1. Compact Stars With a Dyson- Schwinger Quark Model 1 陈 欢 Collaborate with 魏金标（ CUG ）, M. Baldo, F. Burgio and H.-J. Schulze （ INFN ）. 2015“ 中子星与核天体物理 ” 厦门大学天文学系研讨会 中国地质大学（武汉） 数学与物理学院 H. Chen 2015-12-18 XiamenCUG, Wuhan, China

2.  Compact stars  Dense quark matter with a DS model  (proto)Hybrid quark stars  Strange quark matter and quark stars  Summary Outline 2 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen

3. Structure of Compact stars 3 CUG, Wuhan, China 1. A compact star with 2 solar-mass could reach a baryon number density about 1fm -3, quark would become an active degree of freedom, e.g. quark deconfinemt. 2. Possible strange quark stars with stable strange quark matter hypothesis. F.Weber, et.al. astro-ph/0705.2708 H. Chen 2015-12-18 Xiamen

4. Observation of Mass Lattimer 2012 J0348+0432 2.01±0.04 Solar mass J1614-2230 1.97±0.04 Solar mass Science 340, 1233232(2013) Nature 467, 1081(2010) 4 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen

5. Star mass and EOS 5 CUG, Wuhan, China  TOV equation Static spherical in hydrostatic equilibrium NS Strange stars H. Chen 2015-12-18 Xiamen

6. Dyson-Schwinger Equations  Dyson-Schwinger Eqs (DSE)  Equation of motion in QFT  Infinite set of coupled equations => Truncation  Nonlinear => multi-solution (phases) 6 CUG, Wuhan, China  Multi-solution ： Chiral symmetry broken, confined vs. Chiral symmetric, deconfined Neglect CSC H. Chen 2015-12-18 Xiamen

7.  Model of gluon propagator ： Param ： fitting meson properties in vacuum ， free(adjusted), interaction reduction Dyson-Schwinger Equations 7 CUG, Wuhan, China Maris-Tandy Model Medium effects(outlook) H. Chen 2015-12-18 Xiamen

8.  Model of quark-gluon vertex ： Rainbow (RB) approx. 1BC Ball- Chiu(B C) Dyson-Schwinger Equations 8 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen

9. EOS of QM  Thermodynamic of Quark Matter Parameter : 9 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen

10. Single Flavor 10 CUG, Wuhan, China 1. Stiffen QM EOS not only due to dynamical quark mass, but also due to modification of the vector part of quark propagator. H. Chen 2015-12-18 Xiamen

11. Dense Hadron Matter  Hadron matter ： Brueckner-Beth-Goldstone N-N ： Argonne V18, Bonn B(BOB),… TBF ： (micro) density dependent two body force vs. phenomenology Urbana TBF N-Y ： Nijmegen soft core potential  Thermal relation 11 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen

12. Dense NM in Compact Stars  Beta - equilibrium ：  Charge - neutrality ： 12 CUG, Wuhan, China In BBG theory, EOS of NM at high densities depends strongly on TBF, but inclusion of hyperons strongly soften the EOS, given maximum mass of NS about 1.5 solar mass. H. Chen 2015-12-18 Xiamen

13. Hadron-Quark Phase Transition  Maxwell condition  Gibbs condition （ Glendenning ） x: ratio of quark matter in mixed phase  Thermal equilibrium:  Chemical equilibrium:  Mechanic equilibrium: Global charge neutrality All Chemical potentials 13 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen

14. Hadron-Quark Phase Transition 14 CUG, Wuhan, China 1.Comparing with BM, phase transition at much larger densities. 2.For different quark-gluon vertices, set \alpha so that phase transition with Maxwell condition at same density, then the mixed phase with Gibbs condition are almost distinguished. HC, et al. PRD84, 105023 (2011); HC, et al., PRD91, 105002(2015) H. Chen 2015-12-18 Xiamen

15. 15 CUG, Wuhan, China The EOS of the mixed phase and, in consequence, the structure of hybrid stars depends on global effects of gluon propagator( parameter \alpha) and quark-gluon vertex. Hybrid Quark Stars HC, et al. PRD84, 105023 (2011); HC, et al., PRD91, 105002(2015) H. Chen 2015-12-18 Xiamen

16. Hybrid Quark Stars 16 CUG, Wuhan, China Dependence on effective bag constant: H. Chen 2015-12-18 Xiamen

17. H-Q Phase Transition in PNS 17 CUG, Wuhan, China HC, et al. PRD86, 045006(2012) 1. Thermal effects alone shift the onset of the mixed phase to smaller density, while neutrino trapping delays the onset. 2. The onset of the phase transition is shifted to a larger baryonic density and the mixed phase is extended to a much larger region than in BM. 3. In the case of a stiff hadronic EOS, the onset of the mixed phase is at lower density and the mixed phase has a smaller region H. Chen 2015-12-18 Xiamen

18. Structure of PNS 18 CUG, Wuhan, China HC, et al. PRD86, 045006(2012) 1. With neutrino untrapped, hot NS has smaller maximum mass 2. With neutrino trapped, the maximum mass of pure PNS smaller than that of NS, while with DSM, the maximum mass of hybrid PNS is larger than hybrid NS. H. Chen 2015-12-18 Xiamen

19. Strange Quark Matter 19 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen Quark matter at p=0: Mev/fm 3 RB4RB5RB10RB20MITBC2 B max 51.856.671.478.98152.8 B min 49.951.556.458.65952.4

20. Strange Quark Stars 20 CUG, Wuhan, China Under the constraint of stable strange quark matter, the maximum mass of strange stars in our DSE model with different vertices, gluon propagator and bag constants are smaller than 2 solar mass. H. Chen 2015-12-18 Xiamen

21. Strange Quark Stars 21 CUG, Wuhan, China 1.The radius of SQS larger than 1 solar mass are 9-11km 2.The energy release in the conversion of NS into SQS are 0.05-0.18 solar mass ~0.9-3.2(10 53 erg) H. Chen 2015-12-18 Xiamen

22. Summary  Quark matter with DSE : Stiffer EOS than bag model.  Hadron-quark phase transition and EOS: Excluding hyperon by hands Global effects of gluon propagator and vertices.  Hybrid Quark Stars: Possibility of hybrid stars with 2-solar-mass ； Larger maximum mass of PNS, delayed collapse  Strange quark matter and strange stars Possible stable strange quark matter Strange quark stars slightly lighter than 2-solar mass 22 CUG, Wuhan, ChinaH. Chen 2015-12-18 Xiamen

23. Thank You ！ Welcome to CUG, Wuhan 23 CUG, Wuhan, ChinaH. Chen 2015-11-17 Wuhan

24. Strange Quark Stars 24 CUG, Wuhan, China Under the constraint of stable strange quark matter, the maximum mass of strange stars in our DSE model with different vertices, gluon propagator parameters and bag constants are smaller than 2 solar mass. H. Chen 2015-12-18 Xiamen