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Many evolved stars travel through space at supersonic velocities, which leadsto the formation of bow shocks ahead of the star where the stellar windcollides with the interstellar medium (ISM). Herschel observations of the bowshock of $\alpha$-Orionis show that the shock is almost free of instabilities,despite being, at least in theory, subject to both Kelvin-Helmholtz andRayleigh-Taylor instabilities. A possible explanation for the lack ofinstabilities lies in the presence of an interstellar magnetic field. We wishto investigate whether the magnetic field of the interstellar medium (ISM) inthe Orion arm can inhibit the growth of instabilities in the bow shock of$\alpha$-Orionis. We used the code MPI-AMRVAC to make magneto-hydrodynamicsimulations 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 observedmagnetic field strength in the Orion arm of the Milky Way. Our results showthat even a relatively weak magnetic field in the interstellar medium cansuppress the growth of Rayleigh-Taylor and Kelvin-Helmholtz instabilities,which occur along the contact discontinuity between the shocked wind and theshocked ISM. The presence of even a weak magnetic field in the ISM effectivelyinhibits the growth of instabilities in the bow shock. This may explain theabsence of such instabilities in the Herschel observations of $\alpha$-Orionis.

Can the magnetic field in the Orion arm inhibit the growth of instabilities in the bow shock of Betelgeuse?