Post on 19-Jan-2016
Phase transition in hot dense matter
Li Ang (Li Ang ( 李昂李昂 ))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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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
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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 (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
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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
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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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Nucleon 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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Nucleon Stars: Mass – central density relations
Rather extreme scenario for pheno TBF (No delayed collapse):
Maybe unlikely to happen !
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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
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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
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Strange quark matter
Weak-equilibrium condition, where
Charge-neutrality condition
QMDD Model: Stability arguments
(95±25MeV)
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Gibbs Construction
For a certain temperature T and total density ρt ,
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
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Hybrid Stars: EOSs, M-R curve
Hard to distinguish strange stars and hybrid stars at large M&R.
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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
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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.
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Strange stars: EOSs
Small xLarge x
Asymptotically linear
relations
at higher densities
Larger x, stiffer EOS.
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Strange stars: Surface electric field (bare or crusted?)
Xu, R. X., et al. 2001
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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.
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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 )
Sch
warz
schild
lim
it
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
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Radius [km]
M /
Msu
n
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).
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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 reasonableconfinement 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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