Spatially resolved molecular gas conditions in the circumnuclear disc of 3C 84

Abstract: The brightest cluster galaxy NGC 1275, at the centre of the Perseus cluster, hosts the radio-loud AGN 3C 84 and a circumnuclear disc (CND) of cold molecular gas onto which large-scale CO filaments accrete, yet the physical and chemical conditions of the gas in the CND remain poorly constrained. We present a spatially resolved analysis of ALMA CO(2-1), HCN(3-2), and HCO$<sup>+$(3-2) observations at 72 pc. The data are partitioned into beam-sized hexagonal regions and modelled with a Bayesian framework that couples a neural network emulator of time-dependent chemistry (UCLCHEM) with non-LTE radiative transfer (SpectralRadex) to infer the gas density, kinetic temperature, and cosmic ray ionisation rate in each region. All three line ratios peak in the inner disc and decline with radius. The inference shows radial gradients in density ($\log_{10} n({\rm H_2}) \approx 6.3$ to $\sim 5$), kinetic temperature (~200 K to ~160 K), and cosmic ray ionisation rate ($\log_{10}(ζ/ζ_0) \approx 4.9$ to $\sim 3$). Despite the powerful radio AGN, the observed HCN(3-2)/HCO$<sup>+$(3-2) ratio remains $\lesssim 1$ across the disc. Our modelling attributes this to optical depth saturation of HCN(3-2) ($τ\sim 1$-3), which suppresses the intensity ratio even when the HCN abundance exceeds that of HCO$<sup>+$ by a factor of three or more. The HCN/HCO$<sup>+$ intensity ratio therefore cannot be used as an abundance diagnostic without accounting for optical depth, and a low ratio does not necessarily imply weak AGN influence on the chemistry. Azimuthally resolved profiles suggest a localised HCO$<sup>+$/CO enhancement at the western disc boundary, coinciding with the filament-disc accretion interface and consistent with shock processing by velocity shear between the infalling filaments and the rotating disc. These results indicate that the CND is shaped by accretion from its filamentary environment.