Estimating black hole masses in quasars using broad optical and UV emission lines

We review past work using broad emission lines as virial estimators of black hole masses in quasars. Basically one requires estimates of the emitting region radius and virial velocity dispersion to obtain black hole masses. The three major ways to estimate the broad-line emitting region (BLR) radius involve: (1) direct reverberation mapping, (2) derivation of BLR radius for larger samples using the radius-luminosity correlation derived from reverberation measures, and (3) estimates of BLR radius using the definition of the ionization parameter solved for BLR radius (photoionization method). At low redshift (z ≲ 0.7) FWHM Hβ serves as the most widely used estimator of virial velocity dispersion. FWHM Hβ can provide estimates for tens of thousands of quasars out to z ≈ 3.8 (IR spectroscopy beyond z ≈ 1). A new photoionization method also shows promise for providing many reasonable estimates of BLR radius via high S/N IR spectroscopy of the UV region 1300–2000 Å. FWHM Mgiiλ2800 can serve as a surrogate for FWHM Hβ in the range 0.4 ≲ z ≲ 6.5 while civλ1549 is affected by broadening due to non-virial motions and best avoided (i.e. there is no clear conversion factor between FWHM Hβ and FWHM Civλ1549). Most quasars yield mass estimates in the range 7 ≲ log MBH ≲ 9.7. There is no strong evidence for values above 10.0 and there may be evidence for a turnover in the maximum black hole mass near z ≈ 5.