A generalized bondi accretion model for the galactic centre

We develop an analytic, steady-state model for the gas environment in quiescent galactic nuclei.We assume that the mass is constantly supplied by a spherically symmetric distribution of wind emitting stars, and that gravity is solely due to a central supermassive black hole. In such flows, the bulk velocity vanishes at a finite radius, called the stagnation radius. Matter generated below that radius will be accreted onto the black hole, while matter outside it will escape the system. Under certain conditions, the flow may become supersonic at both domains. From dimensional analysis, the stagnation radius is proportional to the ratio between the gravitational parameter of the central black hole and the wind velocity squared. In this work, we demonstrate how to determine the exact position of the stagnation radius. We also obtain radial profiles of the hydrodynamic variables and verify them using a time-dependent hydrodynamic simulation. We delineate the conditions under which radiative cooling can be neglected, and predict the luminosity and spectrum of the free-free X-ray emission from such a system. We use the insights from this work to settle a tension regarding the distribution of wind emitting stars around the Galactic centre, which arose in a previous study. In addition, we describe how radio emission from tidal disruption events can be used to infer information about wind emitting distributions in other galaxies.