Time-delay measurement of MgII broad line response for the highly-accreting quasar HE 0413-4031: Implications for the MgII-based radius-luminosity relation

Abstract

We present the monitoring of the AGN continuum and MgII 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 managed 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 (ICCF), 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 SED modelling, 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 $\sim 0.4$. The MgII line luminosity of HE 0413-4031 responds to the continuum variability as $L_{\mathrm{line}}\propto L_{\mathrm{cont}}^{0.43\pm 0.10}$, which is consistent with the light-travel distance of the location of MgII emission at $R_{\mathrm{out}}\sim 10^{18}\mathrm{cm}$. Using the data of 10 other quasars, we confirm the radius-luminosity relation for broad MgII line, which was previously determined for 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 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.

39 pages (23 pages - Main text, 16 pages - Appendix), 21 figures, 14 tables; accepted for publication in the Astrophysical Journal

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