High-density Symmetry Energy, Non-Newtonian Gravity and the Structure of Neutron Stars. Bao-An Li

Transcription

1 High-density Symmetry Energy, Non-Newtonian Gravity and the Structure of Neutron Stars Bao-An Li Bao-An Li Collaborators: F. Fattoyev, J. Hooker, Weikang Lin and W. G. Newton, TAMU-Commerce Lie-Wen Chen, Shanghai Jiao Tong University Jun Xu, Shanghai Institute of Applied Physics De-Hua Wen, China Southern University of Technology Wei-Zhou Jiang, Southeast University, Nanjing, China

2 Neutron stars as a natural testing ground of grand unification theories of fundamental forces Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century, Committee on the Physics of the Universe, National Research Council E&M Strong force weak What is the dark matter? What is the nature of the dark energy? How did the universe begin? What is gravity? Are there additional spacetime dimensions? What are the masses of the neutrinos, and how have they shaped the evolution of the universe? How do cosmic accelerators work and what are they accelerating? Are protons unstable? Are there new states of matter at exceedingly high density and temperature? How were the elements from iron to uranium made? Is a new theory of matter and light needed at the highest energies?

3 Gravity-EOS Degeneracy in determining properties of neutron stars Strong-field gravity: GR or Modified Gravity?? neutron stars GR+[Modified Gravity] ======== Action S=S gravity +S matter Matter+[Dark Matter]+[Dark Energy]? Content (EOS) of super-dense nuclear matter? For high-density neutron-rich nucleonic matter, the most uncertain part of the EOS is the nuclear symmetry energy

4 An example of EOS-Gravity degeneracy Simon DeDeo, Dimitrios Psaltis Phys. Rev. Lett. 90 (2003) Dimitrios Psaltis, Living Reviews in Relativity, 11, 9 (2008) Uncertain range of EOS Neutron stars are among the densest objects with the strongest gravity General Relativity (GR) may break down at strong-field limit and there is no fundamental reason to choose Einstein s GR over alternative gravity theories Need at least 2 observables to break the degeneracy Stiff EOS: V. R. Pandharipande, Nucl. Phys. A 174, 641 (1971). Soft EOS: R. B. Wiringa, V. Fiks, and A. Fabrocini, Phys. Rev. C38, 1010 (1988) Scalar-Tensor theory with quadratic coupling:

5 J. Antoniadis et al., Science, 26 April 2013, Vol: 340, Issue: 6131 Scalar-Tensor +Nuclear EOS Nuclear EOS used: K 0 =546 MeV and E sym =33.2 MeV B.D. Serot, Phys. Lett. B86, 146 (1979)

6 Among MANY different kinds of modified gravity theories, some predicted that the Gravitational potential has a Yukawa term besides the Newtonian potential at the weak field limit, such as F(R), MOND,.. Without using dark matter, at solar scale scales, these models pass GR tests and can explain astrophysical observations, e.g., The Bullet Cluster 1E evidence shows Modified Gravity in the absence of Dark Matter J. R. Brownstein, J. W. Moffat, Mon.Not.Roy.Astron.Soc.382:29-47,2007

7 Yukawa potential and galaxy rotation curves R.H. Sanders, Astron. Astrophys. 136, L21 (1984).

8 Physics origin of the Yukawa term In grand unification theories, conventional gravity has to be modified due to either geometrical effects of extra space-time dimensions at short length, a new boson or the 5 th force In terms of the gravitational potential String theorists have published TONS of papers on the extra space-time dimensions N. Arkani-Hamed et al., Phys Lett. B 429, (1998); J.C. Long et al., Nature 421, 922 (2003); C.D. Hoyle, Nature 421, 899 (2003) 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, or the fifth force Yasunori Fujii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature 291, (1981) The neutral spin-1 gauge boson U is a candidate, it is light and weakly interacting, Pierre Fayet, PLB675, 267 (2009), C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul, PRL, 92, (2004).

