  Spherical Bondi accretion is used in astrophysics as an approximation to
investigate many types of accretion processes. Two-phase accretion flows that
transition from neutral to ionized have observational support in high-mass star
formation, and have application to accretion flows around any ionizing source,
but the hydrodynamic stability of two-phase Bondi accretion is not understood.
With both semi-analytic and fully numerical methods we find that these flows
may be stable, conditionally stable or unstable depending on the initial
conditions. The transition from an R-type to a D-type ionization front plays a
key role in conditionally stable and unstable flows.
