Probing properties of neutron stars with heavy-ion reactions

1. Bao-An Li & 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 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 • Questions need your help !

2. The multifaceted influence of the isospin dependence of strong interactionand symmetry energy in nuclear physics and astrophysicsJ.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 Esym (ρ) from model predictions using popular interactions Examples: 23 RMF models ρ - Density

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

5. Latest constraints on the symmetry energy at sub-saturation densities (M.B. Tsang) (MDI) 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). (Colo) 46 MeV < L < 111 MeV Masses of nuclei (Danielewicz) 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). Isospin diffusion Chen, Li & Ko (ImQMD Analyses Tsang et al.) Pressure of pure neutron-matter at ρ0 Pigmy Dipole Resonance (PDR) Land/GSI, PRC76, 051603 (2007)

6. Astrophysical impacts of the partially constrained symmetry energy Nuclear constraints on the moment of inertia of neutron starsarXiv: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 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 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 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 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; and The Astrophysical Journal 697, 1549 (2009), arXiv: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 Thermodynamic approach Dynamical approach K0 If one uses the parabolic approximation (PA) Then the stability condition is: Stability condition: >0 Similarly one can use the RPA

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 potential φ(x,y,z) = φ(x+L,y+L,z+L) • Impose parity conservation in the three dimensions: tri-axial shapes allowed, but not asymmetric ones. Solution only in one octant of cell. • Quadrupoleconstraint 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. Transition Density with 3D-Hartree-Fock • 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.

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. Crust Total radius Core

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

18. Pion ratio probe of symmetry energyat supra-normal densities GC Coefficients2

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

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

21. 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 FRIB/MSU, CSR/IMP RIKEN Radioactive Beam Facilities 400 MeV/A

22. Excitation function Central density

23. The most important contributions of nuclear force

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

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? P(r+dr) TOV equation 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. Themoment of inertia provides a sensitive probe to determine g2/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 theIBUU04 transport model The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions stiff ρ soft Default: Gogny force Density ρ/ρ0 Single nucleon potential within the HF approach using a modified Gogny force: The momentum dependence of the nucleon potential is a result of the non-locality of nuclear effective interactions and the Pauli exclusion principle 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).

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

40. HF calculations

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

43. Gravitational waves from elliptically deformed pulsars 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 Breaking stain of crust Mass quadrupole moment EOS B. Abbott et al., PRL 94, 181103 (2005) B.J. Owen, PRL 95, 211101 (2005)

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

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

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 ρ0: 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. Astrophysical implications For pure nucleonic matter 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

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