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_BH), bolometric luminosity (L_bol) and Eddington ratio (λ_Edd) with optical emission-line ratios ([N II] λ6583/Hα, [S II] λλ6716, 6731/Hα, [O I] λ6300/Hα, [O III] λ5007/Hβ, [Ne III] λ3869/Hβ and He II λ4686/Hβ) of hard X-ray-selected active galactic nuclei (AGN) from the BAT AGN Spectroscopic Survey. We show that the [N II] λ6583/Hα ratio exhibits a significant correlation with λ_Edd (R_Pear = -0.44, p-value = 3 × 10^-13, σ = 0.28 dex), and the correlation is not solely driven by M_BH or L_bol. The observed correlation between [N II] λ6583/Hα ratio and M_BH is stronger than the correlation with L_bol, but both are weaker than the λ_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 [N II] 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_Edd and thus M_BH from the measured L_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.