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.
