1. Probing properties of neutron stars with heavy-ion reactions Outline: Symmetry energy at sub-saturation densities and its impacts on astrophysics Example: Core-crust transition density in neutron stars Symmetry energy at supra-saturation densities and its impacts on astrophysics Example : Saving neutron stars with negative symmetry energy at supra-saturation densities with the light-weakly interacting U boson and its implications for cosmology & collaborators: Joshua Edmonson, M. Gearheart, Will Newton, Justin Walker, De-Hua Wen, Chang Xu and Gao-Chan Yong, Texas A&M University-Commerce Lie-Wen Chen and Hongru Ma, Shanghai Jiao-Tung University Plamen G. Krastev, San Diego State University Che-Ming Ko and Jun Xu, Texas A&M University, College Station Wei-Zhou Jiang, Southeast University, Nanjing, China Zhigang Xiao and Ming Zhang, Tsinghua University, China Xunchao Zhang and Wei Zuo, Institute of Modern Physics, China Champak B. Das, Subal Das Gupta and Charles Gale, McGill University Andrew Steiner, Michigan State University Bao-An Li Questions need your help !

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).

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

4. Range of symmetry energy from isospin diffusion More examples of microscopic model predictions

5. M.B. Tsang et al., PRL 92, 062701 (2004) L.W. Chen, C.M. Ko and B.A. Li, PRL 94, 32701 (2005) M. A. Famiano et al., PRL 97, 052701 (2006). (Colo) (M.B. Tsang) (MDI) Pressure of pure neutron-matter at ρ 0 Masses of nuclei (Danielewicz) Isospin diffusion Chen, Li & Ko (ImQMD Analyses Tsang et al.) Pigmy Dipole Resonance (PDR) Land/GSI, PRC76, 051603 (2007) Latest constraints on the symmetry energy at sub-saturation densities Gianluca Colo, arXiv:0902.3739 M. B. Tsang, Yingxun Zhang, P. Danielewicz, M. Famiano, Zhuxia Li, W. G. Lynch, and A. W. Steiner, PRL 102, 122701 (2009). M. Centelles, X. Roca-Maza, X. Vias, and M. Warda, PRL 102, 122502 (2009). G. Lehaut, F. Gulminelli, and O. Lopez, PRL 102, 142503 (2009). 46 MeV < L < 111 MeV

6. 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 Nuclear constraints on properties of neutron star crust Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma, Phys. Rev. C79, 035802 (2009), arXiv:0807.4477; arXiv:0807.4477 and The Astrophysical Journal 697, 1549 (2009), arXiv:0901.2309arXiv:0901.2309

7. 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, TAMU, 2005 Yes, the symmetry energy constrained by intermediate energy heavy-ion experiments is in the same density range of the inner crust

8. 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

10. Pasta phases

11. 3D-Hartree-Fock method for the pasta phase in the inner crust of neutron stars 3D Hartree-Fock calculations with Skyrme energy-density functional Assume one can identify (local) unit cubic cells of matter at a given density and temperature, calculate one unit cell containing A nucleons (A up to 3000) Periodic boundary conditions enforced by using FTs to take derivatives and obtain Coulomb potentialPeriodic boundary conditions enforced by using FTs to take derivatives and obtain Coulomb potential φ(x,y,z) = φ(x+L,y+L,z+L) φ(x,y,z) = φ(x+L,y+L,z+L) Impose parity conservation in the three dimensions:Impose parity conservation in the three dimensions: tri-axial shapes allowed, but not asymmetric ones. Solution only in one octant of cell. Quadrupole constraint placed on neutron density > self consistently explore deformation space (energies of nuclear pasta shapes) Method self-consistently incorporates the nuclear clusters at the bottom of the inner crust together with their surface and curvature energies, and the unbound neutrons William G. Newton, Ph.D thesis, University of Oxford, 2008 William G. Newton and Jirina R. Stone, Physical Review C79, 055801 (2009)

12. By performing calculations at increasing density one can observe the density at which matter becomes uniform (the energy density converges to that of uniform matter) –Above calculations for the SkM* Skyrme parameterization and 500 nucleons in the unit cell. Transition Density with 3D-Hartree-Fock

13. Transition Density with 3D-Hartree-Fock: Comparison with Dynamical Method 3DHF method used to calculate transition density for 4 Skyrmes so far. Consistently about 0.002 fm -3 higher than estimating when uniform matter becomes unstable to small-amplitude long wavelength density perturbations (dynamical method) Dynamical method exact if transition was second order, gives lower limit if transition is first order Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma, Phys. Rev. C79, 035802 (2009), and The Astrophysical Journal 697, 1549 (2009),

16. Core Crust Total radius

17. 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

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

19. 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!

