-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 chi(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 similar to 0.4. The Mgiiline luminosity of HE 0413-4031 responds to the continuum variability as L-line proportional to L-cont(0.43 +/- 0.10), which is consistent with the light-travel distance of the location of Mg II emission at R-out similar to 10(18) cm. Using the data of 10 other quasars, we confirm the radius-luminosity relation for the broad Mgiiline, which was previously determined for the broad H beta line for lower-redshift sources. In addition, we detect a general departure of higher-accreting quasars from this relation in analogy to the H beta sample. After the accretion-rate correction of the light-travel distance, the Mgii-based radius-luminosity relation has a small scatter of only 0.10 dex.