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

2. Pulsar In 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 star: a pulsar. A pulsar is a rapidly rotating neutron star or strang star with intense magnetic fields The representative scale of pulsar: 1.4M(sun), 10km

3. The model of pulsar The Vela Pulsar X-ray image from the Chandra Observatory

4. Magnetic Field If a solar type star collapses to form a neutron star, while conserving magnetic flux, we would have For the sun, B~100 G, so the neutron star would have a field of magnitude 10 11-12 G. This over-simplified estimate actually agrees with the measured values!

5. Effect of Magnetic Field The surface magnetic field of pulsars are 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 strong 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.

6. Our aim: calculate the neutrino emissivity in strange star with extremely intense magnetic field We consider the following weak interaction processes which are taking place at the strange star

7. Based on the Weinerg-Salam-Glashow theory, the Hamiltonian is the and are the weak and hadron current, they are : the transition rate per unit volume of reaction (1) is: Thus the neutrino emissivity of reaction (1) is:

8. Charged Particle in strong magnetic field In the uniform magnetic field B along z axis corresponding to the choice of the gauge field, the electron ’ s energy is expressed as: In the case of super strong magnetic field such that All electron occupy the Landau ground 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 10^15G.

9. Charge neutrality now force the quarks also to occupy the lowest Landau level with u quark spins point in and 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 element should be evaluated using the exact solution of the Dirac equation with magnetic field.

10. The Solution of Dirac Function The Dirac Hamiltonian for an electron with a uniform external magnetic field B is When the electron in the lowest Landau level and spins in the opposite direction of the field, the Dirac wave function for this state is:

11. is the standard wave function of the lowest Landau level; Boost to a finite value of Pz is straightforward; we obtain a wave function:

12. Where is the rapidity, The wave functions of u, d, s quarks is the same form as electron. The difference is they have fraction charge and different spin.

13. Now we can calculate the S matrix, for reaction (1), it is:

14. Note that: So:

15. When we consider the mass of u, d quarks and the electron 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 :

16. Yakovlev & Haensel (2003) Cooling of Strange Star Cooling equation:

17. Direct Application: Strong Magnetic Field On The Transport Properties of Dense Stellar Plasma Next 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 dominated by the quark scattering. The bulk viscosity in strange star matter is dominated by the non-lepton reaction: u + d  u + s

18. The 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 model of pulsar.Maybe it can identify a pulsar neutron star or strange star.

19. “ Standard ” instability region (figure from Andersson & Kokkotas 2001)

20. Summary Strong magnetic field may affect most properties of pulsars: Cooling of pulsars Critical frequency of pulsars Mass-radius of pulsars Phase transition processes in the pulsars

21. Thank You!

22. Direct URCA Process In Strong Magnetic Field We adopt another choice of the gauge field:

23. Astro-ph/0110135 The wave function of the electron:

24. Only when the process involve two charged particles, the neutrino emissivity is independent of Lx, Ly or Lz