Modelling O-star astrospheres with different relative speeds between the
  ISM and the star: 2D and 3D MHD model comparison
  Context. State of the art simulations of astrospheres are modelled using
three-dimensional (3D) magnetohydrodynamics (MHD). An astrospheric interaction
of a stellar wind (SW) with its surrounding interstellar medium (ISM) can only
generate a bow shock if the speed of the interstellar inflow is higher than the
fast magnetosonic speed. Aims. The differences of astrospheres at differing
speeds of the ISM inflow are investigated, and the necessity of the third
dimension in modelling is evaluated. Methods. The model astrosphere of the
runaway O-star $\lambda$ Cephei is computed in both two- and three-dimensional
MHD at four different ISM inflow speeds, one of which is barely faster
(superfast) and one of which is slower (subfast) than the fast magnetosonic
speed. Results. The two-dimensional (2D) and 3D models of astrospheres with ISM
inflow speeds considerably higher than the fast magnetosonic speed are in good
agreement. However, in 2D models, where no realistic SW magnetic field can be
modelled, the downwind structures of the astrospheres vacillate. Models where
hydrodynamic effects are not clearly dominant over the magnetic field show
asymmetries, thus necessitating a 3D approach. The physical times of
simulations of astrospheres with slow ISM inflows can swiftly exceed the
lifetime of the corresponding star. A hitherto unobserved structure has been
found downwind of the astrotail in the subfast 3D model.
