  The adiabatic shock produced by a compact object moving supersonically
relative to a gas with uniform entropy and no vorticity is a source of entropy
gradients and vorticity. We investigate these analytically. The
non-axisymmetric Rayleigh-Taylor and axisymmetric Kelvin-Helmholtz linear
instabilities are potential sources of destabilization of the subsonic
accretion flow after the shock. A local Lagrangian approach is used in order to
evaluate the efficiency of these linear instabilities. However, the conditions
required for such a WKB type approximation are fulfilled only marginally: a
quantitative estimate of their local growth rate integrated along a flow line
shows that their growth time is at best comparable to the time needed for
advection onto the accretor, even at high Mach number and for a small accretor
size. Despite this apparently low efficiency, several features of these
mechanisms qualitatively match those observed in numerical simulations: in a
gas with uniform entropy, the instability occurs only for supersonic accretors.
It is nonaxisymmetric, and begins close to the accretor in the equatorial
region perpendicular to the symmetry axis. The mechanism is more efficient for
a small, highly supersonic accretor, and also if the shock is detached. We also
show by a 3-D numerical simulation an example of unstable accretion of a
subsonic flow with non-uniform entropy at infinity. This instability is
qualitatively similar to the one observed in 3-D simulations of the
Bondi-Hoyle-Lyttleton flow, although it involves neither a bow shock nor an
accretion line.
