Tracking Ionized Sulfur Species
See ticket #433 for a brief description.
I found recombination rates from Nahar 1996. There is a nice table with many more species that could potentially be used in the future.
Ionization rates were a bit more complicated. I used Arnaud & Rothenflug 1985. They give some complicated formulas for the rates of several species. Again, the other species could be implemented in the future. I wrote a separate fortran program which uses these formulas to generate a table of ionization rates. The generated table is in a format that is compatible with astrobear's table and chemistry routines.
I tested my program with H ionization, and I was able to recover the table that we currently use in astrobear. This program is so useful that I'm going to check it into the main repo so that we can use it in the future for other species.
Here are the ionization rates for SII and SIII. The x-axis is log(T) and the y-axis is the rate in units of 10-9cm3s-1.
These follow a trend that is common to ionization rates, and it makes sense that SIII peaks at a higher T than SII. The peaks don't seem that far apart because the ionization potentials (23.4 and 35 eV) are pretty close in log(T) space. Below are the recombination rates for SIV and SIII. Same units as above except the rates are in log space now.
These were straight from a table, no calculations necessary which is quite convenient. Makes sense that SIV recombination rates are a bit higher since it should be harder to ionize SIIII / easier to recombine SIV. This is consistent with the ionization rates as well.
Jets
I tested the implementation with a low resolution, non-MHD, pulsed jet. Below are plots of SII, SIII, and SIV density (from left to right in computational units).
The plot makes sense qualitatively. SII peaks inside the clumps, aka cooling regions. SIII peaks at the edges of clumps and on the wings, aka shocks. There seems to only be SIV on the spur shocks where it is hot enough. I did find a typo in the SIV recombination table which was extremely high at one data point, so there's a chance that the SIV density should be slightly higher but I think it still looks good. We didn't expect much SIV anyways.
Despite that faulty data point, I think it is fair to say that sulfur tracking is working properly. The emission maps should not have changed much, since all I had to do was multiply the output by SII/Stot where Stot = SII + SIII + SIV. The emission maps really need higher resolution to be accurate, so there's no sense in looking at the ones from this run. I am going to set up production runs now.
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