Flash-light on the Ring: hydrodynamic simulations of expandingsupernova shells near supermassive black holes

The way supermassive black holes (SMBH) in galactic centers accumulate their mass is not completely determined. At large scales, it is governed by galactic encounters, mass inflows connected to spirals arms and bars, or due to expanding shells from supernova (SN) explosions in the central parts of galaxies. The investigation of the latter process requires an extensive set of gas dynamical simulations to explore the muti-dimensional parameter space needed to frame the phenomenon. The aims of this paper are to extend our investigation of the importance of supernovae for inducing accretion onto a SMBH and carry out a comparison between the fully hydrodynamic code Flash and the much less computationally intensive code Ring, which uses the thin shell approximation. We simulate 3D expanding shells in a gravitational potential similar to that of the Galactic Center with a variety of homogeneous and turbulent environments. In homogeneous media, we find convincing agreement between Flash and Ring in the shapes of shells and their equivalent radii throughout their whole evolution until they become subsonic. In highly inhomogeneous, turbulent media, there is also a good agreement of shapes and sizes of shells, and of the times of their first contact with the central 1 pc sphere, where we assume that they join the accretion flow. The comparison supports the proposition that a SN occurring at a galactocentric distance of 5 pc typically drives 1 - 3 $M_\odot$ into the central 1 pc around the galactic center.