Relativistic EOS for Supernova Simulations
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1 Relativistic EOS for Supernova Simulations H. Shen Nankai University, Tianjin, China 申虹 In collaboration with H. Toki RCNP, Osaka University, Japan K. Sumiyoshi Numazu College of Technology, Japan K. Oyamatsu W. Wen 南開大学 天津 Aichi Shukutoku University, Japan Nankai University, Tianjin, China Y. N. Wang Nankai University, Tianjin, China 中国
2 Contents Introduction Models used for EOS New version of EOS tables hyperon effects Summary
3 Introduction nuclear physics astrophysics unstable nuclei equation of state supernova explosion proton-neutron star cooling neutron star properties. neutron star matter: charge neutrality; equilibrium; T~0 supernova matter: charge neutrality; fixed fractions; T0 What is the situation about EOS?
4
5 EOS for supernova simulations nonrelativistic EOS (compressible liquid-drop) Lattimer, Swesty, Nucl. Phys. A 535 (1991) 331 relativistic EOS (RMF + Thomas-Fermi) Shen, Toki, Oyamatsu, Sumiyoshi, Nucl. Phys. A 637 (1998) 435 relativistic EOS (RMF) G. Shen, Horowitz, Teige, Phys. Rev. C 82 (2010) EOS (nuclear statistical equilibrium) Hempel, Schaffner-Bielich, Nucl. Phys. A 837 (2010) 210
6 EOS for supernovae wide range temperature (T): 0 ~ 100 MeV proton fraction (Yp): 0 ~ 0.6 Temperature density ( B ): 10 5 ~ g/cm 3 Nuclei Density
7 Models used for EOS uniform matter at high density. proton neutron electron RMF (relativistic Mean Field) non-uniform matter at low density RMF + Thomas-Fermi approximation. nuclei alpha proton neutron electron
8 Why prefer the RMF theory? nuclear many-body methods nonrelativistic relativistic Shell Model Skyrme-Hartree-Fock (SHF) Brueckner-Hartree-Fock (BHF)... Relativistic Mean-Field (RMF) Relativistic Hartree-Fock (RHF) Relativistic Brueckner-Hartree-Fock (RBHF)...
9 Relativity is important! natural explanation of spin-orbit force RBHF BHF natural explanation of three-body force good saturation of nuclear matter relativity Brockmann, Machleidt, Phys. Rev. C 42 (1990) 1965
10 What is the RMF theory? Relativistic Mean Field Theory (RMF),, mean-field approximation: meson field operators are replaced by their expectation values no-sea approximation: contributions from the negative-energy Dirac sea are ignored Applications infinite matter: finite system: flavor SU(2) flavor SU(3) nuclear matter strange hadronic matter nuclei hypernuclei
11 Comparison with nuclear data 2157 nuclei n i i M 2 theo Mexpt i1 2.1 n L.S.Geng, H.Toki, J.Meng, Prog. Theor. Phys. 113 (2005) 785
12 Relativistic Mean Field Theory Lagrangian a L [ i M g g g ] m g g W W m c3 ( ) a a 1 2 a a R R m 4 2 TM1 parameter set a Lagrangian Equations Mean-Field Approximation Calculate everything such as, ps,...
13 Thomas-Fermi approximation * body-centered cubic lattice * parameterized nucleon distribution * RMF input E Ebulk Esurface ECoulomb ELattice Eelectron assume states minimize free energy favorable state
14 Thomas-Fermi approximation parameterized nucleon distribution n i 3 t in out i out ni n i 1 ni, 0r Ri out n, R r R r R i r i i cell H.Shen, H.Toki, K.Oyamatsu, K.Sumiyoshi, Nucl. Phys. A637 (1998) 435
15 Check the parameterization Self-consistent Thomas-Fermi approximation Lagrangian Equations 1 LRMF i M g g g e A ( ) m g 2 g ( ) m c ( ) m ( A) i m ea l 0 l l l m g g g, m g c s v 3, 2 p n g v v, m A e p v l v. b b F b v k U M M M g b 31 U g g e A v 3 2
16 Self-consistent Thomas-Fermi approximation
17 New version of EOS tables EOS1 (1998-version, nucleon) Shen, Toki, Oyamatsu, Sumiyoshi, Prog. Theor. Phys. 100 (1998) 1013 EOS2 (2010-version, nucleon) Shen, Toki, Oyamatsu, Sumiyoshi, Astrophys. J. Suppl. (2011) in press EOS3 (2010-version, nucleon Shen, Toki, Oyamatsu, Sumiyoshi, Astrophys. J. Suppl. (2011) in press
18 Comparison between EOS tables T number of points is increased; upper limit is extended; equal grid is used Yp linear grid is used; upper limit is extended B upper limit is extended; equal grid is used
19 Phase diagrams
20 Distributions in non-uniform matter
21 Heavy nuclei in non-uniform matter
22 Fractions of components with hyperons
23 Effects of hyperons non-nucleonic degrees of freedom hyperons: boson condensates: quarks: u, d, s
24 EOS for supernovae with hyperons C. Ishizuka, A. Ohnishi, K. Tsubakihara, K. Sumiyoshi, S. Yamada, J. Phys. G 35 (2008)
25 Pion condensate
26 Experimental information scattering experiments hypernuclear data NN scattering data > 4000 YN scattering data ~ 40 no YY scattering data single- hypernuclei > 30 double- hypernuclei ~ 4 single-hypernuclei ~ 1
27 Hypernuclear Chart O. Hashimoto, H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) 564
28 Neutron star matter with hyperons include baryon octet -,,,, n p,,, 0-0 U U U U N N N 30 MeV 30 MeV 15 MeV 5 MeV??? Y.N.Wang, H.Shen, Phys. Rev. C 81 (2010)
29 Hypernuclei in the RMF model Single- hypernuclei H.Shen, F.Yang, H.Toki, Prog. Theor. Phys. 115 (2006) 325
30 Hypernuclei in the RMF model Double- hypernuclei H.Shen, F.Yang, H.Toki, Prog. Theor. Phys. 115 (2006) 325
31 Effects of hyperons EOS2 EOS3
32 Summary Relativity is important at high density New versions of EOS tables are available EOS2, EOS3 hyperon can soften EOS at high density Exotic phases are quite uncertain
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