The existence of null points of flow and magnetic fields as prerequisites for the presence of astropauses and their co-location

Abstract: Astropauses can be defined via magnetic or fluid separatrices. For the boundary layer between the stellar wind and the local interstellar medium, two separatrices can occur, the magnetopause and the hydropause. The question is whether they are identical. To address this, we investigate under which conditions the null points of the magnetic and velocity field, which define the corresponding separatrices, coincide spatially. We analysed the case of a non-monotonous pressure distribution driving stationary counterstreaming ideal HD flows and demonstrate that the existence of an extremum of the pressure in the 3D case together with a non-degeneracy condition on the velocity field implies that this point is also a stagnation point. Turning to ideal MHD and considering the regularity of all fields, we formulated the momentum equations, revealing their quasi-linearity. This allowed us to prove the occurrence of null points by examining the rank of the Jacobians of the vector fields. We found that for a given null point of either the velocity or the magnetic field at the pressure extremum, the pendant vector field has a co-located null if the Jacobian of this field is non-singular. We extended the analysis to resistive MHD and further to MHD with general non-ideal terms and proved that if at least one of the first-order momentum equations is ideal, the stagnation point and the magnetic null point are co-located. Even for general fluid theory, the two null points co-locate as long as the curl of the generalised non-ideal terms is zero at one of them or can be represented by a linear operator in the magnetic and velocity field. In general, it is not excluded that the velocity and magnetic nulls are dislocated. However, this would require specific properties of the curl of the non-ideal term, which would reduce the probability of a relaxed quasi-stationary configuration.