Anisotropic shock jump conditions: Theory and observations

The MHD Rankine-Hugoniot (RH) relations for shock waves in a collisionless plasma with bi-Maxwellian distribution functions are considered. While by introducing the pressure anisotropy parameter xi in the RH relations, the number of unknowns -- B, V, n, p and xi (a total of 9) -- becomes one more than the total number of the conservation equations, it is possible to use the observed quantities on both sides of the shock to study the anisotropy changes across the shock. A simple relation for the anisotropy change across the shock is derived as a function of the ratio of magnetic fields m(= B'/B), the shock normal angle theta(sub Bn) and the plasma beta and beta' (primes are downstream values). Since m and theta(sub Bn) can be determined accurately in observation, the reliability of the anisotropy change deduced is mostly dependent on the accuracy of the measurements beta and beta'. We have applied the results to six low-beta quasi-perpendicular (Q perpendicular) laminar bow shock crossings with temperature anisotropy measured in the magnetosheath. In the six test cases, it is found that the predicted pressure anisotropies agree well with those observed in the magnetosheath.