The Fundamental Plane of the Broad-line Region in Active Galactic Nuclei

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 ${cal D}_{_{rm Hbeta}}={rm FWHM}/sigma_{_{rm Hbeta}}$, 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 ($L_{rm bol}/L_{rm Edd}$). At the same time, $dot{mathscr{M}}$ and $L_{rm bol}/L_{rm Edd}$ correlate with ${cal R}_{rm Fe}$, 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 $log(dot{mathscr{M}},L_{rm bol}/L_{rm Edd})=alpha+beta{cal D}_{_{rm Hbeta}}+gamma{cal R}_{rm Fe},$ 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.