Spectral Dependence of the Broad Emission-line Region in Agn

We derive a theoretical relation between RBLR, the size of the broademission-line region of active galactic nuclei, and the observed soft X-ray luminosity and spectrum. We find that in addition to the well known RBLR ∼ L 1/2 scaling, RBLR depends also on the soft X-ray spectral slope. Applying this relation to calculate a predicted BLR radius and emission-line width, we show that including the dependence on the spectrum significantly improves the agreement between the calculated BLR radius and the radius independently determined from reverberation mapping as well as the the agreement between the calculated velocity dispersion and the observed FWHM of the Hβ line. We evaluate a theoretical expression for the line width, providing a physical explanation to the anti-correlation between the soft X-ray slope and the emission-line width observed in narrow-line Seyfert galaxies.