1. Probing properties of neutron stars with heavy-ion reactions Outline: Symmetry energy at sub-saturation densities constrained by heavy-ion collisions at intermediate energies Imprints of symmetry energy on gravitational waves (1) Gravitational waves from elliptically deformed pulsars (2) The axial w-mode of gravitational waves from non-rotating neutron stars Symmetry energy at supra-saturation densities constrained by the FOPI/GSI data on the π - /π + ratio in relativistic heavy-ion collisions Disturbing/Puzzling(Interesting?) implications for neutron stars & collaborators: Plamen G. Krastev, Will Newton, De-Hua Wen and Aaron Worley, Texas A&M University-Commerce Lie-Wen Chen and Hongru Ma, Shanghai Jiao-Tung University Che-Ming Ko and Jun Xu, Texas A&M University, College Station Andrew Steiner, Michigan State University Zhigang Xiao and Ming Zhang, Tsinghua University, China Gao-Chan Yong and Xunchao Zhang, Institute of Modern Physics, China Champak B. Das, Subal Das Gupta and Charles Gale, McGill University Bao-An Li

2. The multifaceted influence of the isospin dependence of strong interaction and symmetry energy in nuclear physics and astrophysics J.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542. A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005). The latest results: talks by Bill Lynch, Hermann Wolter and Pawel Danielewicz Recent progress and new challenges in isospin physics with heavy-ion reactions: Bao-An Li, Lie-Wen Chen and Che Ming Ko Physics Reports, 464, 113-281 (2008) arXiv:0804.3580 arXiv:0804.3580

3. The E sym (ρ) from model predictions using popular interactions Examples: Density 23 RMF models ρ -

4. Symmetry energy and single nucleon potential used in the IBUU04 transport model ρ C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003). B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004). soft stiff MDI single nucleon potential within the HF approach using a modified Gogny force: Density ρ/ρ 0 The momentum dependence of the nucleon potential is a result of the non-locality of nuclear effective interactions and the Pauli exclusion principle The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions Default: Gogny force

5. Momentum and density dependence of the symmetry (isovector) potential Lane potential extracted from n/p-nucleus scatterings and (p,n) charge exchange reactions provides only a constraint at ρ 0 : P.E. Hodgson, The Nucleon Optical Model, World Scientific, 1994 G.W. Hoffmann and W.R. Coker, PRL, 29, 227 (1972). G.R. Satchler, Isospin Dependence of Optical Model Potentials, in Isospin in Nuclear Physics, D.H. Wilkinson (ed.), (North-Holland, Amsterdam,1969)

6. Constraints from both isospin diffusion and n-skin in 208 Pb ρ ρρ ρ Neutron-skin from nuclear scattering: V.E. Starodubsky and N.M. Hintz, PRC 49, 2118 (1994); B.C. Clark, L.J. Kerr and S. Hama, PRC 67, 054605 (2003) Isospin diffusion data: M.B. Tsang et al., PRL. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007) Hartree-Fock calculations A. Steiner and B.A. Li, PRC72, 041601 (05) PREX? implication Transport model calculations B.A. Li and L.W. Chen, PRC72, 064611 (05) 124 Sn+ 112 Sn X=1 X=0 x=-1 MDI potential energy density

7. L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005) (IBUU04) For more details Talk by Bill Lynch (ImQMD) Courtesy of M.B. Tsang X=-1

8. Partially constrained EOS for astrophysical studies Danielewicz, Lacey and Lynch, Science 298, 1592 (2002))

9. Constraining the radii of NON-ROTATING neutron stars APR: K 0 =269 MeV. The same incompressibility for symmetric nuclear matter of K 0 =211 MeV for x=0, -1, and -2 Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006) Nuclear limits ●.

10. Astronomers discover a neutron-star spining at 716 Science 311, 1901 (2006). Plamen Krastev, Bao-An Li and Aaron Worley, APJ, 676, 1170 (2008) RNS code by Stergioulas & Friedman

11. Gravitational waves from elliptically deformed pulsars Mass quadrupole moment Breaking stain of crust EOS B. Abbott et al., PRL 94, 181103 (2005) B.J. Owen, PRL 95, 211101 (2005) Solving linearized Einstein’s field equation of General Relativity, the leading contribution to the GW is the mass quadrupole moment Frequency of the pulsar Distance to the observer

12. Constraining the strength of gravitational waves Plamen Krastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008). Compare with the upper limits of 76 pulsars from LIGO+GEO observations It is probably the most uncertain factor B.J. Owen, PRL 95, 211101 (05) Phys. Rev. D 76, 042001 (2007)

13. Spin-down estimate for fast-spinning NS Aaron Worley, Plamen Krastev and Bao-An Li (2009) The moment of inertia is calculated from RNS instead of using the ellipticity

14. Testing the standard fudicial value of the moment of inertia Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008).

