Protoneutron stars in the Brueckner-Hartree-Fock approach and finite-temperature kaon condensation

Protoneutron stars in the Brueckner-Hartree-Fock approach andfinite-temperature kaon condensation

Li Ang (Li Ang ( 李昂李昂 ))厦门大学

[email protected]

2010. 7. 25 ~ 7. 27, 赤峰

Collaborator: 周先荣（厦门大学） Fiorella Burgio (INFN, Catania)

Hans-Josef Schulze (INFN, Catania)

2/14A. Li@13th核结构大会

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


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

?

Kem eeK :*

...,KnnnHyperons ：

matterquarktoDeconfined


rrdrrrM

rMrr

rprrMrrp

dr

dp

0

2

3

)(4)(

))(2(

)](4)()][()([

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.


In asymmetry nuclear matter, one can define the isospin asymmetry parameter

where

In-medium effectiveInteraction G matrix

V3eff is reduced to a

density-dependent 2-body force

v+v3effv

12 ( , ) , | 12Q

r r r r Ge

r r r r

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


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).


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.


Composition: Temperature effect

Particle fractions as a function of the baryon density in trapped (Ye = 0.4, lower panel) and untrapped (x = 0, upper panel) -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 -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.


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: a3ms = -143 MeV (H.Ohki et al, PRD 2008).

Fairly large onset densities;Kaons strongly disfavored!

(T=30MeV)


Protoneutron Stars: EOSs

2)Less softeningeffect 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:


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;

Protoneutron stars in the Brueckner-Hartree-Fock approach and finite-temperature kaon condensation

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