BAT AGN Spectroscopic Survey-III. An observed link between AGN Eddington   ratio and narrow emission line ratios
  We investigate the observed relationship between black hole mass ($M_{\rm BH}$), bolometric luminosity ($L_{\rm bol}$), and Eddington ratio (${\lambda}_{\rm Edd}$) with optical emission line ratios ([NII] {\lambda}6583/H{\alpha}, [SII] {\lambda}{\lambda}6716,6731/H{\alpha}, [OI] {\lambda}6300/H{\alpha}, [OIII] {\lambda}5007/H{\beta}, [NeIII] {\lambda}3869/H{\beta}, and HeII {\lambda}4686/H{\beta}) of hard X-ray-selected AGN from the BAT AGN Spectroscopic Survey (BASS). We show that the [NII] {\lambda}6583/H{\alpha} ratio exhibits a significant correlation with ${\lambda}_{\rm Edd}$ ($R_{\rm Pear}$ = -0.44, $p$-value=$3\times10^{-13}$, {\sigma} = 0.28 dex), and the correlation is not solely driven by $M_{\rm BH}$ or $L_{\rm bol}$. The observed correlation between [NII] {\lambda}6583/H{\alpha} ratio and $M_{\rm BH}$ is stronger than the correlation with $L_{\rm bol}$, but both are weaker than the ${\lambda}_{\rm Edd}$ correlation. This implies that the large-scale narrow lines of AGN host galaxies carry information about the accretion state of the AGN central engine. We propose that the [NII] {\lambda}6583/H{\alpha} is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure ${\lambda}_{\rm Edd}$ and thus $M_{\rm BH}$ from the measured $L_{\rm bol}$, even for high redshift obscured AGN. We briefly discuss possible physical mechanisms behind this correlation, such as the mass-metallicity relation, X-ray heating, and radiatively driven outflows. 
Kyuseok Oh, Kevin Schawinski, Michael Koss, Benny Trakhtenbrot,   Isabella Lamperti, Claudio Ricci, Richard Mushotzky, Sylva...
astro-ph.GA