A new method to measure the virial factors in the reverberation mapping of active galactic nuclei

Based on the gravitational red shift, which is a prediction of Einstein's general relativity theory, of broad optical emission lines in active galactic nuclei (AGNs), a new method is proposed to estimate the virial factors f in measuring black hole masses MRM by the reverberation mapping of AGNs. The factors f can be measured based on two physical quantities, i.e. the gravitational red shifts zg and the full widths at half maxima vFWHM of broad lines. In the past, it has been difficult to determine the factors f for individual AGNs. We apply this new method to several reverberation-mapped type 1 Seyfert galaxies. There is a correlation between f and the radius of the broad-line region (BLR) rBLR, |$f=5.4 r_{\rm {BLR}}^{0.3}$|⁠, for the gravitationally red-shifted broad lines He ii, He i, Hβ and Hα in the narrow-line type 1 Seyfert galaxy (NLS1) Mrk 110. This correlation results from the influence of the radiation pressure of the accretion disc on the BLR clouds. This influence seems to be more important than usually thought so in AGNs. Mrk 110 has f ≈ 8–16, distinctly larger than the mean 〈f〉 ≈ 1 usually used to estimate MRM for vFWHM. NGC 4593 and NLS1 Mrk 486 have f ≈ 3 and f ≈ 9, respectively. Higher f values of several tens are derived for three other NLS1s. There is a correlation between f and accretion rate |$\dot{\mathscr{M}}_{f=1}$|⁠, |$f=6.8\dot{\mathscr{M}}^{0.4}_{f=1}$| for five objects, where |$\dot{\mathscr{M}}_{f=1}=\dot{M}_{\bullet }/L_{\rm {Edd}}c^{-2}$| as f = 1 is assumed when estimating MRM used in the Eddington luminosity LEdd, |$\dot{M}_{\bullet }$| is the mass accretion rate, and c is the speed of light. These larger f values will produce higher MRM values and lower Eddington ratios.