1. Neutron star radii and the EOS of neutron-rich matter
Wei-Zhou Jiang
Department of Physics, Southeast University, Nanjing
Collaborators:B. A. Li, F. J. Fattoyev，
Students：Qian-Fer Xiang, Dong-Rui Zhang
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2. Outline Radii and mass of neutron stars(NS’s)
Schemes for small NS radii
Summary
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3. 中子星: 基本特点 Formed: supernova explosion N. Stars in Galaxies: ~108-109
Detected: ~ 1000 radio pulsar
Period: ~ 1.6 ms - 5 s
Discovery: 1967, Jocelyn Bell,
A. Hewish
Mass: ~ 1.4 M0 ; Radius: ~ 10 Km
Magnetic field: ~1012 Gauss
Density: 1014 g/cc
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4. P. B. Demorest, et.al. Nature 467, 1081 (2010): 2.0 .
Large-mass neutron stars
T. Guver, et al, Astrophys. J. 712, 964 (2010):
P. B. Demorest, et.al. Nature 467, 1081 (2010): 2.0 .
Sharpilo delay
J. Antoniadis, et al., Science 340, 448 (2013):
2.01 ± 0.04 M☉
Radio-timing observations of the pulsar J and phase-resolved optical spectroscopy of the white-dwarf companion，
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5. Small NS radius Guillot et al. 2013, ApJ 772 Quiescent low-mass X-ray
binary (qLMXB) sources
Ozel, et.al., arXiv: v1
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6. 12/13-18/2015：Shanghai

7. Some radii from individual stars
 Bogdanov (2013) ： 11.1 km of the neutron star in PSR J0437
Poutanen et al.(2014) ：12 and 16 km for 4U  
Factors that affect the extraction of radii: NS distance to the star, NS atmosphere composition, residual accretion… （Miller (2013) .
Precise measurements of NS radii still required
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8. P.Danielewicz, R.Lacey,W.G.Lynch, Science 298(2002)1592
Collective flow data from high energy heavy-ion reactions
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9. Challenges to theoretical models
Large-mass NS’s require stiff EOS, disfavoring non-nucleonic degrees of freedom, such as hyperons, quarks, meson condensates. The inclusion of non-nucleonic degrees of freedeom usually do not reduce significantly the NS radii.
Small NS radii require soft EOS. Stiff EOS’s that produce the 2 solar mass NS give rise to relatively large radii.
The relativistic mean-field models predict the radii of 13-16km. With soft symmetry energy, the radius is just as low 12km. It is very difficult to give the radius of 10 km.
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10. Neutron star radii with various EOS
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11. How to reduce the radii, if small radii established?
By softening the EOS, but difficult:
a different softening of EOS
By new degrees of freedom, but just a few of them, like ∆ resonance [Cai, et al, PRC 92, (2015).]
particles beyond standard model
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12. A scheme to soften EOS EOS softening
Generally with pressure dropping, NS maximum mass reduces, but radius does not decrease significantly.
Pressure unchanged, while energy density increases: Radius reduces with less change in maximum mass
WFF1，Wiringa, et al. 1988, PRC, 38, 1010
RMF models can’t produce small RNS = −1.5 km
Amending term:
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13. Reduction of NS Radii
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14. Interpret amending term as novel in-medium effects
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15. Amending term can be interpreted by the BSM U-boson
Jiang, Li, Fattoyev, EPJA 51，119（2015）
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16. U-boson Beyond standard model, U(1) symmetry
Superpartner of spin-3/2 gravitino
Putative 5th force？
Mediator (gauge particle) of dark matter that may couple to fermions.
Fayet, PLB95, 285 (1980);172, 363 (1986); NPB347, 743(1990);
Fischbach & Talmadge, The Search for Non- NewtonianGravity (Springer-Verlag, Inc., New York, 1999), ISBN ;
Adelberger et al., Annu. Rev. Nucl. Part. Sci. 53,77(2003).
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17. U boson regarded as a candidate of non-Newtonian gravity
Wen/Li/Chen, PRL103, (2009)

18. U-boson in RMF models and neutron stars
( Zhang, et al., PRC83, (2011) ).
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19. In the presence of U-boson, the in-medium effect is favorable to obtain small radii
Zhang, et.al.
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20. Dark matter candidates in NS
Recently many works appear:
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21. DM mass
All possible DM masses range from keV to hundreds of GeV: so many models
Supersymmetric models
In our study, the DM masses are chosen to be a few hundred MeV to a few GeV beyond which the effect is small on the NS mass-radius trajectory
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22. Dark matter in neutron stars
Only gravitational attraction
between normal matter and
dark matter
Xiang，et al
PRC 89, (2014)
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23. NS radii with dark matter
Steiner:PRL 108, (2012)
Effect of Dark Matter?
Guillot et al. 2013, ApJ 772
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24. DM Accretion
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25. Summary
（1）Small NS radii with novel in-medium effects that can be rather universal for all kinds of models
（2） Small NS radii with non-nucleonic degrees of freedom such as dark matter
（3）Precise measurements of NS radii are needed for identifying or ruling out new physics.
Small NS radii: quark stars and/or physics BSM
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26. 谢谢/Thank you！
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