The SDSS-V black hole mapper reverberation mapping project: multi-line dynamical modeling of a highly variable active galactic nucleus with decade-long light curves

We present dynamical modeling of the broad-line region (BLR) of the highly variable active galactic nucleus (AGN) SDSS J141041.25+531849.0 (z = 0.359) using photometric and spectroscopic monitoring data from the Sloan Digital Sky Survey (SDSS) Reverberation Mapping project and the current fifth-generation SDSS Black Hole Mapper program, spanning from early 2013 to early 2023. We model the geometry and kinematics of the BLR in the Hβ, Hα, and Mg ɪɪ emission lines for three different time periods to measure the potential change of structure within the BLR across time and line species. We find a moderately face-on (𝑖_full-state = 29.68^+4.74_-3.62 deg) thick-disk (θ_{opn,full-state} = 42.04^+4.32_-3.96 deg) geometry for most BLRs, with a joint estimate for the mass of the supermassive black hole for each of three time periods, yielding log₁₀(M_BH/M_☉) = 8.10^+0.03_-0.03 when using the full data set. The inferred individual virial factor f ∼ 1.6 is moderately smaller than the average factor for a local sample of dynamically modeled AGNs. There is strong evidence for nonvirial motion, with over 70% of clouds on inflowing/outflowing orbits. We analyze the change in model parameters across emission lines, finding the radii of BLRs for the emission lines are consistent with the following relative sizes R_Hβ ≲ R_MgII ≲ R_Hα. Comparing results across time, we find R_low-state ≲ R_high-state, with the change in BLR size for Hβ being more significant than for the other two lines. The data also reveal complex, time-evolving, and potentially transient dynamics of the BLR gas over a decade-long timescale, encouraging for future dynamical modeling of fine-scale BLR kinematics.