bow shock shape

Now that I did some simulations just looking at the shape and interactions of bow shocks from clumps, I wanted to compare with the formula that I had been using for my mach stem simulations.

It looks like the equation for the shape of the bow shock given by Ostriker (paper) does not work well for different gammas. There is not a big difference in shape between = 5/3 and = 1.01.

From my 2 clumps simulation with separation 40 rclump, you can see that the bow shocks are very different.

Furthermore, the equation does not even come close for my gamma = 5/3 run. I think the Ostriker formula assumes a radiative bow shock, which makes more sense for its shape.

The equation comes closer for gamma = 1.01, but there is still a big discrepancy. Maybe it is accurate for a gamma = 1, but I doubt it comes close enough for the purposes that I need.

This leads me to think that perhaps I have to derive my own formula for bow shock shape from my simulations in order to do a proper mach stem study with astrobear.

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