1. Phase transition in hot dense matter Li Ang ( 李昂 ) Xiamen University liang@xmu.edu.cn 2010. 1.18 ~ 2. 5, 京都 Collaborator: W. Zuo ( 左维 ) (IMP, Lanzhou) G.X. Peng ( 彭光雄 ) (IHEP, Beijing) R.X. Xu ( 徐任新 ) (PKU, Beijing) U. Lombardo, G. F. Burgio (INFN, Catania) Hans-Josef Schulze (INFN, Catania)

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3. 3/28 A. Li@NFQCD10 CONTENT  Introduction ( Open questions, Tools, Nuclear Models)  Hot dense matter ( Quark model, EOSs, composition, M-R curve...)  Hot kaon-condensed matter (n, p, K, e,μ)  Hadron-quark Transition (n, p, u, d, s, e,  )  Strange quark matter(u, d, s, e)  Summary

4. 4/28 A. Li@NFQCD10 A cross-section of a neutron star. Beneath the iron surface, nuclei in the crust quickly go to higher atomic numbers (e.g., lead) bloated with neutrons. Deeper, the crust has free neutrons floating between the nuclei, along with relativistic electrons. Finally, at the base of the crust the nuclei get truly enormous until they literally touch - and then melt to become the liquid interior. Introduction: Open questions ?

5. 5/28 A. Li@NFQCD10 Introduction: Tools S. Shapiro and S. Teukolsky, Black Holes, White Dwarfs and Neutron Stars, 1983 The stable configurations of a (P)NS can be obtained from the well-known hydrostatic equilibrium equations of Tolman, Oppenheimer, and Volkov for pressure p(r) and enclosed mass M(r): Once the EOS p(  ) is specified, for a chosen central value of the energy density, the numerical integration then provides the mass- radius relation.

6. 6/28 A. Li@NFQCD10 In asymmetry nuclear matter, one can define the isospin asymmetry parameter where In-medium effective Interaction G matrix V 3 eff is reduced to a density-dependent 2-body force v+v 3 eff v Defect function For a given total densityρand asymmetryβ.a bare two-body force v as input, solve the Eqs self-consistently ： BG equation s.p. energy s.p. auxiliary potentials BHF Pauli operator (BHF+ Three-body Forces) Lejeune, Mahaux, Baldo, Bombaci, Mathiot, Lombardo, Zuo, Song, Li,…70 -present Introduction: Nuclear Models

7. 7/28 A. Li@NFQCD10 Finite-temperature Extension

8. 8/28 A. Li@NFQCD10  Hot kaon-condensed matter (n, p, K, e,μ)  Chiral kaonic model; Thermal kaons introduced  Composition; Equation of State  Nucleon Stars  Hadron-quark Transition (n, p, u, d, s, e,  )  New Quark-Mass-Density-Dependent (QMDD) Model  Hadron-quark Transition; Hybrid Stars  Strange quark matter (u, d, s, e)  What extent QMDD allowed to study SQM  Strange Stars; Strange Star Candidates Hot dense Matter

9. 9/28 A. Li@NFQCD10  Hot kaon-condensed matter (n, p, K, e,μ)  Chiral kaonic model; Thermal kaons introduced  Composition; Equation of State  Nucleon Stars  Hadron-quark Transition (n, p, u, d, s, e,  )  New Quark-Mass-Density-Dependent (QMDD) Model  Hadron-quark Transition; Hybrid Stars  Strange quark matter (u, d, s, e)  What extent QMDD allowed to study SQM  Strange Stars; Strange Star Candidates Hot dense Matter

10. 10/28 A. Li@NFQCD10 Chiral kaonic model The thermodynamic potential densities due to the condensed kaons and the thermal kaons are introduced as follows: Then the kaonic (charge) density q K is given by T. Tatsumi and M. Yasuhira, Phys. Lett. B441, 9 (1998); Nucl.Phys. A653, 133 (1999); M. Yasuhira and T. Tatsumi, Nucl. Phys. A690, 769 (2001); T. Muto, M. Yasuhira, T. Tatsumi, and N. Iwamoto, Phys. Rev. D67, 103002 (2003); T. Muto, T. Tatsumi, and N. Iwamoto, Phys. Rev. D61, 063001,083002 (2000).

11. 11/28 A. Li@NFQCD10 Thermal kaons introduced Determine the ground state by minimizing the total grand- canonical potential density  KN with respect to the condensate amplitude , keeping (  K ;  ;x) fixed : together with the chemical equilibrium and charge neutrality conditions The composition and the EOS of the kaon-condensed phase in the chemically equilibrated (P)NS matter can be obtained.

12. 12/28 A. Li@NFQCD10 Composition: Temperature effect  Particle fractions as a function of the baryon density in trapped ( Y e = 0.4, lower panel ) and untrapped ( x = 0, upper panel )  -stable matter at the temperatures T = 0, 10, 30, and 50 MeV for a 3 m s = -222 MeV and the micro TBF. Temperature effects mainly in the low- density region, only slightly at high density: 1) Kaon condensate threshold density slightly dependent on the temperature: (0.489, 0.490, 0.492,0.497) for -untrapped, (0.580,0.583,0.589,0.629) for -trapped; 2) The temperature influence on the kaon population above the condensate threshold is very small and regards mainly the small fractions of thermal kaons present before the threshold.

