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The Nuclear Symmetry Energy and Properties of Neutron Stars

The Nuclear Symmetry Energy and Properties of Neutron Stars. Collaborators ： Wei-Zhou Jiang (SEU) Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce) Hong-Ru Ma (SJTU) Gao-Chan Yong (IMP,CAS) De-Hua Wen (SCUT) Zhi-Gang Xiao and Ming Zhang (Tsinghua U)

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The Nuclear Symmetry Energy and Properties of Neutron Stars

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  1. The Nuclear Symmetry Energy and Properties of Neutron Stars Collaborators： Wei-Zhou Jiang (SEU) Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce) Hong-Ru Ma (SJTU) Gao-Chan Yong (IMP,CAS) De-Hua Wen (SCUT) Zhi-Gang Xiao and Ming Zhang (Tsinghua U) Bao-Jun Cai, Rong Chen, Peng-Cheng Chu, Zhen Zhang(SJTU) Lie-Wen Chen (陈列文) (Department of Physicsa and INPAC, Shanghai Jiao Tong University. lwchen@sjtu.edu.cn) 十三届全国中高能核物理大会暨第七届全国中高能核物理专题研讨会, 2009年11月5-7日，中国科学技术大学，合肥，中国

  2. Outline • The nuclear symmetry energy • Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions • The nuclear symmetry energy and neutron stars • Summary and outlook Main References: L.W. Chen, C.M. Ko, B.A. Li, and G.C. Yong, Front. Phys. China 2(3), 327 (2007) [arXiv:0704.2340] B.A. Li, L.W. Chen, and C.M. Ko, Phys. Rep. 464, 113-281 (2008) [arXiv:0804.3580] J. Xu, L.W. Chen, B.A. Li, and H.R. Ma, Phys. Rev. C 79, 035802 (2009) [arXiv:0807.4477] J. Xu, L.W. Chen, B.A. Li, and H.R. Ma, Astrophys. J.697, 1549-1568 (2009) [arXiv:0901.2309] Z.G. Xiao, B.A. Li, L.W. Chen,G.C. Yong, and M. Zhang, Phys. Rev. Lett. 102, 062502 (2009) D.H. Wen, B.A. Li, and L.W. Chen,Phys. Rev. Lett., in press[arXiv:0908.1922]

  3. (Isospin) Symmetry energy term Symmetry energy including surface diffusion effects (ys=Sv/Ss) The Nuclear Symmetry Energy Liquid-drop model W. D. Myers, W.J. Swiatecki, P. Danielewicz, P. Van Isacker, A. E. L. Dieperink,……

  4. The Nuclear Symmetry Energy Symmetric Nuclear Matter (relatively well-determined) Symmetry energy term (poorly known) The Nuclear Matter Symmetry Energy (Parabolic law) EOS of Isospin Asymmetric Nuclear Matter

  5. K0=231±5 MeV PRL82, 691 (1999) Recent results: K0=240±20 MeV G. Colo et al. U. Garg et al. __ Equation of State of symmetric nuclear matter is relatively well determined (1) EOS of symmetric matter around the saturation density ρ0 Giant Monopole Resonance

  6. Equation of State of symmetric nuclear matter is relatively well determined (2) EOS of symmetric matter for 1ρ0< ρ < 3ρ0 from K+ production in HIC’s J. Aichelin and C.M. Ko, PRL55, (1985) 2661 C. Fuchs, Prog. Part. Nucl. Phys. 56, (2006) 1 C. Fuchs et al, PRL86, (2001) 1974 Transport calculations indicate that “results for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenario with a soft EOS.” See also: C. Hartnack, H. Oeschler, and J. Aichelin, PRL96, 012302 (2006)

  7. Use constrained mean fields to predict the EOS for symmetric matter Width of pressure domain reflects uncertainties in comparison and of assumed momentum dependence. The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions High density nuclear matter 2 to 5ρ0 Equation of State of symmetric nuclear matter is relatively well determined (3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0< ρ < 5ρ0 using flow data from BEVALAC, SIS/GSI and AGS P. Danielewicz, R. Lacey and W.G. Lynch,Science 298, 1592 (2002)

