What the Optical Recombination Lines Can Tell Us About the Broad Line Regions of Active Galactic Nuclei

We investigate the effect of a global change in the ionizing continuum level on the behavior of the strong optical broad emission-lines seen in spectra of the nuclear emission-line regions of active galactic nuclei (AGN), including the Balmer lines, HeI 5876, and HeII 4686. Unlike most of the prominent heavy element lines found in the UV, the optical hydrogen and helium recombination lines' emissivities are strongly dependent upon the incident continuum flux, since these lines arise out of excited states whose optical depths depend upon the incident flux of photons. Using photoionization calculations we determine the luminosity-dependent responsivities of these lines for a general model of the broad emission line region (BLR), with the purpose of establishing them as important probes of the physical conditions within the BLR of AGNs. The dependence of these lines' emissivities on the incident photon flux invokes a dependence in their responsivities on distance from the central continuum source. In particular, the responsivities of these lines are generally anti-correlated with the incident photon flux. Thus, their responsivities vary with distance within the BLR for a fixed continuum luminosity and change with time as the continuum source varies. Consequently, after correcting for light travel time effects the response of the Balmer and optical helium lines should generally be strongest during low continuum luminosity states. Responsivity that depends upon photon flux and continuum state may explain a number of outstanding problems currently under investigation in broad line variability studies of these and other emission lines. [Abridged]