A Unified Origin of Faraday Rotation toward 3C 84: The Circumnuclear Ambient Medium within the Parsec-scale Bondi Radius of the Host Galaxy NGC 1275

We present multifrequency 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 over 1–8 pc, following a single power-law trend of RM ∝ 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 to 1.5 μG 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.