The Wardle instability in interstellar shocks .1. Nonlinear dynamical evolution

The nonlinear evolution of unstable C-type shocks in weakly ionized plasmas is studied by means of time-dependent, magnetohydrodynamic simulations. This study is limited to shocks in magnetically dominated plasmas (in which the Alfven speed in the neutrals greatly exceeds the sound speed), and microphysical processes such as ionization and recombination are not followed. Both the two-dimensional simulations of initially planar perpendicular and oblique C-type shocks and the fully three-dimensional simulation of a perpendicular shock are presented. For the cases studied here, the instability results in the formation of dense sheets of gas elongated in the direction of shock propagation and oriented perpendicular to the magnetic field. The formation of a weak J-type front is associated with the growth of the instability from an equilibrium shock structure. After saturation the magnetic field structure consists of arches that bow outward in the direction of shock propagation and are anchored by the enhanced ion-neutral drag in the dense sheets. Analogous to the magnetic buoyancy (Parker) instability, saturation occurs when the magnetic tension in the distorted field lines is balanced by drag in the sheets. For the magnetically dominated shocks studied here, the distortions in the magnetic field that produce saturation are very small. Nonetheless, the enhancements of the ion and neutral densities in the sheets are very large, between 2 and 3 orders of magnitude compared with the preshock values. At these high densities, recombination processes may be important. The sheets evolve slowly in time, so that shocks propagating in a homogeneous medium may leave behind a network of intersecting filaments and sheets of dense gas elongated in the direction of shock propagation and perpendicular to the mean field. The temperature structure and emission properties of unstable C-type shocks in the nonlinear regime are presented in a companion paper.