Parametric Study of the Formation of Magnetohydrodynamic Shocks. II. Slow Shocks
Abstract
As a coronal mass ejection (CME) pushes its way through preceding slower solar wind, the evolution of large disturbances leads to the formation of CMEassociated shocks. The formation process is studied using an MHD model in which the shock discontinuities are treated as surfaces with zero thickness and the exact RankineHugoniot relations are used to calculate the jumps in flow properties at all shock crossings. A series of numerical solutions are carried out under the initial condition that the flow velocity is fieldaligned in the rest frame of reference, and the magnetic field and the thermal pressure are constant throughout the flow field with β = 0.1 and the wave normal angle θ = 15°. The solutions demonstrate the formation of planar slow shocks. The momentum impact compresses the plasma in the interaction region. The pressure fronts steepen to form a pair of forward and reverse slow shocks. The impact is equivalent to the collision of two streams. The dynamical impact of the ejecta on the ambient solar wind can be characterized by a reduced number density analogous to the reduced mass for the elastic collision between two particles. We derived a dimensionless momentum impact parameter related to the product of the reduced number density and the square of the collision speed. The similarity rule predicts that under a given plasma β ratio and the wave normal angle θ, this dimensionless parameter determines the strength of the fully developed shocks. Computer experiments are carried out to verify the theory.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1991
 DOI:
 10.1086/170354
 Bibcode:
 1991ApJ...377..255W
 Keywords:

 HYDROMAGNETICS;
 SHOCK WAVES