Spectral dependence of the broad emission line region in active galactic nuclei

We derive a theoretical relation between R-BLR, the size of the broad emission line region (BLR) of active galactic nuclei (AGNs), and the observed soft X-ray luminosity and spectrum. We show that in addition to the well-known R(BLR)similar to L-1/2 scaling, R-BLR should depend also on the soft X-ray spectral slope, and we derive the expected relation between R-BLR and the X-ray luminosity and spectral index. Applying this relation to calculate a predicted BLR radius for 10 AGNs with reverberation data, we show that including the dependence on the spectrum improves the agreement between the calculated BLR radius and the radius independently determined from reverberation mapping. Similarly, we evaluate an expression for the line width and show that including the dependence on the spectrum significantly improves the agreement between the calculated BLR velocity dispersion and the observed FWHM of the H beta line. The theoretical expression for the line width also provides a physical explanation to the anticorrelation between the soft X-ray slope and the emission-line width observed in narrow-line Seyfert galaxies.