  The instability of Bondi-Hoyle-Lyttleton accretion, observed in numerical
simulations, is analyzed through known physical mechanisms and possible
numerical artefacts. The mechanisms of the longitudinal and transverse
instabilities, established within the accretion line model, are clarified. They
cannot account for the instability of BHL accretion at moderate Mach number
when the pressure forces within the shock cone are taken into account. The
advective-acoustic instability is considered in the context of BHL accretion
when the shock is detached from the accretor. This mechanism naturally explains
the stability of the flow when the shock is weak, and the instability when the
accretor is small. In particular, it is a robust proof of the instability of 3D
accretion when gamma=5/3 if the accretor is small enough, even for moderate
shock strength (M sim 3). The numerical artefacts that may be present in
existing numerical simulations are reviewed, with particular attention paid to
the advection of entropy/vorticity perturbations and the artificial acoustic
feedback from the accretor boundary condition. Several numerical tests are
proposed to test these mechanisms.
