1. Constraining the EOS of neutron-rich nuclear matter and properties of neutron stars with central heavy-ion reactions Outline: Indication on the symmetry energy at sub-saturation densities from the NSCL/MSU isospin diffusion data Astrophysical implications: (1) Core-crust transition density of neutron stars (2) Gravitational waves from elliptically deformed pulsars Indication on the symmetry energy at supra-saturation densities from the FOPI/GSI π - /π + data Summary & collaborators: Wei-Zhou Jiang, Plamen G. Krastev, Richard Nobra, 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. What is the Equation of State in the extended isospin space? (EOS of neutron-rich matter) 18 12 3 symmetry energy ρ=ρn+ρpρ=ρn+ρp 0 1 density Isospin asymmetry Symmetric matter ρn=ρpρn=ρp Energy per nucleon in symmetric matter Energy per nucleon in asymmetric matter δ ρ n : neutron density ρ p : proton density Nucleon density ρ=ρ n +ρ p δ Isospin asymmetry ??? 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 (2008) arXiv:0804.3580 arXiv:0804.3580

3. 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

4. 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). Isospin physics Isospin physicsn/p isoscaling isoscaling isotransport isotransport isodiffusion isodiffusion t/ 3 He isofractionation isofractionation K + /K 0 isocorrelation isocorrelation π-/π+π-/π+π-/π+π-/π+ in Terrestrial Labs (QCD)(Effective Field Theory)

5. 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 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

6. Momentum dependence of the isoscalar potential Compared with variational many-body theory

7. 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)

8. Constraints from both isospin diffusion and n-skin in 208 Pb ρ ρρ ρ 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? J.R. Stone implication Transport model calculations B.A. Li and L.W. Chen, PRC72, 064611 (05)

9. L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005);

10. Neutron Star Crust 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 density and pressure at the transition to calculate the fractional moment of inertia of the curst Can one extract transition density from heavy-ion collisions? Chuck Horowitz at WCI3, Texas, 2005 Yes, the symmetry energy constrained by the isospin diffusion experiments at the NSCL is in the same density range of the inner crust Kazuhiro OyamatsuKazuhiro Oyamatsu, Kei IidaKei Iida Phys. Rev. C75 (2007) 015801 crust core

11. Onset of instability in the uniform n+p+e matter Dynamical approach Thermodynamic approach K0K0 Similarly one can use the RPA Stability condition: If one uses the parabolic approximation (PA) Then the stability condition is: >0

12. What we found about the core-crust transition density It is NOT accurate 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: Thermodynamical method Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma, arXiv:0807.4477arXiv:0807.4477 The quartic term is also important for direct URCA, Andrew Steiner, arXiv:nucl-th/0607040

13. Constraint on the core-crust transition density Kazuhiro OyamatsuKazuhiro Oyamatsu, Kei IidaKei Iida Phys. Rev. C75 (2007) 015801 pasta Need to reduce the error bars with more precise data and calculations! Transition pressure Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma, arXiv:0807.4477arXiv:0807.4477

14. Partially constrained EOS for astrophysical studies Danielewicz, Lacey and Lynch, Science 298, 1592 (2002)) Plamen Krastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008).

15. Astrophysical impacts of the partially constrained symmetry energy Nuclear constraints on the moment of inertia of neutron stars arXiv:0801.1653 arXiv:0801.1653 Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008). Constraining properties of rapidly rotating neutron stars using data from heavy-ion collisions arXiv:0709.3621 arXiv:0709.3621 Plamen Krastev, Bao-An Li and Aaron Worley, The Astrophysical Journal, 676, 1170 (2008) Constraining time variation of the gravitational constant G with terrestrial nuclear laboratory data arXiv:nucl-th/0702080 arXiv:nucl-th/0702080 Plamen Krastev and Bao-An Li, Phys. Rev. C76, 055804 (2007). Constraining the radii of neutron stars with terrestrial nuclear laboratory data Bao-An Li and Andrew Steiner, Phys. Lett. B642, 436 (2006). arXiv:nucl-th/0511064 arXiv:nucl-th/0511064 Nuclear limit on gravitational waves from elliptically deformed pulsars Plamen Krastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008). arXiv:0805.1973 arXiv:0805.1973 Locating the inner edge of neutron star crust using nuclear laboratory data, Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma arXiv:0807.4477 arXiv:0807.4477

