Minchul Kam, Jongho Park, Sascha Trippe, Do-Young Byun, Keiichi Asada, Hiroshi Nagai, Motoki Kino, Luis Ho, Andrew Fabian, Jeffrey Hodgson, Kunwoo Yi, Kenji Toma, Junghwan Oh, Taehyun Jung

We present multi-frequency polarimetric observations of 3C 84 obtained with the Korean VLBI Network at 43-141 GHz, the Very Long Baseline Array at 43 GHz, and the High Sensitivity Array at 8 GHz from 2015 to 2024. We find that the Faraday rotation measure (RM) decreases systematically with distance from the black hole over 1-8 pc, following a single power-law trend of RM proportional to r^{-2.7+/-0.2}. Notably, RM measurements from earlier studies across the same distance range follow the same relation. This consistency across epochs, frequencies, and independent datasets indicates a common and stable external Faraday screen. These results naturally identify the circumnuclear ambient medium within the parsec-scale Bondi radius of the host galaxy NGC 1275 as the origin of the Faraday rotation, thereby resolving a long-standing question about its physical origin. From the RM profile, we derive radial distributions of the electron density and magnetic-field strength in the circumnuclear ambient medium that are consistent with independent constraints. The derived density lies below that of the free-free absorption disk and, when extrapolated inward, remains below the density of the broad-line region. The magnetic-field strength gradually increases from 0.1-1.5 microgauss at the Bondi radius to milligauss-to-gauss levels toward the black hole, providing the first spatially resolved constraint on the magnetic-field strength at parsec-scale distances in an elliptical galaxy. Together, these results present a spatially resolved and physically consistent picture of the circumnuclear environment in NGC 1275.