A note on the compression ratio in MHD shocks

We present an analysis of the compression ratio in MHD shocks. Although the equation describing the compression ratio has been in the literature for decades, we believe that our results are interesting and complementary to the earlier research. We concentrate on the behavior of the compression ratio in a bow shock as a function of the angle between the shock normal and the plasma velocity. For this problem, we find non-unique solutions in certain regimes, which we investigate in detail. We also find regimes where the compression ratio in fast bow shocks achieves a local maximum in more than one location. In the last section, we consider the compression ratio in slow shocks and make some conclusions about the shape of the shock in this flow regime.