Department of Physics, South China Univ. of Tech.

collaborators

Bao-An Li1, Lie-Wen Chen2

1Department of Physics and astronomy, Texas A&M University-Commerce2Institute of Theoretical Physics, Shanghai Jiao Tong University

Super-soft symmetry energy encountering non-Newtonian

gravity in neutron stars

Please read PRL 103, 211102 (2009) for details

De-Hua Wen( 文德华 )

Outline:

I. Symmetry energy and equation of state of nuclear

matter constrained by the terrestrial nuclear data;

II. Super-soft symmetry energy encountering non-Newtonian gravity in

neutron stars.

0 )) (, (( ) sn ymp

nn

p pE E E

symmetry energy

Energy per nucleon in symmetric matter

Energy per nucleon in asymmetric matter

δIsospin asymmetry

matternuclear symmetricmatterneutron puresym )()()( EEE B. A. Li et al., Phys. Rep. 464, 113 (2008)

•Symmetry energy

I. Symmetry energy and equation of state of nuclear matter constrained by the terrestrial nuclear data

Constrain by the flow data of relativistic heavy-ion reactions P. Danielewicz, R. Lacey and W.G. Lynch, Science 298 (2002) 1592

1 2 3 4

0/

Equation of state of the symmetric matter

1. R. B. Wiringa et al., Phys. Rev. C 38, 1010 (1988).

2. M. Kutschera, Phys. Lett. B 340, 1 (1994).

3. B. A. Brown, Phys. Rev. Lett. 85, 5296 (2000).

4. S. Kubis et al, Nucl. Phys. A720, 189 (2003).

5. J. R. Stone et al., Phys. Rev. C 68, 034324 (2003).

6. A. Szmaglinski et al., Acta Phys. Pol. B 37, 277(2006).

7. B. A. Li et al., Phys. Rep. 464, 113 (2008).

8. Z. G. Xiao et al., Phys. Rev. Lett. 102, 062502 (2009).

Many models predict that the symmetry energy first increases and then decreases above certain supra-saturation densities. The symmetry energy may even become negative at

high densities.According to Xiao et al. (Phys. Rev. Lett. 10

2, 062502 (2009)), constrained by the recent

terrestrial nuclear laboratory data, the nucl

ear matter could be described by a super so

fter EOS — MDIx1.

)()1(2

1])()0,([

4

1)(),( sym

2sym

22

EEEE

P ee

II. Super-soft symmetry energy encountering non-Newtonian gravity in neutron stars

加李老师图

• Non-Newtonian Gravity and weakly interacting light boson

1. E. G. Adelberger et al., Annu. Rev. Nucl. Part. Sci. 53, 77(2003).2. M.I. Krivoruchenko, et al., hep-ph/0902.1825v1 and references there in.

The inverse square-law (ISL) of gravity is expected to be violated, especially at less length scales. The deviation from the ISL can be characterized effectively by adding a Yukawa term to the normal gravitational potential

In the scalar/vector boson (U-boson ) exchange picture,

and

Within the mean-field approximation, the extra energy density and the pressure due to the Yukawa term is

Hep-ph\0810.4653v3

PRL-2005,94,e240401 Hep-ph\0902.1825

Experiment constraints on the coupling strength with nucleons g2/(4) and the mass μ (equivalently and ) of hypothetical weakly interacting light bosons.

EOS of MDIx1+WILB

22 / g

D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

M-R relation of neutron star with MDIx1+WILB

D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

Constraints on the coupling strength by the stability and observed global

properties of neutron stars

Conclusion1. It is shown that the super-soft nuclear symmetry energy preferre

d by the FOPI/GSI experimental data can support neutron stars

stably if the non-Newtonian gravity is considered;

2. Observations of pulsars constrain the g2/2 in a rough range of 5

0~150 GeV-2.

Thanks

Appendix

The EOS of nuclear matters with a super-soft symmetry en

ergy (e.g., the original gogny-Hartree-Fock) predicts maxi

mum neutron star masses significantly below 1.4 Msun.

The MDIx1 EOS only can support a maximum stellar mass about 0.1Msun, far smal

ler than the observ-ational pulsar masses.

MDIx1: the symmetric part is described by MDI (Momentum-dependent-interaction) and the symmetry energy is described by the orignal Gogny-hartree-Fock model.

According to Fujii, the Yukawa term is simply part of the matter system in general relativity.

Therefore, only the EOS is modified and the structure equation (TOV equations) remains the same.

Fujii, Y., In Large Scale Structures of the Universe, Eds. J. Audouze et al. (1988), International Astronomical Union.

The energy density distribution of neutron stars described by the MDIx1 (MDIx0) Esym(ρ) with (without) the Yukawa contribution.

D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

The effect of U-boson on nuclear matter EOS depends

on the ratio between the coupling strength and the boson

mass squared g2/2, and thus influence the structure of

neutron stars.

While the coupling between the U-boson ( <1MeV)

and the baryons is very weak, U-bosons do not modify

observational result of nuclear structure and heavy-ion

collisions.

M.I. Krivoruchenko, et al., hep-ph/0902.1825v1

The value of the isospin asymmetry δ at β equilibrium is determined by the chemical equilibrium and charge neutrality conditions, i.e., δ = 1 − 2xp with