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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 ${\cal D}_{_{\rm Hβ}}={\rm FWHM}/σ_{_{\rm Hβ}}$, the ratio of full width at half maximum to the dispersion of broad H$β$, 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$β$ line flux emission. Assembling all AGNs with reverberation mapping measurements of broad H$β$, both from the literature and from new observations reported here, we find a strong bivariate correlation of the form $\log(\dot{\mathscr{M}},L_{\rm bol}/L_{\rm Edd})=α+β{\cal D}_{_{\rm Hβ}}+γ{\cal R}_{\rm Fe},$ where $α=(2.47,0.31)$, $β=-(1.59,0.82)$ and $γ=(1.34,0.80)$. 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.