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Description
It has long been known that supermassive black hole (SMBH) mass correlates with host galaxy properties; the most fundamental of these is the M-sigma relation between SMBH mass and bulge velocity dispersion. In the framework of active galactic nucleus (AGN) wind-driven feedback, AGN luminosity is communicated to the surrounding gas via a quasi-relativistic wind emanating from the accretion disc. The wind shocks the gas with post-shock temperatures reaching 10^10 K. The pressure in the shocked region is significantly higher than that of the interstellar medium (ISM), so the bubble begins to expand. Depending on which of the two processes - expansion or cooling - operates on a shorter timescale, the resulting outflow can be either momentum- or energy-driven. Momentum-driven outflows provide a natural explanation of the observed relation, while energy driving predicts a steeper relation and massive, large-scale outflows. However, it is still unclear if this picture holds in a less idealized multiphase bulge, where cooling likely dominates only in the densest clumps and large-scale energy-driven outflows could escape through the paths in between.
Here we test this with Gadget-3 simulations of a turbulent multiphase bulge. We adopt an initial SMBH mass of 10^8 solar masses and a total gas mass within 1 kpc of 9.4x10^8 solar masses, corresponding to a gas fraction of 0.1, and use an external potential consistent with the M-sigma relation. We perform simulations at several fixed luminosities between 0 and 2.5 times Eddington with AGN phase lasting 1 Myr, with multiple stochastic turbulence realizations producing different distributions of gas clumps at each luminosity.
We find a clear transition near 0.7 times Eddington: above this luminosity, inflow to the black hole is strongly suppressed. Cold dense clumps are pushed with near-pure momentum driving (typical momentum loading around 0.3, far below energy-driven wind prediction of about 30), while the hot energy-driven outflow escapes through low-density channels. This demonstrates that the M-sigma relation can arise from momentum-driven regulation of black hole growth while energy-driven outflows occur simultaneously.