UV Fe II emission model and its relation to broad-line time delays for HE 0413-4031 observed in the optical and IR bands

Fe II emission is a well-known contributor to the UV spectra of active galactic nuclei, and the modeling of this part may affect the results obtained for the MgII emission which is one of the lines used for black hole mass measurement and for cosmological applications. We test different Fe II emission models when modeling the UV emission of the intermediate-redshift quasar HE 0413-4031 with the aim of seeing how the use of a specific template affects the MgII line properties and the measurement of the MgII and UV FeII time delays with respect to the continuum. We use the 11-year monitoring of the selected quasar HE 0413-4031 with the South African Large Telescope (SALT), and we supplement this monitoring with the near-IR spectrum taken with the SOAR telescope which gave access to the H$\beta$ and [OIII] emission lines at the rest frame and allowed for a precise measurement of the redshift. A new redshift determination ($z=1.39117 \pm 0.00017$) using [OIII] lines gave a very different value than the previous determination based only on the UV FeII pseudocontinuum ($z=1.3764$). It favors a different decomposition of the spectrum into Mg II and UV Fe II emissions. The time delay of the Mg II emission ($224^{+21}_{-23}$ days) is not significantly affected. The rest-frame UV FeII time delay ($251^{+9}_{-7}$ days) is consistent with the best-fit FeII FWHM of $4200\,{\rm km/s}$, and hence the FeII-emitting material is more distant than MgII-emitting gas in HE 0413-4031 by 0.023 pc (4700 AU). Moreover, the velocity shift of both Mg II and UV Fe II lines with respect to the systemic redshift is now rather low, below 300 km s$^{-1}$. We construct an updated MgII radius-luminosity ($R-L$) relation from 194 sources, which is flatter than the UV FeII, optical FeII, and H$\beta$ $R-L$ relations. We see a need to create better Fe II templates using the newest version of the code CLOUDY.