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| Internal Energy from the LS and an NSE EOS |
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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:
Baryon internal energy Ye=0.5 |
Baryon internal energy Ye=0.4 |
Baryon internal energy Ye=0.3 |
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:
Total internal energy Ye=0.5 |
Total internal energy Ye=0.4 |
Total internal energy Ye=0.3 |
Total internal energy Ye=0.2 |
NSE Baryon Internal Energy:
Baryon internal energy Ye=0.5 |
Baryon internal energy Ye=0.4 |
Baryon internal energy Ye=0.3 |
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:
Total internal energy Ye=0.5 |
Total internal energy Ye=0.4 |
Total internal energy Ye=0.3 |
Total internal energy Ye=0.2 |
LS and NSE Internal Energies Compared:
Internal energy Ye=0.5 |
Internal energy Ye=0.4 |
Internal energy Ye=0.3 |
Internal energy Ye=0.2 |
In some regions the agreement between LS and NSE is pretty good, in other regions its not too good at all, and in regions where LS predicts a negative energy the agreement is ... well ... horrible.
Internal energy differences Ye=0.5 |
Internal energy differences Ye=0.4 |
Internal energy differences Ye=0.3 |
Internal energy differences Ye=0.2 |