Radius-luminosity and mass-luminosity relationships for active galactic nuclei

Broad-line region (BLR) sizes derived from spectral variability and BLR line widths are used to directly derive the mass (M) of the central objects of ten active galactic nuclei (AGNs) in a uniform manner. It is shown that the luminosity-weighted C IV 1549-emitting BLR radius (R) correlates with the bolometric luminosity L(Bol) and is consistent with R about sq rt L(Bol). The measurements also permit a verification of the Dibai mass-luminosity (M-L) relationship (previously derived indirectly). It is found that L(Bol) is proportional to M exp (1.1 + or - 0.3). It is found that the efficiency factor epsilon, defined as the ratio of L(Bol) to the Eddington luminosity increases from 0.03 in the low-luminosity Seyferts up to 0.06 in the most luminous objects in the sample.