Jump conditions for pressure anisotropy and comparison with the Earth's bow shock

Taking into account the pressure anisotropy in the solar wind, we study the magnetic field and plasma parameters downstream of a fast shock, as functions of upstream parameters and downstream pressure anisotropy. In our theoretical approach, we model two cases: a) the perpendicular shock and b) the oblique shock. We use two threshold conditions of plasma instabilities as additional equations to bound the range of pressure anisotropy. The criterion of the mirror instability is used for pressure anisotropy P (perpendicular to)/P (parallel to) > 1. Analogously, the criterion of the fire-hose instability is taken into account for pressure anisotropy P-perpendicular to/P-parallel to < 1. We found that the variations of the parallel pressure, the parallel temperature, and the tangential component of the velocity are most sensitive to the pressure anisotropy downstream of the shock. Finally, we compare our theory with plasma and magnetic field parameters measured by the WIND spacecraft.