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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