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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