Deconfinement Phase Transition Heating and Thermal Evolution of Neutron Stars
aa r X i v : . [ a s t r o - ph ] N ov Deconfinement Phase Transition Heating and Thermal Evolution of NeutronStars
Kang Miao , , Pan Na-Na , Wang Xiaodong , The college of physics and electron,Henan university , Kaifeng, 475004, Henan, P.R.China.2 -
The institute of astrophysics,Huazhong normal university , Wuhan 430079, Hubei, P.R.China.
ABSTRACT
The deconfinement phase transition will lead to the release of latent heat duringspins down of neutron stars if the transition is the first-order one. We have investigatedthe thermal evolution of neutron stars undergoing such deconfinement phase transition.The results show that neutron stars may be heated to higher temperature.This featurecould be particularly interesting for high temperature of low-magnetic field millisecondpulsar at late stage.Probing the equation of state (EOS) of neutron star matter is a urgent task in studying compactstars. Both the determination of mass-radius relation(1)(2) and spin evolution of compact stars(3)(4)(5)(6)(7)(8)are usual methods. Neutron stars (NSs) cooling is another important tool forthe study of dense matter(9)(10). By comparing cooling models with thermal emission data fromobservations, we can gain insight into the EOS of dense matter inside NSs. Heating source insidethe stars is an important factor effect in the cooling of NSs.It is known that a NS will spin down due to braking (e.g. electric-magnetic radiation orgravitational wave radiation). The deconfinement phase transition from hadronic matter to quarkmatter can continuously occur in NSs during the spins down. Many investigations were interestingin the phase transition which is of the first-order type(11)(12). Such deconfinement processes inducecontinuous release of latent heat. The generation of the energy increases internal energy of the star.It will be called deconfinement heating (DH). DH have been investigated in strange stars, whereneutron drops at the bottom of a crust drip on to the quark matter surface to be instantaneouslydissolved into quark matter(13)(14).Most of the approaches to deconfined matter in NSs use a standard two-phase description ofEOS where the hadron phase and the quark phase are modelled separately and resulting EOS of themixed phase is obtained by imposing Gibbs conditions for phase equilibrium with the constraintthat baryon number as well as electric charge of the system are conserved(15). Assumed thedeconfinement phase transition is a first order phase transition, the deconfinement processes shouldproduce latent heat.Combining with the equation of rotating structure based on Hartle’s perturbation approach(16),we get the total latent heat release unit time for a star in ref(17) H dec ( t ) = Z dedν ˙ ν ( t ) ρ B dV. (1) 2 –We can approximate equation (1) using a expression with a parameter q n (18) H dec ( t ) = q n dN q dν ˙ ν ( t ) (2)here q n is the average value of release energy per necleon transforming into quarks, N q is decon-finement baryon number, ˙ ν is induced by magnetic dipole radiation. In a strange star with nuclearmatter crust, the similar expression has been obtained. However, q n in our model is 10 − timessmaller than that of the strange star model(17)(19).The cooling is realized via two channels - by neutrino emission from the entire star body andby transport of heat from the internal layers to the surface resulting in the thermal emission ofphotons. Neutrino emission is generated in numerous reactions in the interiors of neutron stars,as reviewed, by Page et al. (9). In this paper, we consider the most powerful neutrino emissionincluding nucleon direct Urca (NDU) processes and quark direct Urca (QDU) processes for thematter of NSs. Nucleon superfluidity and quark superconductivity are not included in the model.According to the thermal evolution equation(9), we get the thermal evolution curves with DHshown in Fig.1 which shows the cooling behavior of a 1.5 M ⊙ NS for different magnetic fields(10 − G), where q n is taken to be 0.1 MeV. It is evident that the DH increase the surfacetemperature dramatically. This is extremely different from fast cooling scenario (solid curve). Thestrong field strength induces a rapid spin-down at the beginning while the low field strength leadsto only obvious spin-down at the older ages. In the cases of weak field, stars could maintain hightemperatures even at older ages ( > yrs). The temperature is nearly identified with the valuesobserved from millisecond pulsars, especially for PSR J0437-4715(20).We find DH’s significant effects on the thermal evolution and the effects is much more importantthan the past present heating mechanisms(21)(22)(23)(24). We can find the remarkable changeof temperature in strange stars nuclei where DH leads to too hot millisecond pulsars(14)(25). Infuture, we expect more observational examples in investigating effects of DH mechanism on the NSsthermal evolution. Another problem which remains to be investigated is the unified description ofmiddle-age and old pulsars. The NSs containing MP matter model may be no bad selection whenour combining DH, superfluidity effects in nuclear matter together.This work supported by NFSC under Grant Nos.10603002. I would like to thank Prof X.P.Zheng for the useful disscussion. REFERENCES
M.Alford, et al
Nature , 7(2007)J. M.Lattimer, and M.Prakash,
Science , 536 (2004)J. Madsen,
Phys.Rev.Lett , 10(2000) 3 –X. P.Zheng, S.H.Yang, and J.R.Li, APJ , L135(2003)N.N.Pan,X.P.Zheng, and J.R.Li,
MNRAS , 1359 (2006)X. P.Zheng, et al
New.Astron , 165 (2006)X. P.Zheng,M. Kang, X.W.Liu, and S.H.Yang, Phys.Rev.C , 025809 (2005)X. P.Zheng,X.W.Liu,M. Kang, and S.H.Yang, Phys.Rev.C , 015803 (2004)D.Page, U.Geppert, and F. Weber, Nucl.Phys.A , 497(2006)X.W.Liu, X. P.Zheng, and D.F.Hou
Astropart.phys , 92 (2005)R. D.Pisalski, and F.Wilczek, Phys.Rev.Lett , 338 (1984)R. V.Gavai,J.Potvin, and S.Sanielevici, Phys.Rev.Lett , 2519 (1987)Y. F.Yuan , and J. L.Zhang, Astron&Astrophys ,3711999Y.W.Yu, and X. P.Zheng,
Astron&Astrophys , 1071 (2006)N. K. Glendenning ,
Phys. Rev. D , 1274(1992)J. B.Hartle , ApJ , 1005(1967)M.Kang ,X.P.Zheng, and N.N. Pan, astro-ph/0708.0900 (2007)M.Kang ,X.P.Zheng,
MNRAS , 1503(2007)J. L.Zdunik, P.Haensel and E.Gourgoulhon,
Astron&Astrophys , 535 (2001)O.Kargaltsev, G. G.Pavlov, and R.Romani,
ApJ ,327(2004)A.Reisenegger ,
ApJ , 749(1995)K. S. Cheng ,W. Y. Chau , J. L.Zhang , and H. F.Chau,
ApJ , 235(1992)R.Van,A.Kenneth , B.Link ,and R. I.Epstein,
ApJ , 294(1995)X. P.Zheng, and Y.W.Yu,
Astron&Astrophys , 627 (2006)X. P.Zheng, X.Zhou, and Y.W.Yu,
MNRAS , 1659 (2006)
This preprint was prepared with the AAS L A TEX macros v5.2. G PSR J0437-4715 l og ( T s / K ) log(t/yr) 10 G10 G 10 G 10 G Fig. 1.— Cooling curves of 1.5 M ⊙⊙