Dynamical Modeling of the Broad-line Region with High-mass Active Galactic Nuclei and Constraints on the Virial Factor

Abstract

We present the results of broad-line region (BLR) dynamical modeling for eight high-mass active galactic nuclei (AGNs) from the Seoul National University AGN Monitoring Project, by constraining BLR geometry and kinematics as well as black hole (BH) mass ( M BH ). We find that the H β -emitting BLRs are best described as thick disks viewed at intermediate inclinations, with emission preferentially originating from the far side of the BLR. BLR kinematics show a combination of rotational, inflowing, and outflowing components. By comparing the M BH from dynamical modeling with the virial products based on reverberation lags and line widths, we determine the virial factor f for individual AGNs. Combining our sample with those M BH consistently determined via BLR dynamical modeling, yielding a total of 38 objects, we derive a virial factor for future M BH estimation of log 10 ( f ) pred  = 0.69 ± 0.21 based on σ line,rms and −0.08 ± 0.23 based on FWHM mean . The derived virial factor is consistent with that inferred by aligning the reverberation-mapped AGNs with quiescent galaxies in the M BH – σ * relation, supporting the assumption that local active and inactive galaxies follow the same M BH – σ * relation. Our updated f values exhibit an intrinsic dispersion of ∼0.2 dex, which allows for more precise M BH estimates than those based on the M BH – σ * relation. Our sample extends the reverberation sample with BLR dynamic modeling to the M BH  ∼ [10 8 , 10 8.5 ] M ⊙ , where the virial factor from the AGN M BH – σ * relation remains poorly constrained, underscoring the unique value of dynamical modeling analysis in constraining the M BH of the most massive BHs.