Phase transition in hot dense matter

1. Phase transition in hot dense matter • Li Ang (李昂) • Xiamen University • liang@xmu.edu.cn • 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) 2010. 1.18 ~ 2. 5,京都

3. 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, m) • Strange quark matter(u, d, s, e) • Summary

4. Introduction: Open questions ? 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.

5. Introduction: Tools 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(e) is specified, for a chosen central value of the energy density, the numerical integration then provides the mass-radius relation. S. Shapiro and S. Teukolsky, Black Holes, White Dwarfs and Neutron Stars, 1983

6. (BHF+ Three-body Forces) Introduction: Nuclear Models In asymmetry nuclear matter, one can define the isospin asymmetry parameter For a given total densityρand asymmetryβ.a bare two-body forcev as input, solve the Eqs self-consistently： Pauli operator where BG equation BHF In-medium effective Interaction G matrix s.p. energy Defect function s.p. auxiliary potentials v+v3eff v V3eff is reduced to a density-dependent 2-body force Lejeune, Mahaux, Baldo, Bombaci, Mathiot, Lombardo, Zuo, Song, Li,…70 -present

7. Finite-temperature Extension

8. Hot dense Matter • 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, m) • 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

9. Hot dense Matter • 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, m) • 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

10. 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 qKis 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. Thermal kaons introduced Determine the ground state by minimizing the total grand-canonical potential densitywKNwith respect to the condensate amplitude q , keeping (mK;r;x) fixed: together with the chemical equilibrium The composition and the EOS of the kaon-condensed phase in the chemically equilibrated (P)NS matter can be obtained. and charge neutrality conditions

12. Composition: Temperature effect • Particle fractions as a function of the baryon density in trapped (Ye= 0.4, lower panel) and untrapped (xn = 0, upper panel) b -stable matter at the temperatures T = 0, 10, 30, and 50 MeV for a3ms= -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 n-untrapped, (0.580,0.583,0.589,0.629) for n-trapped; 2) The temperature influence on the kaon population above the condensate thresholdis very small and regards mainly the small fractions of thermal kaons present before the threshold.

13. Composition: Dependence on the KN interaction strength (T=30MeV) The most recent lattice determination of the strangeness content of the proton indicate: a3ms =-143 MeV (H.Ohki et al, PRD 2008). Fairly large onset densities; Kaons strongly disfavored! Onset density strongly dependent : 0.4 ~ 0.6 fm-3 for untrapped matter 0.45 ~ 0.75 fm-3 for trapped matter

14. Nucleon Stars: EOSs Threedifferent strongly idealized stages of the PNS evolution: 1) Temperature plays a minor rolein comparison withneutrino trapping; Same conclusion for pheno TBF; 2)Less softening effect of kaons in trapped matter —— A delayed collapse while cooling down. Any negatively chargedhadron!

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

16. Hot dense Matter • 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, m) • 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

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

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

19. Hadron-quark Transition: Phase diagram For a certain temperature T and total density ρt, and Global neutrality , Where quark fraction : (0 -1) Gibbs Construction Pure quark occurs ~ 0.95 fm-3 Transition occurs ~ 0.15 fm-3

20. Hybrid Stars: EOSs, M-R curve Hard to distinguishstrange stars and hybrid stars at large M&R.

21. Hot dense Matter • 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, m) • 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

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

23. Strange stars: EOSs Asymptotically linear relations at higher densities Larger x, stiffer EOS. Small x Large x

24. Strange stars: Surface electric field (bare or crusted?) Xu, R. X., et al. 2001

25. Strange stars: M, R, Central density, Maximum rotational frequency SS sequences with a linear scaling support the lowestgravitational masses. • 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!

26. Strange Star Candidates 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. Schwarzschild limit How to distinguish the two? Dey M., Bombaci I., Dey J., Ray S., Samanta B. C., 1998, Phys. Lett. B, 438, 123; erratum 1999, Phys. Lett. B, 467, 303 SAX J1808.4Li X D, et al(1999) (Weber 2005 )

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

28. 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.

29. Thank you very much!