Title:
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An Axisymmetric, Radiative Bow Shock Model with a Realistic Treatment of
Ionization and Cooling.
(Stockholm Observatory preprint No. 88)

Authors:
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Alejandro Raga (UNAM, Mexico), Garrelt Mellema (Stockholm) & Peter Lundqvist 
(Stockholm)

Abstract:
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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.

To appear in:
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ApJ Supplement