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

21. FRIB/MSU, CSR/IMP 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 102, 062502 (2009). FAIR/GSI 400 MeV/A

22. Excitation function Central density

23. The most important contributions of nuclear force

26. At saturation density Using Paris potential I. Bombaci and U. Lombardo PRC 44, 1892 (1991) Using the Reid93 interaction PRC68, 064307 (2003)

27. What will happen if the short-range repulsive tensor force is included at high densities?

28. 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

29. Is the negative symmetry energy “unpleasant” or unphysical? Unpleasant ! E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeffer, NPA627, 710 (1997); NPA635, 231 (1998). Repeated by several others in other papers Unphysical ! Quoted by several people Why ? The only reason seems to be that “ neutron stars will then collapse while they do exist in nature”

30. How neutron stars are stablized? TOV equation P(r+dr) P(r) Gravity Nuclear pressure

31. Do we really know gravity at the Fermi distance? So far, down to the 10 fm level, there is NO violation of the ISL

32. Extra dimension at short length or a new Boson? String theorists have published TONS of papers on the extra dimension In terms of the gravitational potential Repulsive Yukawa potential due to the exchange of a new boson proposed in the super-symmetric extension of the Standard Model of the Grand Unification Theory The neutral spin-1 gauge boson U is a candidate, it can mediate the interaction among dark matter particles, e.g., Pierre Fayet, PLB675, 267 (2009), C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul, PRL, 92, 101301 (2004).

33. Influences of the U-boson on Neutron stars It has NO effect on finite nuclei M.I. Krivoruchenko, et al., ep-ph/0902.1825v1, De-Hua Wen et al. (2009)

34. EOS of MDIx1+WILB

35. M-R relation of neutron star with MDIx1+WILB

36. The moment of inertia provides a sensitive probe to determine g 2 /  2

37. Questions and possible answers? What is causing the uncertain symmetry energy at high densities? (short-range tensor force??) How can one trace back to the underlying force from observables in nuclear reactions? Effective interactions, such as Skyrme and Gogny can lead to various high-density behavior of the symmetry energy, but they do not have the explicit Tensor force, ?? None of the transport models using explicit tensor force, but yet, … ….

38. 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

39. Two-body force: Gogny force One-body potential

40. HF calculations

42. 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

43. 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

44. 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)

45. 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)

46. 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

47. W. Reisdorf et al. for the FOPI collaboration, NPA781 (2007) 459 IQMD: Isospin-Dependent 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!

48. 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)

49. 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 Astrophysical implications K 0 =211 MeV is used, higher incompressibility for symmetric matter will lead to higher masses systematically

50. Summary Based on model analyses of intermediate energy heavy-ion collision 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

51. Is π - /π + ratio really a good probe of the symmetry energy at supra-normal densities? (Tetsuya Murakami and possibly many others) 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

52. 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)

53. Asymmetric nuclear matter In hyperonic matter

54. 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

55. 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

56. 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

57. 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

58. 58Gravitational 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

59. 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

60. 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”

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

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

63. 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

64. RIKEN-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

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

66. 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)

67. Symmetry energy from isoscaling analyses D.V. Shetty, S.J. Yennello and G.A. Souliotis Phys. Rev. C75 (2007) 034602; Phys. Rev. C76 (2007) 024606 X=0 Range of symmetry energy from isospin diffusion

68. Gravitational Radiation from Rotating Neutron Stars (Pulsars) Wobbling neutron star R-modes “Mountain” on neutron star Accreting neutron star

69. 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? implication Transport model calculations B.A. Li and L.W. Chen, PRC72, 064611 (05)

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

71. 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)

72. 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 ●.

73. (completely due to general relativity)

74. 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

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