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 ${\cal D}_{_{\rm
H\beta}}={\rm FWHM}/\sigma_{_{\rm H\beta}}$, 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 ($L_{\rm bol}/L_{\rm Edd}$). 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 $\log(\dot{\mathscr{M}},L_{\rm
bol}/L_{\rm Edd})=\alpha+\beta{\cal D}_{_{\rm H\beta}}+\gamma{\cal R}_{\rm
Fe},$ 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.
