2022ApJS..261...30M

The identification of a virial broadening estimator in the quasar UV rest frame suitable for black hole mass computation at high redshift has become an important issue. We compare the H I Balmer Hβ line width to the ones of two intermediate-ionization lines: the Al III λ1860 doublet and the C III] λ1909 line, over a wide interval of redshift and luminosity (0 ≲ z ≲ 3.5; $43\lesssim \mathrm{log}L\lesssim 48.5$ [erg s^–1]), for 48 sources belonging to the quasar population characterized by intermediate to high values of the Eddington ratio (Population A). The present analysis indicates that the line widths of Al III λ1860 and Hβ are highly correlated and can be considered equivalent for most Population A quasars over five orders of magnitude in luminosity; for C III] λ1909, multiplication by a constant correction factor ξ ≈ 1.25 is sufficient to bring the FWHM of C III] in agreement with that of Hβ. The statistical concordance between low-ionization and intermediate-ionization lines suggests that they predominantly arise from the same virialized part of the broad-line region. However, blueshifts of modest amplitude (few hundred kilometers per second) with respect to the quasar rest frame and an excess (≲1.1) Al III broadening with respect to Hβ are found in a fraction of our sample. Scaling laws to estimate M_BH of high-redshift quasars using the Al III and C III] line widths have rms scatter ≈0.3 dex. The Al III scaling law takes the form $\mathrm{log}{M}_{\mathrm{BH}}\approx 0.58\mathrm{log}{L}_{\mathrm{1700,44}}+2\mathrm{logFWHM}+0.49$ [M_⊙].