Xiaoxia Zhang, Taotao Fang, Shulan Yan, Si-Yue Yu, Feng Yuan

The relationship between supermassive black holes and the multiphase circumgalactic medium is central to understanding the co-evolution of galaxies and their central black holes. We investigate this relationship using the IllustrisTNG100 simulation with a sample of 5089 central galaxies at $z=0$, measuring the partial correlation between central black hole mass and the mass of cold ($T < 10^4$K), cool ($10^4 \le T < 10^5$K), warm ($10^5 \le T < 10^6$K), and hot ($T \ge 10^6$K) gas within $0.03R_{200}$, $0.15R_{200}$, and $R_{200}$, after accounting for stellar and dark matter halo mass. We find that after removing these confounding factors, black hole mass shows a significant negative partial correlation ($ρ\approx -0.37$) with cold gas within $R_{200}$ and $0.15R_{200}$, whereas warm and hot gas exhibit no substantial intrinsic correlation. The residual plane reveals a threshold pattern: galaxies with over-massive black holes show systematically reduced cold gas, consistent with the cumulative impact of AGN feedback. The anti-correlation persists across environments with a weak trend in local density, and varies with galaxy type (star-forming, green valley, and quenched). These results provide a quantitative multiphase diagnostic of AGN feedback in TNG and support a picture in which feedback progressively removes cold gas, offering testable predictions for future multiwavelength surveys.