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 10 active galactic nuclei (AGNs) in a uniform manner. It is shown that the luminosity-weighted C IV λ1549- emitting BLR radius (R) correlates with the bolometric luminosity (L_Bol_) and is consistent with R ~ L^1/2^_Bol_. The measurements also permit a verification of the Dibai mass-luminosity (M-L) relationship (previously derived indirectly). We find that L_Bol_ is proportional to M^1.1+/-0.3^. We find that the efficiency factor ɛ (defined as the ratio of L_Bol_ to the Eddington luminosity, L_Edd_) increases from 0.03 in the low-luminosity Seyferts up to 0.06 in the most luminous objects in the sample.