2013ApJ...771...31N

Black hole mass estimation in quasars, especially at high redshift, involves the use of single-epoch spectra with signal-to-noise ratio and resolution that permit accurate measurement of the width of a broad line assumed to be a reliable virial estimator. Coupled with an estimate of the radius of the broad-line region (BLR) this yields the black hole mass M_BH. The radius of the BLR may be inferred from an extrapolation of the correlation between source luminosity and reverberation-derived r_BLR measures (the so-called Kaspi relation involving about 60 low-z sources). We are exploring a different method for estimating r_BLR directly from inferred physical conditions in the BLR of each source. We report here on a comparison of r_BLRestimates that come from our method and from reverberation mapping. Our "photoionization" method employs diagnostic line intensity ratios in the rest-frame range 1400-2000 Å (Al III λ1860/Si III] λ1892, C IV λ1549/Al III λ1860) that enable derivation of the product of density and ionization parameter with the BLR distance derived from the definition of the ionization parameter. We find good agreement between our estimates of the density, ionization parameter, and r_BLR and those from reverberation mapping. We suggest empirical corrections to improve the agreement between individual photoionization-derived r_BLR values and those obtained from reverberation mapping. The results in this paper can be exploited to estimate M_BH for large samples of high-z quasars using an appropriate virial broadening estimator. We show that the width of the UV intermediate emission lines are consistent with the width of Hβ, thereby providing a reliable virial broadening estimator that can be measured in large samples of high-z quasars.