  Betelgeuse, the bright, cool red supergiant in Orion, is moving
supersonically relative to the local interstellar medium. The star emits a
powerful stellar wind which collides with this medium, forming a cometary
structure, a bow shock, pointing in the direction of motion. We present the
first 3D hydrodynamic simulations of the formation and evolution of
Betelgeuse's bow shock. The models include realistic low temperature cooling
and cover a range of plausible interstellar medium densities and stellar
velocities between 0.3 - 1.9 cm-3 and 28 - 73 km/s. We show that the flow
dynamics and morphology of the bow shock differ substantially due to the
preferential growth of Rayleigh-Taylor or Kelvin-Helmholtz instabilities in the
models. The former dominate the models with slow stellar velocities resulting
in a clumpy bow shock sub-structure, whereas the latter produce a smoother,
more layered sub-structure in the fast models. If the mass in the bow shock
shell is low, as seems to be implied by the AKARI luminosities (~0.003 Msun),
then Betelgeuse's bow shock is very young and is unlikely to have reached a
steady state. The circular nature of the bow shock shell is consistent with
this conclusion. Thus, our results suggest that Betelgeuse entered the red
supergiant phase only recently.
