The Nuclear Symmetry Energy and Properties of Neutron Stars Lie-Wen Chen ( 陈列文 ) (Department of Physicsa and INPAC, Shanghai Jiao Tong University. 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 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)

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: ] B.A. Li, L.W. Chen, and C.M. Ko, Phys. Rep. 464, (2008) [arXiv: ] J. Xu, L.W. Chen, B.A. Li, and H.R. Ma, Phys. Rev. C 79, (2009) [arXiv: ] J. Xu, L.W. Chen, B.A. Li, and H.R. Ma, Astrophys. J. 697, (2009) [arXiv: ] Z.G. Xiao, B.A. Li, L.W. Chen,G.C. Yong, and M. Zhang, Phys. Rev. Lett. 102, (2009) D.H. Wen, B.A. Li, and L.W. Chen, Phys. Rev. Lett., in press [arXiv: ]

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

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

Equation of State of symmetric nuclear matter is relatively well determined (1) EOS of symmetric matter around the saturation density ρ 0 Giant Monopole Resonance K 0 =231±5 MeV PRL82, 691 (1999) Recent results: K 0 =240±20 MeV G. Colo et al. U. Garg et al. __

(2) EOS of symmetric matter for 1ρ 0 < ρ < 3ρ 0 from K + production in HIC’s J. Aichelin and C.M. Ko, PRL55, (1985) 2661 C. Fuchs, Prog. Part. Nucl. Phys. 56, (2006) 1 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.” C. Fuchs et al, PRL86, (2001) 1974 Equation of State of symmetric nuclear matter is relatively well determined See also: C. Hartnack, H. Oeschler, and J. Aichelin, PRL96, (2006)

(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ 0 < ρ < 5ρ 0 using flow data from BEVALAC, SIS/GSI and AGS Use constrained mean fields to predict the EOS for symmetric matter Width of pressure domain reflects uncertainties in comparison and of assumed momentum dependence. P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002) The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions High density nuclear matter 2 to 5ρ 0 Equation of State of symmetric nuclear matter is relatively well determined

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

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

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

Heavy-Ion Accelerator Facilities 1.HIRFL, CSR/HIRFL (China) 2.GANIL (France) 3.GSI (Germany) 4.NSCL/MSU,FRIB/MSU 5.RIKEN (Japan) A E (MeV/u) HIRFL GANIL NSCL/MSU CSR/HIRFL RIKEN GSI Dubna, LBL, ORNL, TAMU, INFN, KVI,… High Energy HI Accelerator Facilities: AGS,RHIC/BNL SPS,LHC/CERN Medium Energy HI Accelerator Facilities

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 ……

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

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

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 σ exp b. In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σ in-medium c. Mean-field consistent cross section due to m* Isospin-dependent Pauli Blocking Isospin-dependent BUU (IBUU) model Transport model for HIC’s EOS

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

(IBUU04) (ImQMD) X=-1 Tsang et al., PRL 102, (2009) Symmetry Energy at Sub-saturation Densities Chen/Ko/Li, PRL 94, (2005) (Subsaturation ： <ρ/ρ 0 <1.2)

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

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) The Nuclear Symmetry Energy and Neutron Stars core-crust transition

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

Core-Crust Transition Density: Parabolic Law fails! (1)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: Not so surprise: Zhang/Chen, CPL 18 (2000) 142 Steiner, Phys.Rev. C74 (2006) Higher-order term effects on direct URCA Xu/Chen/Li/Ma, PRC79, (2009)

(2) Locating the inner edge of neutron star crust Kazuhiro OyamatsuKazuhiro Oyamatsu, Kei IidaKei Iida Phys. Rev. C75 (2007) pasta Xu/Chen/Li/Ma, PRC79, (2009) Xu/Chen/Li/Ma, ApJ 697, 1547 (2009), arXiv: Parabolic Approximation has been assumed !!! Significantly less than their fiducial values: ρ t = fm -3 and P t =0.65 MeV/fm 3

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

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

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

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 For pure nucleonic matter??? New Physics??? Supersoft symmetry energy at HD ? K 0 =211 MeV is used, higher incompressibility for symmetric matter will lead to higher masses systematically ? (5) HD Esym and properties of neutron stars

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

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: A neutral spin-1 boson: 1.Very light; 2.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 , Eds. J. Audouze et al. (1988), International Astronomical Union.

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

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 K asy =-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 IV. Summary and Outlook

Thanks ！

(5) Inner Crust EOS Dependence Xu/Chen/Li/Ma, ApJ 697, 1549 (2009), arXiv: 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