Understanding the Broad-line Region of Active Galactic Nuclei with Photoionization. II. Slim disks, Self-shadowing, and BLR sizes

Reverberation-mapping (RM) measurements have revealed that high-accretion-rate active galactic nuclei (AGNs) systematically lie below the canonical broad-line region (BLR) radius - optical continuum luminosity (R-L) relation, exhibiting shorter lags than predicted for fixed 5100\AA luminosity. The physical origin of these offsets remains debated. We investigate how accretion-flow structure and BLR cloud properties affect the emissivity-weighted BLR radius using analytic slim-disk SEDs and photoionization calculations on a two-dimensional axisymmetric grid. As the accretion rate approaches and exceeds the Eddington limit, geometric thickening of the inner disk produces anisotropic illumination and self-shadowing, reducing ionizing flux seen by low-latitude BLR clouds and flattening the R-L relation at high L/LEdd. Self-shadowing at high accretion rates reproduces the observed R-L trend in the RM AGN sample reasonably well, but this effect alone is insufficient to explain the observed lag offset in low-mass ($\sim10^{7}M_\odot$) systems with high accretion rates. Motivated by accretion-disk density scalings, we further explore models in which the BLR gas density increases toward lower black hole mass or higher accretion rate. We find that an accretion-rate-dependent BLR density enhancement further improves agreement with observed RM data, where the BLR gas density increases by a factor of 3-5 for one dex increase in $\dot{m}$. Variations in BLR opening angles produce a less important effect on BLR sizes. These results demonstrate that self-consistent modeling of accretion disk SED, BLR illumination and photoionization, and gas density variations can fully explain the observed distribution of AGNs in the BLR size - optical luminosity plane. This framework provides a physically motivated link between accretion-flow structure and BLR observables across a broad range of black-hole properties.