Cococubed.com Internal Energy from the LS and an NSE EOS
Home Astronomy research Software instruments    Stellar equation of states    EOS with ionization    EOS for supernovae    Chemical potentials    Stellar atmospheres    Voigt Function    Jeans escape    Polytropic stars    Cold white dwarfs    Hotter white dwarfs    Cold neutron stars    Stellar opacities    Neutrino energy loss rates    Ephemeris routines    Fermi-Dirac functions    Galactic chemical evolution    Coating an ellipsoid    Universal two-body problem    Nuclear reaction networks    Nuclear statistical equilibrium    Laminar deflagrations    CJ detonations    ZND detonations    Fitting to conic sections    Unusual linear algebra    Derivatives on uneven grids    Pentadiagonal solver    Quadratics, Cubics, Quartics    Supernova light curves    Exact Riemann solutions    1D PPM hydrodynamics    Verification problems    Plane - cube Intersection    Phyllotaxis    The pendulum    Circular and elliptical 3 body    MESA    MESA-Web    FLASH    Zingale's software    Brown's dStar    GR1D code    Iliadis' STARLIB database    Herwig's NuGRID    Meyer's NetNuc Presentations Illustrations Videos Bicycle adventures AAS Journals 2019 JINA R-process Workshop 2019 MESA Marketplace 2019 MESA Summer School 2019 AST111 Earned Admission Teaching materials Education and Public Outreach 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: 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 Internal energy differences Ye=0.5 Internal energy differences Ye=0.4 Internal energy differences Ye=0.3 Internal energy differences Ye=0.2