  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.