  8. On Earth!!! Transport Theory In Heaven!!! General Relativity EOS for Asymmetric Nuclear Matter Isospin Effects in HIC’s … Neutron Stars … Many-Body Theory Nuclear Force Many-Body Theory Structures of Radioactive Nuclei, SHE … Isospin Physics with Heavy-Ion Collisions HIC’s induced by neutron-rich nuclei (CSR/Lanzhou,FRIB,GSI, RIKEN……) Most uncertain property of an asymmetric nuclear matter Density Dependence of the Nuclear Symmetry Energy Isospin Nuclear Physics What is the isospin dependence of the in-medium nuclear effective interactions??? Most recent review (169 pages): Bao-An Li, Lie-Wen Chen, and Che Ming Ko, Physics Reports 464, 113-281 (2008)

  9. The Symmetry Energy The multifaceted influence of the nuclear symmetry energyA.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005). Isospin physics

  10. LHC Deconfinement Chiral symmetry restoration Hadron gas Nucleon gas Liquid isospin Science 312, 190 (2006) QCD Phase Diagram

  11. 104 GSI 103 CSR/HIRFL RIKEN E (MeV/u) NSCL/MSU 102 GANIL 10 HIRFL 1 200 250 50 150 300 100 A Heavy-Ion Accelerator Facilities • HIRFL, CSR/HIRFL (China) • GANIL (France) • GSI (Germany) • NSCL/MSU,FRIB/MSU • RIKEN (Japan) Medium Energy HI Accelerator Facilities Dubna, LBL, ORNL, TAMU, INFN, KVI,… High Energy HI Accelerator Facilities: AGS,RHIC/BNL SPS,LHC/CERN

  12. Nuclear Matter EOS: Many-Body Approaches • Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Green’s Function (SCGF) Theory Variational Many-Body (VMB) approach …… • Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) …… • Phenomenological Approaches Relativistic mean-field (RMF) theory • Relativistic Hartree-Fock (RHF) • Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations • Phenomenological potential models ……

  13. Z.H. Li et al., PRC74, 047304(2006) Dieperink et al., PRC68, 064307(2003) Chen/Ko/Li, PRC72, 064309(2005) Chen/Ko/Li, PRC76, 054316(2007) BHF The Nuclear matter symmetry energy

  14. Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list !)

  15. Transport model for HIC’s Isospin-dependent BUU (IBUU) model • Solve the Boltzmann equation using test particle method • Isospin-dependent initialization • Isospin- (momentum-) dependent mean field potential • Isospin-dependent N-N cross sections • a. Experimental free space N-N cross section σexp • b. In-medium N-N cross section from the Dirac-Brueckner • approach based on Bonn A potential σin-medium • c. Mean-field consistent cross section due to m* • Isospin-dependent Pauli Blocking EOS

  16. Transport model: IBUU04 Isospin- and momentum-dependent potential (MDI) Das/Das Gupta/Gale/Li, PRC67,034611 (2003) Chen/Ko/Li, PRL94,032701(2005) Li/Chen, PRC72, 064611 (2005)

  17. Symmetry Energy at Sub-saturation Densities (Subsaturation：0.2-0.3<ρ/ρ0<1.2) Chen/Ko/Li, PRL 94, 032701 (2005) Tsang et al., PRL 102, 122701 (2009) (ImQMD) (IBUU04) X=-1

  18. Symmetry energy at High Densities IBUU04, Xiao/Li/Chen/Yong/Zhang, PRL102, 062502(2009) A Supersoft Esym at supra-saturation densities !!! M. Zhang et al., PRC80,034616(2009)

  19. The Nuclear Symmetry Energy and Neutron Stars Lattimer/Prakash, Science 304, 536 (2004) core-crust transition • Neutron star has solid crust over liquid core. • Rotational glitches: small changes in period from sudden unpinning of superfluid vortices. • Evidence for solid crust. • 1.4% of Vela moment of inertia glitches. • Needs to know the transition density to calculate the fractional moment of inertia of the crust Link et al., PRL83,3362(99)

