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Connecting Star Formation Quenching with Galaxy Structure and Supermassive Black Holes through Gravitational Heating of Cooling Flows

Recent observations suggested that star formation quenching in galaxies is related to galaxy structure. Here we propose a new mechanism to explain the physical origin of this correlation. We assume that while quiescent galaxies are maintained quenched by a feedback mechanism, cooling flows in the hot halo gas can still develop intermittently. We study cooling flows in a large suite of around 90 hydrodynamic simulations of an isolated galaxy group, and find that the flow development depends significantly on the gravitational potential well in the central galaxy. If the galaxy's gravity is not strong enough, cooling flows result in a central cooling catastrophe, supplying cold gas and feeding star formation to galactic bulges. When the bulge grows prominent enough, compressional heating starts to offset radiative cooling and maintains cooling flows in a long-term hot mode without producing cooling catastrophe. Our model thus describes a self-limited growth channel for galaxy bulges, and naturally explains the connection between quenching and bulge prominence. In particular, we explicitly demonstrate that $M_{*}/R_{\rm eff}^{1.5}$ is a good structural predictor of quenching. We further find that the gravity from the central supermassive black hole also affects the bimodal fate of cooling flows, and predict a more general quenching predictor to be $M_{\rm bh}^{1.6}M_{*}/R_{\rm eff}^{1.5}$, which may be tested in future observational studies.