  Betelgeuse, the bright red supergiant (RSG) in Orion, is a runaway star. Its
supersonic motion through the interstellar medium has resulted in the formation
of a bow shock, a cometary structure pointing in the direction of motion. We
present the first 3D hydrodynamic simulations of the formation and evolution of
Betelgeuse's bow shock. We show that the bow shock morphology depends
substantially on the growth timescale for Rayleigh-Taylor versus
Kelvin-Helmholtz instabilities. We discuss our models in light of the recent
Herschel, GALEX and VLA observations. If the mass in the bow shock shell is low
(~few x 0.001 Msun), as seems to be implied by the AKARI and Herschel
observations, then Betelgeuse's bow shock is very young and is unlikely to have
reached a steady state. The circular, smooth bow shock shell is consistent with
this conclusion. We further discuss the implications of our results, in
particular, the possibility that Betelgeuse may have only recently entered the
RSG phase.
