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Probing properties of neutron stars with heavy-ion reactions Bao-An Li & 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 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 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 The Esym (ρ) from model predictions using popular interactions 1 2 E Esym ( ) E ( ) pure neutron matter E ( )symmetric nuclear matter 2 2 Examples: 23 RMF models ρ - Density Symmetry energy and single nucleon potential used in the IBUU04 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 ρ soft Default: Gogny force Density ρ/ρ0 MDI single nucleon potential within the HF approach using a modified Gogny force: ' B 1 U ( , , p, , x ) Au ( x ) Al ( x ) B( ) (1 x ) 8 x 2 ' 0 0 0 1 0 2C , f ( r, p ') 2C , ' f ' ( r, p ') 0 0 d3p' d3p' 1 ( p p ') 2 / 2 1 ( p p ') 2 / 2 1 2 Bx 2 Bx , ' , Al ( x ) 121 , Au ( x ) 96 , K 211MeV 2 1 1 0 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). 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 U n / p U isoscalar U Lane Scientific, 1994 U Lane (U n U p ) / 2 V1 R Ekin , G.W. Hoffmann and W.R. Coker, PRL, 29, 227 (1972). G.R. Satchler, Isospin Dependence of Optical Model V1 28 6MeV, R 0.1 0.2 Potentials, in Isospin in Nuclear Physics, for E kin 100 MeV D.H. Wilkinson (ed.), (North-Holland, Amsterdam,1969) Constraints from both isospin diffusion and n-skin in 208Pb Isospin diffusion data: MDI potential energy density M.B. Tsang et al., PRL. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007) Transport model calculations B.A. Li and L.W. Chen, PRC72, 064611 (05) 124Sn+112Sn implication PREX? ρρ Hartree-Fock calculations A. Steiner and B.A. Li, PRC72, 041601 (05) 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) Symmetry energy constrained at sub-saturation densities 31.6( / 0 ) 0.69 Esym ( ) 31.6( / 0 )1.05 between the x=0 and x=-1 lines, agrees extremely well with the APR L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005) (ImQMD) (IBUU04) For more details Talk by Bill Lynch Courtesy of M.B. Tsang Partially constrained EOS for astrophysical studies Danielewicz, Lacey and Lynch, Science 298, 1592 (2002)) Constraining the radii of NON-ROTATING neutron stars Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006) ● . APR: K0=269 MeV. The same incompressibility for symmetric nuclear matter of K0=211 MeV for x=0, -1, and -2 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). 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) 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 Phys. Rev. D 76, 042001 (2007) It is probably the most uncertain factor B.J. Owen, PRL 95, 211101 (05) 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 Testing the standard fudicial value of the moment of inertia Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008). (completely due to general relativity) The EOS of neutron-rich matter enters here: The first w-mode The frequency is inversely proportional to the compactness of the star MNRAS, 299 (1998) 1059-1068 MNRAS, 310, 797 (1999) Imprints of symmetry energy on the axial w-mode De-Hua Wen, Bao-An Li and Plamen G. Krastev (2009) 8.8 8.6 wI MDIx0 8.4 MDIx-1 APR 8.2 (kHz) 8.0 7.8 7.6 7.4 7.2 5 wII 4 (kHz) 3 2 1 0 1.0 1.2 1.4 1.6 1.8 2.0 M(Msun) 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) 0.45 0.30 MDIx0 wI MDIx0 wII MDIx-1 0.25 MDIx-1 0.40 APR APR Re(M) FIT 0.20 Re(M) 0.35 0.15 0.30 0.10 0.25 0.05 0.00 0.60 0.24 0.55 0.22 Im(M) Im(M) 0.50 0.20 0.45 0.18 0.40 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.12 0.14 0.16 0.18 0.20 0.22 0.24 M/R M/R The Esym (ρ) from model predictions using popular interactions 1 2 E Esym ( ) E ( ) pure neutron matter E ( )symmetric nuclear matter 2 2 Examples: EOS of pure neutron matter Alex Brown, RMF 23PRL85, 5296 (2000). models ρ ??? ??? APR - Density 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 Why? Can the modern effective field theory verify this? Example: proton fraction with 10 interactions leading to negative symmetry energy Negative symmetry energy Isospin separation instability because of the Esym 2 term, for symmetric matter, it is energetically more favoriable to write =0=1-1, i.e., pure neutron matter + pure proton matter x 0.048[ Esym ( ) / Esym ( 0 )]3 ( / 0 )(1 2 x )3 Pion ratio probe of symmetry energy GC 0 Coefficients2 at supra-normal densities nn 0 1 5 a) Δ(1232) resonance model pp 5 1 0 in first chance NN scatterings: np(pn) 1 4 1 (negelect rescattering and reabsorption) 5 N 2 NZ ( N )2 5Z 2 NZ Z R. Stock, Phys. Rep. 135 (1986) 259. b) Thermal model: (G.F. Bertsch, Nature 283 (1980) 281; A. Bonasera and G.F. Bertsch, PLB195 (1987) 521) exp[2( n p ) / kT ] n m 1 1 3 m m n p (V V ) VCoul kT {ln bm ( T ) ( )} n p m asy asy p m m 2 n p H.R. Jaqaman, A.Z. Mekjian and L. Zamick, PRC (1983) 2782. c) Transport models (more realistic approach): Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701, and several papers by others Is π-/π+ ratio really a good probe of the symmetry energy at supra-normal densities? XL=XH=1 XL=XH=-2 X L X for 0 X H X for 0 1 2 0 N *0 Sub-saturation density: 5% Supra-saturation densities: 25% ( )like 3 3 t 1 2 * N 3 3 Isospin asymmetry reached in heavy-ion reactions Symmetry energy 48 48 density E( , ) E( , 0) Esym ( ) 2 E/A=800 MeV, 124 124 197 197 b=0, t=10 fm/c t=10 fm/c t=10 fm/c Correlation between the N/Z and the π-/ π+ 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 (K0=211 MeV is used in the results shown here) (distance from the center of the reaction system) 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) 151-169 100 3 0 corresponding to Esym ( ) (22 / 3 1) EF ( ) 2 / 3 8 0 5 0 Need a symmetry energy softer than the above to make the pion production region more neutron-rich! E(, ) E(,0) Esym ( ) 2 low (high) density region is more neutron-rich with stiff (soft) symmetry energy 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 Quantum Molecular Dynamics C. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. Stoecker, W. Greiner Eur.Phys.J. A1 (1998) 151-169 100 3 0 corresponding to Esym ( ) (22 / 3 1) EF ( ) 2 / 3 8 0 5 0 Need a symmetry energy softer than the above to make the pion production region more neutron-rich! E(, ) E(,0) Esym ( ) 2 low (high) density region is more neutron-rich with stiff (soft) symmetry energy 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. 400 MeV/A Excitation function Central density IF the conclusion is right, For pure nucleonic matter Disturbing implications? 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 ? n e Summary • The symmetry energy at sub-saturation densities is constrained to 31.6( / 0 )0.69 Esym ( ) 31.6( / 0 )1.05 L=86 25 MeV It agrees extremely well with the APR prediction • The FOPI/GSI pion data indicates a symmetry energy at supra-saturation densities much softer than the APR prediction

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