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Initial Comparison of LS and an NSE EOS




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Contact: F.X.Timmes
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Mass fraction of alpha particles:
The abundances of neutrons, protons, and alpha particles is probably the fundamental quantities to focus on as the thermodynamic variables will more-or-less follow the composition.

image
Alpha wall from NSE (fxt)
image
Alpha wall from NSE (meyer)
image
Alpha wall from LS

The differences between the two NSE calculations (fxt and brad meyer) at temperatures of 1012 K is understood; different extrapolations procedures are used for temperatures larger than where the tabulated data runs out. The alpha wall from the LS EOS is shorter, not as thick, and in a a slightly location. The incipient proto-neutron star lives in the lower right where heavy nuclei live. When the shock wave passes the material climbs the alpha wall, ending in the region in the upper left where alpha-particles, neutrons and protons live.

Mass fraction of neutron and protons:

image
Neutrons from NSE
image
Neutrons from LS
image
Protons from NSE
image
Protons from LS

Since the NSE + stellar EOS and the LS EOS basically agree in the neutron and proton abundances, this might be telling us that the problem isn't in the neutron and proton chemical potentials. The alpha-particle plots above then seem to suggest that the LS EOS isn't quite hitting the right average charge, zbar, in regions where NSE should be a good approximation.

Entropy Differences:

image
Entropy (LS - NSE)
This plot shows that the LS EOS and the NSE + stellar EOS can differ by as much as 30%. Red contours indicate regions where LS gives more entropy, while black indicates regionsindicate regions where NSE gives more entropy. The green contour at 0% is where they two equations of state agree. Are these 30% differences in the entropy significant in a core-collapse calculation?