pre-run analysis for 3D cooling jets

Cooling Length

I've been following this Blondin paper to prepare for the 3D cooling jet simulations. ​http://adsabs.harvard.edu/abs/1990ApJ...360..370B. Section III is especially important because this is where the cooling length is defined. The analytic expression is there, but for analysis Blondin uses the numerical approximation from 1D simulations. I am therefore using my 1D radiative shock module to come up with my own formula for the cooling length.

Blondin's cooling length formula is going to be different because he did not use the DM curve. His cooling curve is based on a nonequilibrium ionization calculation by Kafatos (1973). Hartigan, Raymond, and Hartmann (1987) also have a different cooling curve and therefore a different cooling length formula. Blondin's is proportional to vs4 and Hartigan's is proportional to vs4.67.

The goal is to get a formula such that where dcool is the cooling length, na is the ambient number density, and vs is the shock velocity. b and a are the free parameters to be solved for. The formulas from Blondin and Hartigan do not match my data very well.

Source b (1016) a Sum of Error2
Blondin 4.5 4 125.96
Hartigan 1.80 4.67 121.39
Mine 3.51 3.2 10.42

Here, vs is in units of 100 km/s to give dcool in cm. Obviously, my formula is going to do the best because it's based on my data.

It is also important to note that the cooling lengths that I am calculating use a floor temperature of 8000 K just like Blondin. Hartigan's cooling length allows for cooling down to 1000 K.

Cooling Strength

Now, the cooling strength can be defined as: where rj is the jet radius, vj is the jet velocity, and is the density contrast (jet/ambient). The idea is to keep rj, vj, and na fixed. Then, you change the jet density and therefore changing in order to test different cooling strengths.

For some reason, I cannot reproduce the chi's that are reported in the Blondin paper. I've looked over my work several times, and I cannot find any errors. Maybe the paper has a calculational error or a typo somewhere. When I calculate chi for their "standard run" using their formula I get 0.27, but they claim that it should be 0.55. Not sure whether I should ignore the discrepancy and just do my own calculations, or if this needs to be resolved before moving on.

UPDATE

After doing more calculations for different sets of parameters, I realized that all of my cooling strengths were exactly ½ of the cooling strengths in the Blondin paper. It seems that Blondin either forgot a factor of 2 in their formula for chi, or all of their cooling strengths should really be ½ of what they reported.

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