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Can supernova shells feed supermassive black holes in galactic nuclei?

We simulate shells created by supernovae expanding into the interstellar medium (ISM) of the nuclear region of a galaxy, and analyze how the shell evolution is influenced by the supernova (SN) position relative to the galactic center, by the interstellar matter (ISM) density, and by the combined gravitational pull of the nuclear star cluster (NSC) and supermassive black hole (SMBH).We adopted simplified hydrodynamical simulations using the infinitesimally thin layer approximation in 3D (code RING) and determined whether and where the shell expansion may bring new gas into the inner parsec around the SMBH. The simulations show that supernovae occurring within a conical region around the rotational axis of the galaxy can feed the central accretion disk surrounding the SMBH. For ambient densities between 10$^3$ and 10$^5$ cm$^{-3}$, the average mass deposited into the central parsec by individual supernovae varies between 10 to 1000 solar masses depending on the ambient density and the spatial distribution of supernova events. Supernova occurring in the aftermath of a starburst event near a galactic center can supply two to three orders of magnitude more mass into the central parsec, depending on the magnitude of the starburst. The deposited mass typically encounters and joins an accretion disk. The fate of that mass is then divided between the growth of the SMBH and an energetically driven outflow from the disk.