Can the magnetic field in the Orion arm inhibit the growth of
  instabilities in the bow shock of Betelgeuse?
  Many evolved stars travel through space at supersonic velocities, which leads
to the formation of bow shocks ahead of the star where the stellar wind
collides with the interstellar medium (ISM). Herschel observations of the bow
shock of $\alpha$-Orionis show that the shock is almost free of instabilities,
despite being, at least in theory, subject to both Kelvin-Helmholtz and
Rayleigh-Taylor instabilities. A possible explanation for the lack of
instabilities lies in the presence of an interstellar magnetic field. We wish
to investigate whether the magnetic field of the interstellar medium (ISM) in
the Orion arm can inhibit the growth of instabilities in the bow shock of
$\alpha$-Orionis. We used the code MPI-AMRVAC to make magneto-hydrodynamic
simulations of a circumstellar bow shock, using the wind parameters derived for
$\alpha$-Orionis and interstellar magnetic field strengths of $B\,=\,1.4,\,
3.0$, and $5.0\, \mu$G, which fall within the boundaries of the observed
magnetic field strength in the Orion arm of the Milky Way. Our results show
that even a relatively weak magnetic field in the interstellar medium can
suppress the growth of Rayleigh-Taylor and Kelvin-Helmholtz instabilities,
which occur along the contact discontinuity between the shocked wind and the
shocked ISM. The presence of even a weak magnetic field in the ISM effectively
inhibits the growth of instabilities in the bow shock. This may explain the
absence of such instabilities in the Herschel observations of $\alpha$-Orionis.