9 Torsion balance Upper limits on the strength α and range λ of the Yukawa term M.I. Krivoruchenko et al., PRD 79, (2009) E.G. Adelberger et al., PRL 98, (2007) D.J. Kapner et al., PRL 98, (2007) Serge Reynaud et al., Int. J. Mod. Phys. A20, 2294 (2005)

10 Influences of the Yukawa term on Neutron stars

11 High-density symmetry energy is the most uncertain part of the EOS of super-dense nucleonic matter, except possible phase transitions E(r n,r p ) = E 0 (r n = r p ) + S(r) r - r n p ç r æ ç è ö ø 2 +o(d 4 ) Terrestrial lab constraints?? P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002)) B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008) M.B. Tsang et al., Phys. Rev. C86, (2012)

12 Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities Data: W. Reisdorf et al. NPA781 (2007) 459 Calculations: IQMD and IBUU04 Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009)

13 Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron Stars De-Hua Wen, Bao-An Li and Lie-Wen Chen, PRL 103, (2009) EOS including the Yukawa contribution g 2 / 2 Mass-shedding limit g a 2 2 / NSof 50 GeV 2 1.4Msun and R tosupport 12 km

14 Effects of Yukawa term on properties of neutron stars M-R relation EOS m r/r 0 Oscillation frequencies

15 Summary There is a degeneracy between poorly understood strong-field gravity and super-dense nuclear EOS in determining properties of neutron stars At least two observables are needed to break the EOS-gravity degeneracy, i.e., determine simultaneously the strong-field gravity and super-dense nuclear EOS

16 1 E 2 hat E is the Equation of State of neutron-rich nucleonic matter? sym( ) E( ) 2 pure neutron matter E( ) symmetric nuclear matter 2 12 symmetry energy Isospin asymmetry δ 12 n p E( n, p) E0 ( n p) Es ym( ) 12 E(, ) n p Energy per nucleon in symmetric matter Energy per nucleon in asymmetric matter Normal density of nuclear matter g/cm density ρ=ρ n +ρ p Isospin asymmetry

17 Characterization of symmetry energy near normal density The physical importance of L In npe matter in the simplest model of neutron stars at ϐ-equilibrium In pure neutron matter at saturation density of nuclear matter Many other astrophysical observables, e.g., radii, core-crust transition density, cooling rate, oscillation frequencies and damping rate, etc of neutron stars

18 Thanks to the hard work of many of you Community averages with physically meaningful error bars? E ( ) 31.6 MeV and L( ) 62.4 MeV sym 0 0 albeit without physically meaningful error bars

19 W.G. Newton, talk at NN2012 Chen, Ko and Li, PRL (2005) Upper limit Agrawal et al. PRL (2012) Lower limit Time Line

20 Super-Soft Can the symmetry energy become negative at high densities? Yes, it happens when the tensor force due to rho exchange in the T=0 channel dominates At high densities, the energy of pure neutron matter can be lower than symmetric matter leading to negative symmetry energy Example: proton fractions with interactions/models leading to negative symmetry energy M. Kutschera et al., Acta Physica Polonica B37 (2006) x 0.048[ E ( ) / E ( )] ( / )( 1 2 x) sym sym

21 Symmetry energy and single nucleon potential MDI used in the IBUU04 transport model ρ soft The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions. It is the coefficient of the 3-body force term Default: Gogny force Density ρ/ρ 0 Potential energy density Single nucleon potential within the HF approach using a modified Gogny force: B U p A A B 1 ' 2 (,,,, x) u( x) l( x) ( ) (1 x ) 8 x C f ( r, p ') 2C f ( r, p ') d p ' d p ', 3, ' 3 ' ( p p' ) / 0 1 ( p p') / ' 1 2Bx 2Bx, ', Al( x) 121, Au( x) 96, K MeV C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, (2003). B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, ; NPA 735, 563 (2004).

22 A challenge: how can neutron stars be stable with a super-soft symmetry energy? If the symmetry energy is too soft, then a mechanical instability will occur when dp/dρ is negative, neutron stars will then all collapse while they do exist in nature TOV equation: a condition at hydrodynamical equilibrium Gravity For npe matter Nuclear pressure P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002)) dp/dρ<0 if E sym is big and negative (super-soft)

23 Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron Stars De-Hua Wen, Bao-An Li and Lie-Wen Chen, PRL 103, (2009) EOS including the Yukawa contribution g 2 / 2

24 Promising Probes of the E sym (ρ) in Nuclear Reactions At sub-saturation densities Global nucleon optical potentials from n/p-nucleus and (p,n) reactions Thickness of n-skin in 208 Pb measured using various approaches and sizes of n-skins of unstable nuclei from total reaction cross sections n/p ratio of FAST, pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusion/transport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t/ 3 He ratio and their differential flow Towards supra-saturation densities π - /π + ratio, K + /K 0? Neutron-proton differential transverse flow n/p ratio of squeezed-out nucleons perpendicular to the reaction plane Nucleon elliptical flow at high transverse momentum t- 3 He differential and difference transverse flow (1) Correlations of multi-observable are important (2) Detecting neutrons simultaneously with charged particles is critical B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)