Numerical simulations of AGN wind feedback on black hole accretion: probing down to scales within the sphere of influence

Abstract

Several processes may limit the accretion rate onto a super-massive black hole (SMBH). Two processes that are commonly considered (e.g., for sub-grid prescriptions) are Bondi-Hoyle-Lyttleton accretion and the Eddington limit. A third one is AGN wind feedback. It has been long suggested that such a wind feedback regulates the final SMBH mass, however, it has been shown recently that AGN winds can also regulate the average accretion rate at a level consistent with observations of high redshift AGNs. In this paper we study the effect of wind feedback on the accretion rate using 2D, high resolution hydrodynamic simulations, that incorporate a self-consistent wind injection scheme and resolves the SMBH sphere of influence. Two different cases are explored and compared: one in which the initial gas density is uniform, and one in which it has an isothermal sphere profile. We also compare simulations with and without cooling. Our main finding is that for reasonable parameters, AGN feedback always limits the accretion rate to be far below the Bondi-Hoyle-Lyttleton limit. For typical wind parameters and a uniform ISM densities of the order $1 {cm}^{-3}$, the accretion rate is found to be several orders of magnitudes smaller than that inferred in large samples of high redshift AGNs. On the other hand, the accretion rate obtained for initially isothermal density profile is found to be consistent with the observations, particularly when cooling is included. Furthermore, it roughly scales as $\sigma^{5}$ with the velocity dispersion of the bulge, in accord with the $M-\sigma$ relation.