Mach Stems: Cooling Strength ==> Effective Gamma

Below is a new set of 2-D runs designed to explore how the strength of radiative cooling affects Mach stem formation and size. An approximation of the critical angle for Mach stem formation depends only on the adiabatic index gamma. We hypothesize that the cooling strength implies an "effective" gamma such that very weak cooling implies a gamma of 5/3 and very strong cooling implies a gamma of 1.

Furthermore, if a Mach stem forms, its size is limited to the smaller of the cooling length and the clump diameter. Thus, as cooling strength increases (decreasing cooling length), the size of the Mach stem should decrease.

Here are the important parameters: 

vs = 50 km/s
M = 5.2
T = 8322.56 K
nclump/namb = 5000
tfinal = 100 yrs
Rclump = 10 AU
dcool / Rclump Ambient Density [cm-3] d / Rclump Cooling Run Effective Gamma Run
30 3.18 5 1.46
10 9.77 4 1.25
3 33.95 3 1.19
1 108.21 2.4 1.14
0.3 388.55 unstable ⇐ 1.10
0.1 1252.4 unstable ⇐ 1.10

Then, there are 5 more runs with M = 30 and T = 250.047 K.

dcool / Rclump Ambient Density [cm-3] d / Rclump Cooling Run Effective Gamma Run
30 3.634 5 1.50
10 11.16 4 1.30
3 38.76 3 1.18 No image "M30_dcool30_g1.18.png" attached to Blog: Mach Stems: Cooling Strength ==> Effective Gamma
1 123.30 unstable ⇐ 1.10

The effect of cooling is stronger than I had anticipated, and I'm not sure if we can use Pat's figure from his recent Mach stem paper to make quantitative comparisons. However, qualitatively, we are already proving our point, and more simulations with lowered gamma instead of cooling can lead to values for effective gamma.

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