Dissipation and acoustic tunnelling about the sonic horizon of Bondi accretion

Viscous dissipation, as a small perturbative effect about the Bondi flow, shrinks its sonic sphere. An Eulerian perturbation on the steady flow gives a wave equation and the corresponding dispersion relation. The perturbation is a high-frequency travelling acoustic wave, in which small dissipation is taken iteratively. The wave, propagating radially outwards against the bulk inflow, is blocked just within the sonic horizon, where the amplitude of the wave diverges because of viscosity. The blocked acoustic wave can still tunnel outward through the horizon with a viscosity-dependent decaying amplitude, scaled by the analogue Hawking temperature. The escape of acoustic waves (analogue Hawking phonons) through the sonic horizon is compatible with the radial contraction of the sonic sphere.