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1、带强磁场奇异星的 中微子发射率刘学文指导老师：郑小平华中师范大学物理科学与技术学院PulsarIn 1967 at Cambridge University, Jocelyn Bell observed a strange radio pulse that had a regular period of 1.3373011 seconds. The team at Cambridge was able to determine that the pulse had to be of natural origin and concluded that it was a new type of s

2、tar: a pulsar.A pulsar is a rapidly rotating neutron star or strang star with intense magnetic fieldsThe representative scale of pulsar: 1.4M(sun), 10kmThe model of pulsarThe Vela PulsarX-ray image from the Chandra ObservatoryMagnetic FieldIf a solar type star collapses to form a neutron star, while

3、 conserving magnetic flux, we would have 21022967 105 1010nssunsunnsnssunBRBR BB For the sun, B100 G, so the neutron star would have a field of magnitude 1011-12 G.This over-simplified estimate actually agrees with the measured values!Effect of Magnetic Field The surface magnetic field of pulsars ar

4、e observed to be G, at the core region the magnetic field may reach up to G. So strong magnetic field must affect most of the important properties of pulsars. The elementary processes, e.g. weak and electromagnetic processes taking place at the core region should also change significantly. The stron

5、g magnetic field affect the equation of dense star matter and as a consequence the gross-properties of pulsars, e.g. mass-radius relation, rotational frequency and the phase transition process in the core region.111410 1018191010Our aim: calculate the neutrino emissivity in strange star with extreme

6、ly intense magnetic fieldWe consider the following weak interaction processes which are taking place at the strange starBased on the Weinerg-Salam-Glashow theory, the Hamiltonian isthe and are the weak and hadron current, they are :the transition rate per unit volume of reaction (1) is:Thus the neut

7、rino emissivity of reaction (1) is: Charged Particle in strong magnetic fieldIn the uniform magnetic field B along z axis corresponding to the choice of the gauge field , the electrons energy is expressed as: In the case of super strong magnetic field such that All electron occupy the Landau ground

8、state which correspond to v=0 state with electron spins pointing in the direction opposite to the magnetic field.In strange star, it is about 1015G. (0,2,2,0)AyBxB22(21)ezeEpmeBs 22() 2eeeBmCharge neutrality now force the quarks also to occupy the lowest Landau level with u quark spins point in and

9、the d, s quark point opposite the direction of the field.In this situation the charged particles are highly polarized. The perturbation theory is no long valid. The matrix elementshould be evaluated using the exact solution of the Dirac equation with magnetic field.455cos(1)(1)2fceudGSd X The Soluti

10、on of Dirac FunctionThe Dirac Hamiltonian for an electron with a uniform external magnetic field B isWhen the electron in the lowest Landau level and spins in the opposite direction of the field, the Dirac wave function for this state is:,001( )( , )00zm pmrx y ( )HpeA rm( , )mx y is the standard wa

11、ve function of the lowest Landau level;1222112( , )|()4!mmmeBx yxiyexpeBxym Boost to a finite value of Pz is straightforward; we obtain a wave function:*0cosh( )( , )( , )0sinhezeezeip z iE tip z iE teemmeezzMeerx yx y UELLWhere is the rapidity, 2cosh2Emmsinh2zpEmEmmThe wave functions of u, d, s qua

12、rks is the same form as electron. The difference is they have fraction charge and different spin. *0cosh( )( , )0sinhdzdip z iE tddmdzMerx yEL*0cosh( )( , )0sinhszsip z iE tssmszMerx yELcosh0( )( , )sinh0uzuip z iE tuumuzMerx yELNow we can calculate the S matrix, for reaction (1), it is:2223002cos1!

13、2( )3()! !2lnnfcnlzGnSeBnl lV L55(1)(1)eudMUU UU2(2 )() ()duedzuzezzEEEEPPPPM2SWVTNote that:22(2 )() ()duedzuzezzEEEEPPPP2(2 )() ()zduedzuzezzLTEEEEPPPP222(2 )(0)(2 )() ()duedzuzezzEEEEPPPPSo:3136(1)(1)222(2 )zdzzuzzezdeuVd PL dPL dPL dPE WfffV When we consider the mass of u, d quarks and the electr

14、on are zero, the neutrino emissivity can be expressed analytically:The relativistic expression of the neutrino eimssivity of reaction (1) for B=0 is given as :222225224001!24cos(3) 15 (5)(2( )3()! !(2 )lnnFcnlxynGeBTnl lL L 226457cos(1 cos)840FcpedueGT Yakovlev & Haensel (2003)()vvrdTCLLdt Cooling o

15、f Strange StarCooling equation:vvLVDirect Application: Strong Magnetic Field On The Transport Properties of Dense Stellar PlasmaNext we want to use this method to calculate the shear viscosity and bulk viscosity of strange matter in strong magnetic field.The shear viscosity in strange star matter is

16、 dominated by the quark scattering.The bulk viscosity in strange star matter is dominated by the non-lepton reaction: u + d u + sThe critical angular velocity for a given stellar model as a function of temperature one solves the equation:The critical angular velocity is a strong restriction on the m

17、odel of pulsar.Maybe it can identify a pulsar neutron star or strange star.“Standard” instability region (figure from Andersson & Kokkotas 2001)SummaryStrong magnetic field may affect most properties of pulsars:Cooling of pulsarsCritical frequency of pulsarsMass-radius of pulsarsPhase transition processes in the pulsarsThank You!Direct URCA Process In Strong Magnetic FieldWe adopt another choice of the gauge field:(0,0,0)AxBAstro-ph/0110135The wave function of the