Response functions as diagnostics of the broad-line region in active galactic nuclei

Abstract

We present response functions for a large number of emission lines covering a wide variety of ionization states emitted from a spherical broad-line region (BLR). The line emissivities are calculated using a photoionization code for a cloud distribution where the cloud properties and covering factor are constrained by a pressure law. Emissivity-weighted and responsivity-weighted response functions are compared for different lines emitted from the same spatially extended BLR gas, and we discuss their dependences on the radial ionization parameter and density gradients. Depending on the local physical conditions, we show that some lines can have negative response functions, particularly if the BLR contains a region of optically thin clouds. This possibility has important implications for attempts to deduce the BLR structure from monitoring data, and is inconsistent with the assumption, implicit in the maximum entropy method, that the response function is positive. We find that comparison of the response functions for lines of different ionization states is a powerful diagnostic of the run of physical conditions in the BLR. In particular, we show that the observed difference in the lag of the high- and low-ionization lines can be reproduced even when these lines are emitted by the same ensemble of clouds, and therefore that different geometries for the clouds that emit these lines may not be required.