15. (completely due to general relativity)

16. MNRAS, 299 (1998) 1059-1068 The first w-mode The frequency is inversely proportional to the compactness of the star The EOS of neutron-rich matter enters here: MNRAS, 310, 797 (1999) axial polar

17. Imprints of symmetry energy on the axial w-mode De-Hua Wen, Bao-An Li and Plamen G. Krastev (2009)

18. Scaling of the frequency and decay rate of the w-mode MNRAS, 299 (1998) 1059-1068 MNRAS, 310, 797 (1999) L. K. Tsui and P. T. Leung, MNRAS, 357, 1029(2005) ; APJ 631, 495(05); PRL 95, 151101 (2005) De-Hua Wen, Bao-An Li and Plamen G. Krastev (2009)

19. The E sym (ρ) from model predictions using popular interactions Examples: Density 23 RMF models ρ - EOS of pure neutron matter Alex Brown, PRL85, 5296 (2000). APR ???

20. Can the symmetry energy becomes negative at high densities? Yes, due to the isospin-dependence of the nuclear tensor force The short-range repulsion in n-p pair is stronger than that in pp and nn pairs At high densities, the energy of pure neutron matter can be lower than symmetric matter leading to negative symmetry energy Example: proton fraction with 10 interactions leading to negative symmetry energy Why? Can the modern effective field theory verify this?

21. Pion ratio probe of symmetry energy at supra-normal densities GC Coefficients 2

22. Is π - /π + ratio really a good probe of the symmetry energy at supra-normal densities? Sub-saturation density: 5% Supra-saturation densities: 25% X=1 X=-2 X=0 X=-1 X L =X H =1 X L =-2, X H =1 X L =1, X H =-2 X L =X H =-2 π π

23. E/A=800 MeV, b=0, t=10 fm/c 48 124 197 Isospin asymmetry reached in heavy-ion reactions Symmetry energy density

24. t=10 fm/c Correlation between the N/Z and the π - / π + (distance from the center of the reaction system) t=10 fm/c Another advantage: the π - / π + is INsensitive to the incompressibility of symmetric matter and reduces systematic errors, but the high density behavior of the symmetry energy (K 0 =211 MeV is used in the results shown here)

25. W. Reisdorf et al. for the FOPI/GSI collaboration, NPA781 (2007) 459 IQMD: Isospin-Dependent Quantum Molecular Dynamics C. HartnackC. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka,Rajeev K. PuriJ. AichelinJ. Konopka S.A. BassS.A. Bass, H. Stoecker, W. GreinerH. StoeckerW. Greiner Eur. Phys. J. A1 (1998) 151-169 π - /π + ratio as a probe of symmetry energy at supra-normal densities low (high) density region is more neutron-rich with stiff (soft) symmetry energy Need a symmetry energy softer than the above to make the pion production region more neutron-rich!

26. W. Reisdorf et al. for the FOPI collaboration, NPA781 (2007) 459 IQMD: Isospin-Dependent Quantum Molecular Dynamics C. HartnackC. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka,Rajeev K. PuriJ. AichelinJ. Konopka S.A. BassS.A. Bass, H. Stoecker, W. GreinerH. StoeckerW. Greiner Eur.Phys.J. A1 (1998) 151-169 Near-threshold π - /π + ratio as a probe of symmetry energy at supra-normal densities low (high) density region is more neutron-rich with stiff (soft) symmetry energy Need a symmetry energy softer than the above to make the pion production region more neutron-rich! IQMD

27. FRIB/MSU RIKEN Radioactive Beam Facilities N/Z dependence of pion production and effects of the symmetry energy Zhi-Gang Xiao, Bao-An Li, L.W. Chen, G.C. Yong and. M. Zhang PRL (2009) in press. FAIR/GSI 400 MeV/A

28. Excitation function Central density

29. 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 IF the conclusion is right, Disturbing implications? K 0 =211 MeV is used, higher incompressibility for symmetric matter will lead to higher masses systematically ?

30. Asymmetric nuclear matter In hyperonic matter

31. Summary The symmetry energy at sub-saturation densities is constrained to The FOPI/GSI pion data indicates a symmetry energy at supra-saturation densities much softer than the APR prediction It agrees extremely well with the APR prediction