Broad emission lines in active galactic nuclei ( AGNs ) mainly arise from gas photoionized by continuum radiation from an accretion disk around a central black hole .
The shape of the broad-line profile , described by { \cal D } _ { { } _ { H \beta } } = { FWHM } / \sigma _ { { } _ { H \beta } } , the ratio of full width at half maximum to the dispersion of broad H \beta , reflects the dynamics of the broad-line region ( BLR ) and correlates with the dimensionless accretion rate ( \dot { \mathscr { M } } ) or Eddington ratio ( L _ { bol } / L _ { Edd } ) .
At the same time , \dot { \mathscr { M } } and L _ { bol } / L _ { Edd } correlate with { \cal R } _ { Fe } , the ratio of optical Fe ii to H \beta line flux emission .
Assembling all AGNs with reverberation mapping measurements of broad H \beta , both from the literature and from new observations reported here , we find a strong bivariate correlation of the form \log ( \dot { \mathscr { M } } ,L _ { bol } / L _ { Edd } ) = \alpha + \beta { \cal D } _ { { } _ { H% \beta } } + \gamma { \cal R } _ { Fe } , where \alpha = ( 2.47 , 0.31 ) , \beta = - ( 1.59 , 0.82 ) and \gamma = ( 1.34 , 0.80 ) .
We refer to this as the fundamental plane of the BLR .
We apply the plane to a sample of z < 0.8 quasars to demonstrate the prevalence of super-Eddington accreting AGNs are quite common at low redshifts .