Spectral Dependence of the Broad Emission-Line Region in AGN

Abstract

We derive a theoretical relation between $R_{BLR}$, the size of the broad-emission-line region of active galactic nuclei, and the observed soft X-ray luminosity and spectrum. We show that in addition to the well known $R_{BLR}\sim L^{1/2}$ scaling, $R_{BLR}$ should depend also on the spectral shape and 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 ten AGN with reverberational 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$β$ line.