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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 ($λ_{\rm Edd}$) with optical emission line ratios ([NII] λ6583/Hα, [SII] λλ6716,6731/Hα, [OI] λ6300/Hα, [OIII] λ5007/Hβ, [NeIII] λ3869/Hβ, and HeII λ4686/Hβ) of hard X-ray-selected AGN from the BAT AGN Spectroscopic Survey (BASS). We show that the [NII] λ6583/Hα ratio exhibits a significant correlation with $λ_{\rm Edd}$ ($R_{\rm Pear}$ = -0.44, $p$-value=$3\times10^{-13}$, σ = 0.28 dex), and the correlation is not solely driven by $M_{\rm BH}$ or $L_{\rm bol}$. The observed correlation between [NII] λ6583/Hα ratio and $M_{\rm BH}$ is stronger than the correlation with $L_{\rm bol}$, but both are weaker than the $λ_{\rm Edd}$ 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] λ6583/Hα is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure $λ_{\rm Edd}$ 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.