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We test the recently proposed (Mediavilla et al. 2018) black hole massscaling relationship based on the redshift {with respect to the quasar's restframe} of the Fe III$\lambda\lambda$2039-2113 line blend. To this end, we fitthis feature in the spectra of a well suited sample of quasars, observed withX-shooter at the Very Large Telescope (VLT), whose masses have beenindependently estimated using the virial theorem. For the quasars of thissample we consistently confirm the redshift of the FeIII$\lambda\lambda$2039-2113 blend and find that it correlates with the squaredwidths of H$\beta$, H$\alpha$ and Mg II, which are commonly used as a measureof $M_{BH}/R$ to determine masses from the virial theorem. The averagedifferences between virial and Fe III$\lambda\lambda$2039-2113 redshift basedmasses are 0.18$\pm 0.21$ dex, 0.18$\pm 0.22$ dex and 0.14$\pm 0.21$ dex, whenthe full widths at half maximum (FWHM) of the H$\beta$, H$\alpha$ and MgIIlines are, respectively, used. The difference is reduced to 0.10$\pm 0.16$ dexwhen the standard deviation, $\sigma$, of {the} MgII line is used, instead. Wealso study the high S/N composite quasar spectra of the Baryon OscillationSpectroscopic Survey (BOSS), finding that the Fe III$\lambda\lambda$2039-2113redshifts and Mg II squared widths, $FWHM_{MgII}^2$, match very well thecorrelation found for the individual quasar spectra observed with X-shooter.This correlation is expected if the redshift is gravitational.

Measuring Supermassive Black Hole Masses: Correlation between the Redshifts of the Fe III UV Lines and the Widths of Broad Emission Lines