Density jump for oblique collisionless shocks in pair plasmas: physical solutions

Collisionless shocks are frequently analyzed using the magnetohydrodynamics (MHD) formalism, even though MHD assumes a small mean free path. Yet, isotropy of pressure, fruit of binary collisions and assumed in MHD, may not apply in collisionless shocks. This is especially true within a magnetized plasma, where the field can stabilize an anisotropy. In a previous article \citep{BretJPP2022b}, a model was presented capable of dealing with the anisotropies that may arise at the front crossing. It was solved for any orientation of the field with respect to the shock front. Yet, for some values of the upstream parameters, several downstream solutions were found. Here, we complete the work started in \cite{BretJPP2022b} by showing how to pick the physical solution out of the ones offered by the algebra. This is achieved by 2 means: 1) selecting the solution that has the downstream field obliquity closest to the upstream one. This criterion is exemplified on the parallel case and backed up by Particle-in-Cell simulations. 2) Filtering out solutions which do not satisfy a criteria already invoked to trim multiple solutions in MHD: the evolutionarity criterion, that we assume valid in the collisionless case. The end result is a model in which a given upstream configuration results in a unique, or none (like in MHD), downstream configuration. The largest departure from MHD is found for the case of a parallel shock.