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Using six years of spectroscopic monitoring of the luminous quasar HE 0435-4312 (z = 1.2231) with the Southern African Large Telescope, in combination with photometric data (CATALINA, OGLE, SALTICAM, and BMT), we determined a rest-frame time delay of days between the Mg ii broad-line emission and the ionizing continuum using seven different time-delay inference methods. Time-delay artifact peaks and aliases were mitigated using the bootstrap method and prior weighting probability function, as well as by analyzing unevenly sampled mock light curves. The Mg ii emission is considerably variable with a fractional variability of ∼5.4%, which is comparable to the continuum variability (∼4.8%). Because of its high luminosity (L3000 = 1046.4 erg s−1), the source is beneficial for a further reduction of the scatter along the Mg ii -based radius–luminosity relation and its extended versions, especially when the highly accreting subsample that has an rms scatter of ∼0.2 dex is considered. This opens up the possibility of using the high-accretor Mg ii -based radius–luminosity relation for constraining cosmological parameters. With the current sample of 27 reverberation-mapped sources, the best-fit cosmological parameters (Ωm, ΩΛ) = (0.19; 0.62) are consistent with the standard cosmological model within the 1σ confidence level. [ABSTRACT FROM AUTHOR]

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 Rout ∼ 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]