This program calculates the time-dependent molar abundances Y_i of the
13 isotopes involved in the CNO cycle. It's a work in progress, and
I'm still learning so some of it may be wrong (the beta-decay stuff in
particular)...
Nuclear network ODEs are notoriously stiff, meaning different isotopes
change on enormously different time scales. Resolving these changes
without integrating over stupidly small intervals is
challenging. Fortunately some very smart numerical analysts have
solved these sorts of problems for us.
This program integrates the network ODEs using the implicit
Bulirsch-Stoer method of Bader-Deuflhard, which is built into the GNU
Scientific Library. (See "Numerical Recipes" for detailed descriptions
of these algorithms.) The NR collection also comes with a
Bulirsch-Stoer algorithm but the NR license sucks and one cannot
legally publish the source code or any modification thereof, even
though uploaded copies of the entire NR source (both Fortran and C
versions) are laughably easy to find.
I've not tested this code extensively except in Solar-ish
environments. For reasonable results try a temperature of 15 MK and a
density of 150 g/cm^3. The initial abundances should be mostly
hydrogen, with at least a tiny bit of C12. (In an earlier version of
this code I spent 2 full days trying to figure out why my abundances
never changed over any amount of time. Turns out my initial C12
abundances was 0. Derp.) You should see the abundances change on
timescales of ~ Gyr. These are roughly the lifetimes of stars on the
main sequence so it makes sense that the initial hydrogen depletes
over this amount of time.
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DEPENDENCIES
1.) GNU Scientific Library (v1.15)
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REFERENCES
1.) F. X. Timmes 1999 ApJS 124 241 (doi:10.1086/313257)
2.) Press, W. H. et al. "Numerical Recipes: The Art of Scientific Computing."
3rd ed. Cambridge UP, 2007. (ISBN-10: 0521884071; ISBN-13: 978-0521884075)
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