  20. Onset of instability in the uniform n+p+e matter 2. Thermodynamic approach 1. Dynamical approach k0 (neglecting Coul.) If one uses the parabolic approximation (PA) Stability condition: Then the stability condition is: >0 Or , similarly one can use 3. the RPA

  21. Core-Crust Transition Density: Parabolic Law fails! Xu/Chen/Li/Ma, PRC79, 035802 (2009) • It is NOT enough to know the symmetry energy, • one almost has to know the exact EOS of n-rich matter Why? Because it is the determinant of the curvature matrix that determines the stability condition Example: Higher-order term effects on direct URCA Zhang/Chen, CPL 18 (2000) 142 Steiner, Phys.Rev. C74 (2006) 045808 Not so surprise:

  22. (2) Locating the inner edge of neutron star crust pasta Significantly less than their fiducial values: ρt=0.07-0.08 fm-3 and Pt=0.65 MeV/fm3 Xu/Chen/Li/Ma, PRC79, 035802 (2009) Kazuhiro Oyamatsu, Kei Iida Phys. Rev. C75 (2007) 015801 Parabolic Approximation has been assumed !!! Xu/Chen/Li/Ma, ApJ 697, 1547 (2009), arXiv:0901.2309

  23. (3) Constraints on M-R relation of NS EOS of Neutron Star Matter

  24. (Empirical estimate Link et al., PRL83,3362(99)) (Isospin Diff) (3) Constraints on M-R relation of NS Lattimer Prakash

  25. (4) Properties of neutron star crusts Xu/Chen/Li/Ma, ApJ 697, 1549 (2009), arXiv:0901.2309 core crust total Neutron skin v.s. Esym: Chen/Ko/Li, PRC72,064309(2005) Larger L leads to thicker neutron-skin , but thinner neutron star crust !!!

  26. (5) HD Esym and properties of neutron stars For pure nucleonic matter??? New Physics??? Supersoft symmetry energy at HD ? K0=211 MeV is used, higher incompressibility for symmetric matter will lead to higher masses systematically The softest symmetry energy that the TOV is still stable is x=0.93 giving M_max=0.11 solar mass and R=>28 km ?

  27. Supersoft symmetry energy at high densities

  28. Supersoft symmetry energy at high densities Among 119 Skyrme forces, there are 55 forces are consistent with the flow data !! Among the 55 forces, there are: 18 forces giving supersoft symmetry energy 19 forces giving soft symmetry energy 18 forces giving normal symmetry energy

  29. Supersoft HD Symmetry Energy: Neutron Stars and Fifth Force ??? Supersoft symmetry energy at HD non-Newtonian gravity in neutron stars??? Wen/Li/Chen, PRL, in press, arXiv:0908.1922 • A neutral spin-1 boson: • Very light; • Weakly coupled to baryons • (Fayet et al: U-soson?) The Yukawa term is simply part of the matter system in general relativity. Consequently, the Einstein equation remains the same and only the EOS is modifed. -----Y. Fujii: in Large Scale Structures of the Universe, page 471-477, Eds. J. Audouze et al. (1988), International Astronomical Union.

  30. Supersoft HD Symmetry Energy: Neutron Stars and Fifth Force ??? Wen/Li/Chen, PRL, in press, arXiv:0908.1922

  31. IV. Summary and Outlook • The isospin diffusion data, Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the • sub-saturation density behavior of the symmetry energy • (L=86±25 MeV and Kasy=-500±50 MeV) • Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a supersoft Esym at high densities. • Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at subsaturation density region. • Supersoft Esym at high densities may give constraints on violation of the inverse-square-law of gravity

  32. Thanks！

  33. (5) Inner Crust EOS Dependence Xu/Chen/Li/Ma, ApJ 697, 1549 (2009), arXiv:0901.2309 • The mass is insensitive to the inner crust EOS • The radius is sensitive to the inner crust EOS for a softer symmetry energy • The inner crust EOS has tiny effects on the ΔI/I when ΔI/I is small

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