Protoneutron stars in the Brueckner-Hartree-Fock approach and finite-temperature kaon condensation
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Transcript of 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
2010. 7. 25 ~ 7. 27, 赤峰
Collaborator: 周先荣(厦门大学) Fiorella Burgio (INFN, Catania)
Hans-Josef Schulze (INFN, Catania)
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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
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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
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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.
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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
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Finite-temperature Extension
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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).
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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.
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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.
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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)
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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:
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Protoneutron Stars: Mass – central density relations
Rather extreme scenario for pheno TBF (No delayed collapse):
Maybe unlikely to happen !
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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;
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