Equation of state for supernovae and neutron stars

Transcription

1 Equation of state for supernovae and neutron stars H. Shen Nankai University, Tianjin, China 申虹南開大学天津中国 In collaboration with H. Toki RCNP, Osaka University, Japan K. Sumiyoshi Numazu College of Technology, Japan K. Oyamatsu Aichi Shukutoku University, Japan Z. W. Zhang Shanghai Jiao Tong University, China S. S. Bao Nankai University, Tianjin, China X. H. Wu Nankai University, Tianjin, China

2 Contents Introduction Models used for EOS Several versions of EOS tables Λ hyperon effects Symmetry energy and finite size 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 Lattimer-Swesty EOS, H. Shen EOS, G. Shen EOS, Hempel EOS

4 EOS for supernovae single nucleus approximation J. M. Lattimer and F. D. Swesty, Nucl. Phys. A 535, 331 (1991) liquid-drop model with Skyrme force H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, Prog. Theor. Phys. 100, 1013 (1998) H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, Astrophys. J. Suppl. 197, 20 (2011) Thomas-Fermi with RMF (TM1) G. Shen, C. J. Horowitz, S. Teige, Phys. Rev. C 83, (2011) Hartree calculation with RMF (NL3) nuclear statistical equilibrium M. Hempel and J. Schaffner-Bielich, Nucl. Phys. A 837, 210 (2010) A.S. Botvina, I.N. Mishustin, Nucl. Phys. A 843, 98 (2010) S. Furusawa, K. Sumiyoshi, S. Yamada, H. Suzuki, Astrophys. J. 772, 95 (2013) S. Typel, G. Ropke, T. Klahn, D. Blaschke, H. Wolter, Phys. Rev. C 81, (2010)

5 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

6 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

7 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)...

8 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

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 a 1 W W 1 m 1 c ( ) a a 1 2 a a R R m TM1 parameter set 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) l i m ea 0 l l l m g g g, s 2 3 m g c, 2 3 v 3 m g 2 p v p v A e l v n v., p n n p M M g v g g ea 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 by K.Sumiyoshi

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

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

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

30 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)

31 Effects of hyperons EOS2 EOS3

32 symmetry energy and finite size effects liquid-gas phase transition in supernova matter * * * * * spinodal instability (no surface and Coulomb) determined by the curvature of the free energy bulk calculation (no surface and Coulomb) phase equilibrium determined by the Gibbs conditions coexisting phases (CP) (surface and Coulomb perturbatively) phase equilibrium determined by the Gibbs conditions compressible liquid-drop (CLD) (minimization of free energy) phase equilibrium determined by minimization Thomas-Fermi (TF) (realistic description)

33 S. S. Bao and H. Shen, Phys. Rev. C9 3 (2016) symmetry energy and finite size effects Esym=36.9 L=110.8 Esym=31.3 L=47.2

34 symmetry energy and finite size effects S. S. Bao and H. Shen, Phys. Rev. C9 3 (2016)

35 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

36 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

37 EOS for neutron stars T 0, ~ g/cm non-uniform matter e+a e+n+a g/cm g/cm 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)

38 Symmetry energy pasta phases; crust-core K. Oyamatsu, K. Iida, Phys. Rev. C 75, (2007) B. A. Li, L. W. Chen, C. M. Ko, Phys. Rep. 464, 113 (2008) F. Grill, C. Providência, S. S. Avancini, Phys. Rev. C 85, (2012) Z. Zhang, L. W. Chen, Phys. Lett. B 726, 234 (2013) S. S. Bao, H. Shen, Phys. Rev. C 89, (2014) S. S. Bao, J. N. Hu, Z. W. Zhang, H. Shen, Phys. Rev. C 90, (2014) S. S. Bao, H. Shen, Phys. Rev. C 91, (2015) adjust g V fix symmetry energy at 0.11 fm 3 different symmetry energy slope L saturation property neutron star mass ~2 M finite nuclei TM1 set IUFSU set

39 S. S. Bao, H. Shen, Phys. Rev. C 91, (2015) symmetry energy size of Wigner-Seitz cell size of pasta structure

40 Phase diagram of inner crust smaller L corresponds to more pasta phases smaller L corresponds to larger crust-core transition density

41 distributions of neutrons and protons neutron proton L=110 MeV neutron proton L=47.2 MeV self-consistent Thomas-Fermi with the IUFSU model

42 Crust-core transition transition density proton fraction

43 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

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

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

46 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)

47 finite size effects on hadron-quark phase transition X. H. Wu and H. Shen, in preparation

48 Summary Relativity is important at high density Several EOS tables are available Hyperons and quarks can soften EOS Phase transition depends on symmetry energy Exotic phases are quite uncertain

49 Thank you!