13. 13/28 A. Li@NFQCD10 Composition: Dependence on the KN interaction strength 0.4 ~ 0.6 fm -3 for untrapped matter 0.45 ~ 0.75 fm -3 for trapped matter Onset density strongly dependent : The most recent lattice determination of the strangeness content of the proton indicate: a 3 m s = -143 MeV (H.Ohki et al, PRD 2008). Fairly large onset densities; Kaons strongly disfavored! (T=30MeV)

14. 14/28 A. Li@NFQCD10 Nucleon Stars: EOSs 2)  Less softening effect of kaons in trapped matter —— A delayed collapse while cooling down. 1) Temperature plays a minor role in comparison with neutrino trapping; Same conclusion for pheno TBF; Any negatively charged hadron! Three different strongly idealized stages of the PNS evolution:

15. 15/28 A. Li@NFQCD10 Nucleon Stars: Mass – central density relations Rather extreme scenario for pheno TBF (No delayed collapse): Maybe unlikely to happen !

16. 16/28 A. Li@NFQCD10  Hot kaon-condensed matter (n, p, K, e,μ)  Chiral Model; Thermal kaons introduced  Composition; Equation of State  Nucleon Stars  Hadron-quark Transition (n, p, u, d, s, e,  )  New Quark-Mass-Density-Dependent (QMDD) Model  Hadron-quark Transition; Hybrid Stars  Strange quark matter (u,d,s,e)  What extent QMDD allowed to study SQM  Strange Stars; Strange Star Candidates Hot dense Matter

17. 17/28 A. Li@NFQCD10 The variation of the quark mass with density mimics the strong interaction between quarks. Quark confinement Asymptotic freedom Improvement: z =1/3 instead of z =1 (linear scaling). G.X. Peng et al, 2000-2005 New Quark-Mass-Density-Dependent Model Quark model with chiral mass scaling

18. 18/28 A. Li@NFQCD10 Strange quark matter Weak-equilibrium condition, where Charge-neutrality condition QMDD Model: Stability arguments (95±25MeV)

19. 19/28 A. Li@NFQCD10 Gibbs Construction For a certain temperature T and total density ρ t, and Global neutrality, Where quark fraction : (0 -1) Hadron-quark Transition: Phase diagram Transition occurs ~ 0.15 fm -3 Pure quark occurs ~ 0.95 fm -3

20. 20/28 A. Li@NFQCD10 Hybrid Stars: EOSs, M-R curve Hard to distinguish strange stars and hybrid stars at large M&R.

21. 21/28 A. Li@NFQCD10  Hot kaon-condensed matter (n, p, K, e,μ)  Chiral Model; Thermal kaons introduced  Composition; Equation of State  Nucleon Stars  Hadron-quark Transition (n, p, u, d, s, e,  )  New Quark-Mass-Density-Dependent (QMDD) Model  Hadron-quark Transition; Hybrid Stars  Strange quark matter (u,d,s,e)  What extent QMDD allowed to study SQM  Strange Stars; Strange Star Candidates Hot dense Matter

22. 22/28 A. Li@NFQCD10 What extent QMDD allowed to study SQM * Linear scaling: x = 1 eg Fowler et al. 1981, Chakrabarty 1991; Widely used; Phenomenological. * Cubic scaling: x = 1/3 eg Peng et al. 2000 Developed recently; Based on quark chiral and linear confinement. * Other forms eg Dey et al.1998, Wang 2000, Zhang & Su 2003. Where   x is treated as a FREE parameter (0.1 -3) ；  C is determined by stability arguments (the true strong-interaction ground state). ● ● ● ● ● 95 Large uncertainty in the quark mass formulas: Let the system lying in the same binding state (for each x), to check the x-dependence.

23. 23/28 A. Li@NFQCD10 Strange stars: EOSs Small x Large x Asymptotically linear relations at higher densities Larger x, stiffer EOS.

24. 24/28 A. Li@NFQCD10 Strange stars: Surface electric field (bare or crusted?) Xu, R. X., et al. 2001

25. 25/28 A. Li@NFQCD10 Strange stars: M, R, Central density, Maximum rotational frequency  The mass–radius relations of SSs for all considered models: 注 ： 1) M(R) curves for the lower boundaries are shown with grey lines: Larger x, wide regime allowed! 2) Contours of the maximum rotation frequencies are given by the light grey curves: Larger x, faster spining! SS sequences with a linear scaling support the lowest gravitational masses.

26. 26/28 A. Li@NFQCD10 SAX J1808.4 Li X D, et al (1999) ① NS model favored for most observations; ② SS model needed for some observations. NS and SS both possible, and May transit from each other. How to distinguish the two? (Weber 2005 ) Schwarzschild limit Strange Star Candidates Dey M., Bombaci I., Dey J., Ray S., Samanta B. C., 1998, Phys. Lett. B, 438, 123; erratum 1999, Phys. Lett. B, 467, 303

27. 27/28 A. Li@NFQCD10 Radius [km] M / M sun Li, Peng,Lu...in progress QMDD model with x = 1/3 Kaaret et al 2007 Strange Star Candidates Dey M., Bombaci I., Dey J., Ray S., Samanta B. C., 1998, Phys. Lett. B, 438, 123; erratum 1999, Phys. Lett. B, 467, 303 None of the present astrophysical observations can prove or confute the existence of SSs (or NSs).

28. 28/28 A. Li@NFQCD10 Summary Finite temperature plays a minor role compared to neutrino trapping, which generally decreases the stellar maximum mass in the absence of a kaon condensate, and increases it with a condensate. If recent very small values for the strangeness content of the proton are confirmed, kaon condensation may be totally suppressed in our modelb; It is found that the mixed phase can occur, for a reasonable confinement parameter, near the normal nuclear saturation density and goes over to pure quark matter at about 5 times the saturation. The onset of mixed and quark phases is compatible with the observed class of low-mass neutron stars. Strange star sequences with a linear scaling support the lowest gravitational masses; The variation of the scaling causes an order of magnitude change of the strong electric field on the quark surface, and may have some astrophysical implications.

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