Understanding the Broad-line Region of Active Galactic Nuclei with Photoionization. I. the Moderate-Accretion Regime

Over three decades of reverberation mapping (RM) studies on local broad-line active galactic nuclei (AGNs) have measured reliable black-hole (BH) masses for $> 100$ AGNs. These RM measurements reveal a significant correlation between the Balmer broad-line region size and the AGN optical luminosity (the $R-L$ relation). Recent RM studies for AGN samples with more diverse BH accretion parameters (e.g., mass and Eddington ratio) reveal a substantial intrinsic dispersion around the average $R-L$ relation, suggesting variations in the overall spectral energy distribution shape as functions of accretion parameters. Here we perform a detailed photoionization investigation of expected broad-line properties as functions of accretion parameters, using the latest models for the AGN continuum implemented in {\tt qsosed}. We compare theoretical predictions with observations of a sample of 67 $z\lesssim0.5$ reverberation-mapped AGNs with both rest-frame optical and UV spectra in the moderate-accretion regime (Eddington ratio $\lambda_{\rm Edd}\equiv L/L_{\rm Edd}<0.5$). The UV/optical line strengths and their dependences on accretion parameters can be reasonably well reproduced by the locally-optimally-emitting cloud (LOC) photoionization models. We provide quantitative recipes that use optical/UV line flux ratios to infer the ionizing continuum, which is not directly observable. In addition, photoionization models with universal values of ionization parameter ($\log U_{\rm H}=-2$) and hydrogen density ($\log n({\rm H})=12$) can qualitatively reproduce the observed global $R-L$ relation for the current AGN sample. However, such models fail to reproduce the observed trend of decreasing BLR size with $L/L_{\rm Edd}$ at fixed optical luminosity, which may imply that the gas density increases with the accretion rate.