BLR sizes and the X-ray spectrum in AGN

Recent ROSAT studies of narrow-line Seyfert 1 galaxies revealed these objects (with FWHM $H_{\beta} \le 2000 km s^{-1}$) generally show steeper soft X-ray spectra than broad line Seyfert 1's and that there are no AGN with broad lines and steep X-ray spectra. We derive a simple theoretical model which explains the observed correlation between the line width and the spectral index for Seyfert 1 galaxies by assuming the line width is due to gravitational velocity dispersion and showing that steeper soft X-ray spectra yield larger BLR radii. We test the model over a hetrogeneous (normal and narrow-line) sample of some 50 AGN finding a good agreement with the data. We give empirical relations for the dependence of the line width and Eddington ratio on the X-ray luminosity and apply variability analyses for direct estimation of the mass part in the line width.