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)
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