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The Nuclear Symmetry Energy and Neutron Star Crusts

The Nuclear Symmetry Energy and Neutron Star Crusts. Collaborators ： Wei-Zhou Jiang (South-East U.) Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce)

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The Nuclear Symmetry Energy and Neutron Star Crusts

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  1. The Nuclear Symmetry Energy and Neutron Star Crusts Collaborators： Wei-Zhou Jiang (South-East U.) Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce) Gao-Chan Yong (IMP,CAS) Hong-Ru Ma (SJTU) Zhi-Gang Xiao and Ming Zhang (Tsinghua U.) Lie-Wen Chen (陈列文) (Department of Physics, Shanghai Jiao Tong University) Compact stars in the QCD phase diagram II May 20‐24, 2009, Beijing

  2. Outline • EOS of asymmetric nuclear matter and the nuclear symmetry energy • Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions • The nuclear symmetry energy and neutron star crusts • 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]

  3. Transport Theory 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 … I. EOS of Asymmetric Nuclear Matter and the Nuclear Symmetry Energy Isospin Physics in medium energy nuclear physics 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 What is the isospin dependence of the in-medium nuclear effective interactions???

  4. IMP CIAE Radioactive beam facilities are being built around the world World status of Rare Isotope Accelerators Providing new opportunities for both nuclear physics and astrophysics

  5. Many-Body Approaches to Nuclear Matter EOS • 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 ……

  6. 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

  7. 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)

  8. 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)

  9. 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,……

  10. The Nuclear Symmetry Energy Symmetric Nuclear Matter Symmetry energy term The Nuclear Matter Symmetry Energy (Parabolic law) EOS of Asymmetric Nuclear Matter

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

  12. II. 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 !)

  13. 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

  14. 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)

  15. in neutron-rich matter In-medium Nucleon-nucleon cross sections:Effective mass scaling model • Neglecting medium effects on the transition matrix • Medium effects: • effective mass on the incoming current in initial state and level density of the final state is the reduced mass of the colliding pair NN in medium J.W. Negele and K. Yazaki, PRL 47, 71 (1981) V.R. Pandharipande and S.C. Pieper, PRC 45, 791 (1992) M. Kohno et al., PRC 57, 3495 (1998) D. Persram and C. Gale, PRC65, 064611 (2002). • In-medium cross sections are reduced • nn and pp cross sections are splitted • due to the neutron-proton effective mass slitting in neutron-rich matter Li/Chen, PRC72 (2005)064611

  16. Symmetry Energy: Sub-saturation density behaviors (1) Isospin diffusion Chen/Ko/Li, PRL94(05); PRC72(05); Li/Chen, PRC72(05) IBUU04 (2) Isospin scaling (3) Double n/p ratio ImQMD Zhang et al. PLB664(08) Shetty et al. PRC75(07);PRC76(07)

  17. g 0.45gi 0.95 0.4gi 1.05 0.4gi 1 IBUU04 : S~31.6(r/ro) 0.69g1.05 Consistent constraints from the 2analysis of three observables S=12.5(r/ro)2/3+ 17.6(r/ro) gi 0.4gi 1.05 Symmetry Energy: Sub-saturation density behaviors ImQMD: Double n/p ratios and two isospin diffusion measurements Tsang/Zhang/Danielewicz/Famiano/Li/Lynch/Steiner, PRL 102, 122701 (2009)

  18. Symmetry Energy: Sub-saturation density behaviors Chen/Ko/Li, PRL 94, 032701 (2005) Tsang et al., PRL 102, 122701 (2009) (ImQMD) (IBUU04) X=-1

  19. High density behaviors: Kaon Probe Aichelin/Ko, PRL55, 2661 (1985):Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li, QF Li et al., M. Di Toro et al., …) Theory: Famiano et al., PRL97, 052701 (2006) Exp.: Lopez et al. FOPI, PRC75, 011901(R) (2007) K0/K+ yield is not so sensitive to the symmetry energy! Lower energy and more neutron-rich system??? Subthreshold K0/K+ yield may be a sensitive probe of the symmetry energy at high densities

  20. High density behaviors: Pion Probe IBUU04, Xiao/Li/Chen/Yong/Zhang, PRL102, 062502(2009) M. Zhang et al., arXiv:0904.0447 A Quite Soft Esym at supra-saturation densities !!!

  21. core-crust transition III. The Nuclear Symmetry Energy and Neutron Star Crusts Lattimer/Prakash, Science 304, 536 (2004) • 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)

  22. 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

  23. 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:

  24. (2) Locating the inner edge of neutron star crust Significantly less than their fiducial values: ρt=0.07-0.08 fm-3 and Pt=0.65 MeV/fm3 pasta 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

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

  26. (4) Properties of neutron star crusts Xu/Chen/Li/Ma, ApJ 697, 1549 (2009), arXiv:0901.2309 Larger L leads to thicker neutron-skin , but thinner neutron star crust !!!

  27. (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 dI/I when dI/I is small

  28. (6) HD Esym and properties of neutron stars For pure nucleonic matter??? New Physics??? Soft 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 ?

  29. 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 quite soft 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 sub-saturation density region. • Crosscheck is definitely needed !!!

  30. Thanks！

  31. Institute of Nuclear, Particle, Astronomy and Cosmology-INPAC, Shanghai Jiao Tong University http://physics.sjtu.edu.cn/iwdd09/index.html

  32. International workshop on nuclear dynamics in heavy-ion reactions and the symmetry energy (IWND2009) August 22–25, Shanghai, China Organizers Shanghai Institute of Applied Physics, CAS Shanghai Jiao Tong University Beijing Normal University Institute of Modern Physics, CAS

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