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

Abstract

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 ${\mathcal{D}}_{{}_{\mathrm{H}{\hat{\mathrm{I}}}^2}}=\mathrm{FWHM}/\ddot{I}{ƒ}_{{}_{\mathrm{H}{\hat{\mathrm{I}}}^2}}$, the ratio of full width at half maximum to the dispersion of broad H${\hat{I}}^2$, reflects the dynamics of the broad-line region (BLR) and correlates with the dimensionless accretion rate ($\dot{\mathcal{M}}$) or Eddington ratio ($L_{\mathrm{bol}}/L_{\mathrm{Edd}}$). At the same time, $\dot{\mathcal{M}}$ and $L_{\mathrm{bol}}/L_{\mathrm{Edd}}$ correlate with ${\mathcal{R}}_{\mathrm{Fe}}$, the ratio of optical Fe II to H${\hat{I}}^2$ line flux emission. Assembling all AGNs with reverberation mapping measurements of broad H${\hat{I}}^2$, both from the literature and from new observations reported here, we find a strong bivariate correlation of the form $\log (\dot{\mathcal{M}},L_{\mathrm{bol}}/L_{\mathrm{Edd}})=\hat{I}\pm +{\hat{I}}^2{\mathcal{D}}_{{}_{\mathrm{H}{\hat{\mathrm{I}}}^2}}+{\hat{I}}^3{\mathcal{R}}_{\mathrm{Fe}},$ where $\hat{I}\pm =(2.47,0.31)$, ${\hat{I}}^2=-(1.59,0.82)$ and ${\hat{I}}^3=(1.34,0.80)$. 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.

5 pages, 2 figures, 1 table, accepted for publication in The Astrophysical Journal Letters