16. Gravitational Waves = “ Ripples in space-time” What are Gravitational Waves? Amplitude parameterized by (tiny) dimensionless strain h: h(t) = DL/L LxLx L x [1 + h(t)] Traveling GW F + and F x : plus and cross polarization, bounded between -1 and 1 h 0 – amplitude of the gravitational wave signal,  – polarization angle of signal  – inclination angle of source with respect to line of sight,  (t)- phase of pulsar The expected signal has the form (P. Jaranowski, Phys. Rev. D58, 063001 (1998) ) : proper separation between two masses Gravity J.B. Hartle

17. Test General Relativity: –Quadrupolar radiation? Travels at speed of light? –Unique probe of strong-field gravity Gain different view of Universe: –Sources cannot be obscured by dust / stellar envelopes –Detectable sources are some of the most interesting, least understood in the Universe –Opens up entirely new non-electromagnetic spectrum Why do we need to study Gravitational Waves? Michael Landry LIGO Hanford Observatory and California Institute of Technology

18. 18Gravitational Waves LIGO VIRGO GEO TAMA ACIGA LISA Gravitational Wave Interferometer Projects LIGO, GEO, TAMA; VIRGO taking data; LISA is a ESA-NASA project Michelson-Morley IFO

19. Compact binary inspiral: “chirps” Possible sources of Gravitational Waves: Supernovae / GRBs: “bursts” Elliptically deformed pulsars: “periodic” Examples Orbital decay of the Hulse-Taylor binary neutron star system (Nobel prize in 1993) is the best evidence so far. Non-radial oscillations of neutron stars

20. 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

21. Solid black lines: LIGO and GEO science requirement, for T=1 year Circles: upper limits on gravitational waves from known EM pulsars, obtained from measured spindown Only known, isolated targets shown here LIGO GEO The LIGO Scientific Collaboration,LIGO Scientific Collaboration Phys. Rev. D 76, 042001 (2007) Estimate of gravitational waves from spinning-down of pulsars Assumption: spinning-down is completely due to the GW radiation “Standard fiducial value”

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

23. The ellipticity of pulsars EOS Plamen Krastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008).

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

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

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

27. 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 NOT sensitive to the incompressibility of symmetric matter, but the high density behavior of the symmetry energy (K 0 =211 MeV is used in the results shown here)

28. Formation of dense, asymmetric nuclear matterSoft Stiff Soft E sym Stiff E sym density Symmetry energy n/p ratio at supra-normal densities Central density π - / π + probe of dense matter

29. 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!

30. Stiff symmetry energy Softer symmetry energy FRIB? APR N/Z dependence of pion production and effects of the symmetry energy

31. MSU-TPC? ? Zhigang XiaoZhigang Xiao, Bao-An Li, Lie-Wen Chen, Gao-Chan Yong, Ming ZhangBao-An LiLie-Wen Chen Gao-Chan YongMing Zhang arXiv:0808.0186 Excitation function Central density

32. The softest symmetry energy that the TOV is still stable is x=0.93 giving M_max=0.1 solar mass and R=>40 km For pure nucleonic matter Astrophysical implications K 0 =211 MeV is used, higher incompressibility for symmetric matter will lead to higher masses systematically

33. 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

34. Asymmetric nuclear matter In hyperonic matter

35. Summary Based on the NSCL/MSU data, the symmetry energy at sub-saturation densities is constrained to The FOPI/GSI pion data indicates a symmetry energy at supra-saturation densities softer than the APR prediction