Nuclear equation of state for supernovae and neutron stars

Transcription

1 Nuclear equation of state for supernovae and neutron stars H. Shen Nankai University, Tianjin, China 申虹 In collaboration with 南開大学 天津 H. Toki RCNP, Osaka University, Japan 中国 K. Sumiyoshi Numazu College of Technology, Japan K. Oyamatsu Aichi Shukutoku University, Japan Z. W. Zhang Nankai University, Tianjin, China S. S. Bao Nankai University, Tianjin, China QCS2014 Beijing, China, Oct , 2014

2 Contents Introduction Models used for EOS New version of EOS tables hyperon effects EOS for neutron stars Summary

3 Introduction nuclear physics astrophysics unstable nuclei equation of state What is the status of EOS? supernova explosion proton-neutron star cooling neutron star properties. neutron star matter: charge neutrality; equilibrium; T~0 supernova matter: charge neutrality; fixed fractions; T0 For neutron stars, there are many EOS s, but For supernovae, there are only a few EOS s available

4 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

5 Models used for EOS at high density uniform matter proton neutron electron RMF (relativistic Mean Field) non-uniform matter at low density RMF + Thomas-Fermi approximation. nuclei alpha proton neutron electron

6 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)...

7 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

8 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

9 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

10 Relativistic Mean Field Theory Lagrangian a L[ i M g g g ] m g g WW m c3( ) a a 1 2 a a R R m TM1 parameter set a Lagrangian Equations Mean-Field Approximation Calculate everything such as, p, s...

11 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

12 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. A 637 (1998) 435

13 Check the parameterization Self-consistent Thomas-Fermi approximation Lagrangian Equations 1 LRMF i M g g g e A ( ) m g2 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. n n M M g p vp ggea v g g

14 Self-consistent Thomas-Fermi approximation Z. W. Zhang, H. Shen, Astrophys. J. 788 (2014) 185

15 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. 197 (2011) 20 EOS3 (2010-version, nucleon Shen, Toki, Oyamatsu, Sumiyoshi, Astrophys. J. Suppl. 197 (2011)

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17 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

18 Phase diagrams H.Shen, H.Toki, K.Oyamatsu, K.Sumiyoshi, Astrophys. J. Suppl. 197 (2011) 20

19 Distributions in non-uniform matter

20 Heavy nuclei in non-uniform matter

21 Fractions of components with hyperons

22 Effects of hyperons non-nucleonic degrees of freedom hyperons: boson condensates: quarks: u, d, s

23 EOS for supernovae with hyperons C. Ishizuka, A. Ohnishi, K. Tsubakihara, K. Sumiyoshi, S. Yamada, J. Phys. G 35 (2008)

24 Pion condensate

25 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

26 Hypernuclear Chart O. Hashimoto, H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) 564

27 Hypernuclei in the RMF model Single- hypernuclei H. Shen, F. Yang, H. Toki, Prog. Theor. Phys. 115 (2006) 325

28 Hypernuclei in the RMF model Double- hypernuclei H. Shen, F. Yang, H. Toki, Prog. Theor. Phys. 115 (2006) 325

29 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)

30 Effects of hyperons EOS2 EOS3

31 EOS for neutron stars F. Weber, Prog. Part. Nucl. Phys. 54 (2005) 193 Nature Science J. M. Lattimer, Annu. Rev. Nucl. Part. Sci. 62 (2012) 485

32 Neutron star properties LS180 Skyrme K=180 Esym=29.3 HShen RMF TM1 K=281 Esym=36.1 GShen RMF NL3 K=272 Esym=37.4 FSU1.7 RMF K=230 Esym=32.6

33 EOS for neutron stars T 0, ~ g/cm non-uniform matter e+a e+n+a 410 g/cm /3 uniform matter (e,) + (n,p) hyperons quarks... N. Chamel, P. Haensel Living Rev. Relativity 11 (2008) 10 H. Shen, PRC 65 (2002) M. Okamoto, T. Maruyama, K. Yabana, T. Tatsumi, PRC 88 (2013)

34 Can hyperons exist in neutron stars? RMF GM1 K=300 Esym=32.5 U U U Model: σωρ Model: σωρϕ Y. N. Wang, H. Shen, PRC 81 (2010) M max 1.70 M M max 2.18 M 50 L M 2.18 max ( ss ) m 1020 MeV S. Weissenborn, D. Chatterjee, J. Schaffner-Bielich, NPA 881 (2012) 62

35 Can quarks exist in neutron stars? RMF model + MIT bag model K. Schertler, C. Greiner, J. Schaffner-Bielich, M. Thoma, NPA 677 (2000) 463

36 Can quarks exist in neutron stars? K. Schertler, C. Greiner, J. Schaffner-Bielich, M. Thoma, NPA 677 (2000) 463

37 Can quarks exist in neutron stars? RMF model + NJL model TM1: no mixed phase no quark phase NL3: has mixed phase no quark phase F. Yang, H. Shen, PRC 77 (2008)

38 Summary Relativity is important at high density Several EOS tables are available Hyperons and quarks can soften EOS Exotic phases are quite uncertain

39 Thank you!