Abstract
Astrospheres are the interaction regions between the stellar wind and the ambient interstellar medium, which consists of various HD (or MHD) discontinuities. Astropause is a tangential discontinuity that separates the two flows, and its structure is described by one of the separatrices of the fluid flow.
In 2D, there must be at least one X-type null point (X-point) close to the apex. This analysis aims to study hydrodynamically the geometrical and topological structures of the streamlines in the vicinity of the X-point.
As the flow close to the apex can be considered incompressible, one can make use of stream functions to describe such flows. The definition of streamlines, along with the equations of ideal HD, gives a single, (non-)linear elliptic partial differential equation, known as the Grad-Shafranov equation (GSE).
This equation is analysed by approximating the stream function as a Laurent series to various orders, and assuming specific forms for the pressure function. Depending on the choice of the pressure function and the coefficients of the chosen ansatz, either the original null point can become an X-point of higher order, or more null points can appear in its vicinity.