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Internal Energy from the LS and an NSE EOS




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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

The electron-positron portion of the two equations of state are identical. Differences between the two EOS routines originate from the model used for nucleons (interacting nucleons in a liquid dropish model versus non-interacting Boltzmann nucleons), and the model used for the composition.

LS Baryon Internal Energy:
image
Baryon internal energy Ye=0.5
image
Baryon internal energy Ye=0.4
image
Baryon internal energy Ye=0.3
image
Baryon internal energy Ye=0.2


In certain regions of the rho-T plane, the internal energy contributions from baryons are negative. In fact, they are so large that they overwhelm the electron-positron contribution, making the total internal energy negative. This is not a good thing. There are some ideas floating about that the negativity is "simply" a different choice of the "zero-point energy", the rest mass energy of a free neutron in LS, and (perhaps) the unexcited C12 nucleus (zero mass excess) in NSE.

LS Total Internal Energy:
image
Total internal energy Ye=0.5
image
Total internal energy Ye=0.4
image
Total internal energy Ye=0.3
image
Total internal energy Ye=0.2


NSE Baryon Internal Energy:
image
Baryon internal energy Ye=0.5
image
Baryon internal energy Ye=0.4
image
Baryon internal energy Ye=0.3
image
Baryon internal energy Ye=0.2


Even though the baryons in the NSE-based model are a perfect gas, the surface isn't planar because of the changing composition. This causes the ripples in the surface. Note the internal energy is never negative :)

NSE Total Internal Energy:
image
Total internal energy Ye=0.5
image
Total internal energy Ye=0.4
image
Total internal energy Ye=0.3
image
Total internal energy Ye=0.2


LS and NSE Internal Energies Compared:
image
Internal energy Ye=0.5
image
Internal energy Ye=0.4
image
Internal energy Ye=0.3
image
Internal energy Ye=0.2


image
Internal energy differences Ye=0.5
image
Internal energy differences Ye=0.4
image
Internal energy differences Ye=0.3
image
Internal energy differences Ye=0.2