Direct numerical testing of stationary shock model with low Mach number shock observations

Using mixed observational-theoretical-numerical analysis, we have tested to what extent the observed profile of a low-Mach number quasi-perpendicular shock is consistent with the shock model, in which the shock front is formed due to the ion interaction with the stationary and one-dimensional field structure. Using observational data for the magnetic profile of the November 26, 1977, shock with "noise" removed and theoretically predicted cross-shock electric field, we have numerically traced the ion trajectories in this shock structure, assuming an initial Maxwellian distribution of incident ions with the observed temperature. We found no reflected ions, although some fraction of ions were almost reflected, making loops inside the ramp and acquiring energies typical for ordinary reflected ions. The number of these quasi-reflected ions is sensitive to the ion beta and cross-shock potential. We have applied the pressure balance condition to verify the consistency of the numerically derived ion pressure with the observed profile. The good agreement found shows that the shock is stationary and that its structure is indeed mostly due to the particle interaction with static fields in the shock front, while time-dependent features (such as turbulence) may provide fine tuning.