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 (lambda(Edd)) with optical emission-line ratios ([N II] lambda 6583/H alpha, [S II] lambda lambda 6716, 6731/H alpha, [O I] lambda 6300/H alpha, [O III] lambda 5007/H beta, [Ne III] lambda 3869/H beta and He II lambda 4686/H beta) of hard X-ray-selected active galactic nuclei (AGN) from the BAT AGN Spectroscopic Survey. We show that the [N II] lambda 6583/H alpha ratio exhibits a significant correlation with lambda(Edd) (R-Pear = -0.44, p-value = 3 x 10(-13), sigma = 0.28 dex), and the correlation is not solely driven by M-BH or L-bol. The observed correlation between [N II] lambda 6583/H alpha ratio and M-BH is stronger than the correlation with L-bol, but both are weaker than the lambda(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] 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(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.