Based on the gravitational redshift , one 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 M _ { RM } by the reverberation mapping of AGNs .
The factors f can be measured on the basis of two physical quantities , i.e .
the gravitational redshifts z _ { g } and full widths at half maxima v _ { FWHM } 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 Seyfert 1 galaxies .
There is a correlation between f and broad-line region ( BLR ) radius r _ { BLR } , f = 5.4 r _ { BLR } ^ { 0.3 } , for the gravitationally redshifted broad lines He II , He I , H \beta and H \alpha in narrow-line Seyfert 1 galaxy ( NLS1 ) Mrk 110 .
This correlation results from the radiation pressure influence of the accretion disc on the BLR clouds .
The radiation pressure influence seems to be more important than usually thought in AGNs .
Mrk 110 has f \approx 8–16 , distinctly larger than the mean \langle f \rangle \approx 1 , usually used to estimate M _ { RM } in the case of v _ { FWHM } .
NGC 4593 and NLS1 Mrk 486 has f \approx 3 and f \approx 9 , respectively .
Higher f values of several tens are derived for three other NLS1s .
There is a correlation between f and accretion rate \mathscr { \dot { M } } _ { f = 1 } , f = 6.8 \mathscr { \dot { M } } ^ { 0.4 } _ { f = 1 } for five objects , where \mathscr { \dot { M } } _ { f = 1 } = \dot { M } _ { \bullet } / L _ { Edd } c ^ { -2 } as f = 1 is assumed to estimate M _ { RM } used in the Eddington luminosity L _ { Edd } , \dot { M } _ { \bullet } is the mass accretion rate , and c is the speed of light .
These larger f values will produce higher M _ { RM } values and lower Eddington ratios .