On BLR Size Estimates in Reverberation Models

Following the approach of Melnikov & Shevchenko (2008), we explore how the nonlinearity in the emission-line luminosity L_l of a broad-line region cloud, in its dependence on the ionizing continuum flux F_i incident on the cloud, affects estimates of the size of the broad-line region by means of cross-correlation methods. We show that the estimates obtained by straightforward cross-correlation of emission-line and continuum light curves can significantly underestimate the BLR size. We demonstrate examples of direct reverberation modelling of AGN emission-line light curves taking into account the nonlinearity of the “L_l-F_i” relation. This nonlinearity allows one to explain the differences in the time lags for different lines. Cross-correlation estimates of the BLR size turn out to be small in comparison to the estimates obtained by the direct reverberation modelling.