Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

2.52SGIISkkT8SkMSkT1SkT1sSkT2SkT3SkT3sSkT7SkT8SkT9M=1.95M ( M O•)1.510.507 8 9 10 11 12 13 14 15R ( km )Figure 6.4: This figure shows the Skyrme force models which cannot produce a 1.97M ⊙neutron star.final candidates for the nuclear force model of EOS table. Fig.6.5 shows the Skyrme forcemodels which have too large radii for a given mass of neutron stars. Mathematically, thesehappen because of large L so it should be emphasized that L is another important nuclearconstant which should be extracted from nuclear experiments or astrophysical observations.Of all three tests, we can see that SLy0, ... , SLy10, and our FRTF I, II, Gaussian modelsare good enough to be used as a nuclear force model. Fig.6.6 shows the mass and radiusrelation of Skyrme force models and our finite range force models, which are suitable formake an EOS table.We did not take a test with any relativistic mean field models † , since they usually have largeL so they cannot make allowed regions of mass and radius in neutron stars.To summarize (Appendix E), the nuclear force models which pass the 3 tests would haveS v ≃ 32 MeV, L ≃ 46 MeV, K ≃ 230 MeV, and ρ o ≃ 0.16fm −3 .6.4 Free energyThe fundamental idea of making an EOS table is to minimize free energy or free energydensity for a given ρ, T, and Y p . In the Liquid Droplet approach, the free energy in theWigner-Seitz cell consists of the contributions from finite nuclei and nucleons outside finitenuclei. Fig. 6.7 shows the schematic picture inside the Wigner-Seitz cell. The heavy nuclei isin phase equilibrium with nucleons and alpha particles outside. The free energy per baryoncontribution from heavy nuclei can be divided into,f N = f bulk +f Coul +f surf +f trans (6.14)† The R 1.4M⊙ ∝ L 1/4 so RMF cannot make the allowed region.88