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 12/13-18/2015：Shanghai

Outline Radii and mass of neutron stars(NS’s) Schemes for small NS radii Summary 12/13-18/2015：Shanghai

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 12/13-18/2015：Shanghai

P. B. Demorest, et.al. Nature 467, 1081 (2010): 2.0 . Large-mass neutron stars T. Guver, et al, Astrophys. J. 712, 964 (2010): 1.74 . 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 J0348+0432 and phase-resolved optical spectroscopy of the white-dwarf companion， 0.165-0.185 12/13-18/2015：Shanghai

Small NS radius Guillot et al. 2013, ApJ 772 Quiescent low-mass X-ray binary (qLMXB) sources Ozel, et.al., arXiv:1505.05155v1 12/13-18/2015：Shanghai

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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 1608-52.  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 12/13-18/2015：Shanghai

P.Danielewicz, R.Lacey,W.G.Lynch, Science 298(2002)1592 Collective flow data from high energy heavy-ion reactions 12/13-18/2015：Shanghai

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. 12/13-18/2015：Shanghai

Neutron star radii with various EOS 12/13-18/2015：Shanghai

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, 015802 (2015).] particles beyond standard model 12/13-18/2015：Shanghai

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 = 9.1+1.3−1.5 km Amending term: 12/13-18/2015：Shanghai

Reduction of NS Radii 12/13-18/2015：Shanghai

Interpret amending term as novel in-medium effects 12/13-18/2015：Shanghai

Amending term can be interpreted by the BSM U-boson Jiang, Li, Fattoyev, EPJA 51，119（2015） 12/13-18/2015：Shanghai

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 0-387-98490-9; Adelberger et al., Annu. Rev. Nucl. Part. Sci. 53,77(2003). 12/13-18/2015：Shanghai

U boson regarded as a candidate of non-Newtonian gravity Wen/Li/Chen, PRL103, 211102 (2009)

U-boson in RMF models and neutron stars ( Zhang, et al., PRC83, 035801(2011) ). 12/13-18/2015：Shanghai

In the presence of U-boson, the in-medium effect is favorable to obtain small radii Zhang, et.al. 12/13-18/2015：Shanghai

Dark matter candidates in NS Recently many works appear: 12/13-18/2015：Shanghai

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 12/13-18/2015：Shanghai

Dark matter in neutron stars Only gravitational attraction between normal matter and dark matter Xiang，et al PRC 89, 025803 (2014) 12/13-18/2015：Shanghai

NS radii with dark matter Steiner:PRL 108, 081102 (2012) Effect of Dark Matter? Guillot et al. 2013, ApJ 772 12/13-18/2015：Shanghai

DM Accretion 12/13-18/2015：Shanghai

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 12/13-18/2015：Shanghai

谢谢/Thank you！ 12/13-18/2015：Shanghai