We test the recently proposed ( Mediavilla et al .
2018 ) black hole mass scaling relationship based on the redshift with respect to the quasar ’ s rest frame of the Fe III \lambda \lambda 2039-2113 line blend .
To this end , we fit this feature in the spectra of a well suited sample of quasars , observed with X-shooter at the Very Large Telescope ( VLT ) , whose masses have been independently estimated using the virial theorem .
For the quasars of this sample we consistently confirm the redshift of the Fe III \lambda \lambda 2039-2113 blend and find that it correlates with the squared widths of H \beta , H \alpha and Mg II , which are commonly used as a measure of M _ { BH } / R to determine masses from the virial theorem .
The average differences between virial and Fe III \lambda \lambda 2039-2113 redshift based masses are 0.18 \pm 0.21 dex , 0.18 \pm 0.22 dex and 0.14 \pm 0.21 dex , when the full widths at half maximum ( FWHM ) of the H \beta , H \alpha and MgII lines are , respectively , used .
The difference is reduced to 0.10 \pm 0.16 dex when the standard deviation , \sigma , of the MgII line is used , instead .
We also study the high S/N composite quasar spectra of the Baryon Oscillation Spectroscopic Survey ( BOSS ) , finding that the Fe III \lambda \lambda 2039-2113 redshifts and Mg II squared widths , FWHM _ { MgII } ^ { 2 } , match very well the correlation found for the individual quasar spectra observed with X-shooter .
This correlation is expected if the redshift is gravitational .