Thermal Evolution of Rotating neutron Starsand Signal of Quark Deconfinement

Henan University, Kaifeng, China

Miao Kang

Model of neutron stars(hybrid stars)

The energy release of quark deconfinement

Thermal evolution of hybrid stars and quark deconfinement signature

Conclusion and Discussion

Model of hybrid starsMaxwell construction (a sharp tran

sition takes place between the two charge-neutral hadron and quark phase)(Baym & Chin ,1976,Phys.Lett.B, 62,241 )

Gibbs construction (the transition can occur through the formation of a mixed phase of hadron matter and quark matter, total charge neutrality being achieved by a positively charged amount of hadron matter and a negatively charged amount of quark matter)

(Glendenning N. K., 1992, Phys. Rev. D, 46,127

4)

Model of hybrid starsGibbs condition at zero temperature

between hadron phase and quark phase

Equation of state (EOS)

Quark matter• Composition: u,d,s,e

• Model: effective mass bag model considering medium effect(MIT)

• Idea: quasi-particle approximation

• Parameters: bag constant B, coupling constant g, the current mass of s quark ms

(Schertler et al. Nucl.Phys.A(1997) )

Equation of state (EOS)

Hadron matter

• Composition: n,p,e,

• Model:

subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS

(Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J,170 299(1971))

nuclear densities: Argonne EOS

(Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998))

*18 UIXV

the nucleon interaction with the inclusion of a parameterized

three-body force and relativistic boost corrections

• Composition: n,p,e,

• Model:

subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS

(Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J,170 299(1971))

nuclear densities: Argonne EOS

(Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998))

• Composition: n,p,e,

• Model:

subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS

(Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J,170 299(1971))

nuclear densities: Argonne EOS

(Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998))

• Composition: n,p,e,

• Model:

subnuclear densities: Baym-Pethick-Sutherland(BPS) EOS

(Baym,G.,Pethick,C.,Sutherland,P. Astrophys.J,170 299(1971))

nuclear densities: Argonne EOS(APR)

(Akmal A., Pandharipande V. R., Ravenhall D. G.,Phys.Rev.C58,1804(1998))

Equation of state (EOS)

• B=85,108,136• g=3.0

• Ms =150.0MeV

3fmMeV

Structure evolution of hybrid stars

Static configuration

TOV equation(Oppenheimer & Volkoff

Phys.Rev,55 374(1939))

Structure evolution of hybrid stars

static

Maximum rotation frequency Rotation configuration

Perturbative Approach

(Hartle J. B., 1967, ApJ, 150, 1005)

Quark deconfinement

Nucleon direct Urca process

B=108 3fmMeV

Energy release of deconfinement

Non-linear dissipation (Professor Zheng xiaoping) The deconfine phase transition from hadron matter to quark matt

er may continuously occurs during spin-down of NSs.

The density of any given fluid element increases, changing its equilibrium state. The relaxation toward the new equilibrium appears accordingly if the transition has nonlinear phase structure by Gibbs construction. So the two phases are not quite equilibrium and binding energy is stored that can be released by phase transition.

Energy release of deconfinement Energy release per baryon

The total heat luminosity

The simple parameterized form0.1MeV

Energy release of deconfinement

The number of quarks

converting into baryons

Kang M., Zheng X. P., 2007, MNRAS, 375,1503

Neutrino emission

• Hadron matter:

nucleon direct Urca (NDU)

nucleon modified Urca(NMU)

nucleon bremsstrahlung(NB)

• Quark matter:

quark direct Urca (QDU)

quark modifiedUrca (QMU)

quark bremsstrahlung(QB)

Glen & Sutherland 1980

Heat capacity

Neutrino emission luminosity

Surface photon luminosity

Thermal evolution of hybrid stars

•A quite clear magnetic-field dependence

•Deconfinement heating can produce a characteristic rise of surface temperature

•Deconfinement heating dominate the behavior of thermal evolution

•Low magnetic field (B=10^9G) produces a sharp jump in surface temperature

1.6 solar mass

0 1 2 3 4 5 6 7 84.5

5.0

5.5

6.0

6.5 1.5 M

1.6 M

1.7 M

Log(

Ts /

K)

Log(t/yr)

Thermal evolution of hybrid starsdeconfinement heating delay the cooling

observational data can be explained well

Magnetic Bm=10^12,10^11 Gauss

Without DH

0 1 2 3 4 5 6 7 8 9

4.8

5.0

5.2

5.4

5.6

5.8

6.0

6.2

6.4

6.6

1.5M

1.6M

1.7M

log

(Ts /

K)

Log(t/yr)

Thermal evolution of hybrid stars

Magnetic Bm=10^9,10^8 Gauss

• High temperatures of stars at older ages(>10^9) yrs

• A period of increase of surface temperature

• A evidence of existence of deconfinement quark matter?

4 5 6 7 8 9 102.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

1.5M

1.6M

1.7M

PSR J0437-4715

Log(t/yr)

Conclusion

• Explore the signal of quark matter appearing through theoretical simulation of thermal evolution curves of hybrid stars with deconfinement heating.

• Rise of surface temperature of stars is derived from the deconfinement heating.

• Rise of surface temperature accompany quark matter appearing

• It may be a evidence for existence of quark matter, if a heating period is observed for a very old pulsar.

Discussion

• The mass range of deconfined signal emerging can be changed with varying of some parameters(bag constant B, coupling constant g).

• The deconfinement heating rate is different for various stages of stars. This may lead to special effect of short timescale behaviors due to local heat deposit and enhanced neutrino emission. The details of evolution in years is worth discussion in future researches.

Different bag constant

0.0 0.2 0.4 0.6 0.8 1.00.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

B(0

)[fm

-3]

B=85MeV fm-3

M=0.74M

0.80.89

0.2 0.4 0.6 0.8 1.0

B=96MeV fm-3

1.11

1.25

1.32

0.2 0.4 0.6 0.8 1.0

B=108MeV fm-3

/max

1.4

1.5

1.6

1.64

0.2 0.4 0.6 0.8 1.0

B=122MeV fm-3

1.83

1.7

1.6

0.2 0.4 0.6 0.8 1.0

B=136MeV fm-3

1.9

1.8

1.7

0 1 2 3 4 5 6 74.5

5.0

5.5

6.0

6.5

7.0 1.5 M

1.6 M

1.7 M

Log(

Ts /

K)

Log(t/yr)