Temporal evolution of magnetic molecular shocks II. Analytics of the   steady state and semi-analytical construction of intermediate ages
  In the first paper of this series (Paper I) we computed time dependent simulations of multifluid shocks with chemistry and a transverse magnetic field frozen in the ions, using an adaptive moving grid. In this paper, we present new analytical results on steady-state molecular shocks. Relationships between density and pressure in the neutral fluid are derived for the cold magnetic precursor, hot magnetic precursor, adiabatic shock front, and the following cooling layer. The compression ratio and temperature behind a fully dissociative adiabatic shock is also derived. To prove that these results may even hold for intermediate ages, we design a test to locally characterise the validity of the steady state equations in a time-dependent shock simulation. Applying this tool to the results of Paper I, we show that most of these shocks (all the stable ones) are indeed in a quasi-steady state at all times, i.e. : a given snapshot is composed of one or more truncated steady shock. Finally, we use this property to produce a construction method of any intermediate time of low velocity shocks (u < 20 km/s) with only a steady-state code. In particular, this method allows one to predict the occurrence of steady CJ-type shocks more accurately than previously proposed criteria. 
P. Lesaffre, J.-P. Chi\`eze, S. Cabrit, G. Pineau des For\^ets