Protoneutron stars in the Brueckner-Hartree-Fock approach and finite-temperature kaon condensation Li Ang (李昂) 厦门大学 liang@xmu.edu.cn Collaborator: 周先荣（厦门大学） Fiorella Burgio (INFN, Catania) Hans-Josef Schulze (INFN, Catania) 2010. 7. 25 ~ 7. 27, 赤峰

Hot kaon-condensed matter (n, p, K, e,μ) CONTENT Introduction (Open questions, Tools, Nuclear Models) Hot kaon-condensed matter (n, p, K, e,μ) Chiral kaonic model; Thermal kaons introduced Composition; Equation of State Protoneutron Stars Summary

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.

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

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

Finite-temperature Extension

Hot kaon-condensed matter: 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 qK 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).

together with the chemical equilibrium Thermal kaons introduced Determine the ground state by minimizing the total grand-canonical potential density wKN with 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

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 threshold is very small and regards mainly the small fractions of thermal kaons present before the threshold.

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

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

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

Summary In conclusion, we have presented microscopic calculations of hot asymmetric nuclear matter; Effects of finite temperature are included consistently in both the nucleonic and the kaonic part of the interaction. 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 model;

Thank you very much!