An Axisymmetric, Radiative Bow Shock Model with a Realistic Treatment of   Ionization and Cooling
  We have chosen a reduced set of 18 ionization rate equations (for ions of H, C, N, O, S and Ne), which allow us to obtain a moderately accurate estimate of the non-equilibrium radiative cooling function. We evaluate the accuracy of this approach by comparing our cooling function with previous calculations, computed with a more extended set of ions, for the case of gas that cools from a high temperature at constant density. We also compute steady, plane shock models, which we find to compare well with models calculated with much more detailed microphysics. Using our reduced set of rate equations, we present a simulation of a radiative bow shock formed by a supersonic, plane stream impinging on a rigid sphere. The parameters for the calculation are chosen as to approximately represent typical values found for Herbig-Haro objects, and to give a cooling distance to bow shock radius ratio of 1/10. This simulation is done with an adaptive grid code, which allows a reasonably high resolution (with greater than or equal to 25 points) of the standoff distance between the bow shock and the rigid obstacle. Contrary to the standard expectation, we find that the bow shock standoff distance in the stagnation region is considerably shorter than the cooling distance behind a plane-parallel shock. Also, the centrifugal pressure is found to play an important role in determining the structure of the recombin- ation region. This appears to partially invalidate previous bow shock models based on a ``quasi-1D'' approach, at least for the particular parameters chosen for the present simulation. Finally, we present tabulations of the cooling rates that have been used (for the different species), in order to facilitate the inclusion of this treatment in other gasdynamic codes. 
A. Raga (UNAM), G. Mellema (Stockholm) and P. Lundqvist (Stockholm)