Probe into Magnetic Field and Initial Period of Neutron Star

1. Probe into Magnetic Field and Initial Period of Neutron Star

2. Basis • Two models • 72 Pulsars data with transverse velocities( form Dr Wang, possible recycle pulsars are deducted)

3. Superfluid Vortex of NS Vortex flow Vortex core (normal neutrons)

4. Spin-down by neutrino radiation from superfluid vortex(Basic theory: Peng et al.1982) • It is general believed that neutron superfluid in the interior of neutron stars is in a vortex state, and the vortex lines are parallel to the rotation axis of the neutron star. • The circularly moved neutrons may emit neutrino pairs owning to the weak interaction of the neutral current. • Radiation power: the superfluid neutrons plus normal neutrons • Rotation energy of the neutron star keeps infusing to the supfluid vortices via “Ekman pump mechanism”. n is the vortex quantum number; is the energy gap caused by the interaction of attraction of the wave between neutrons.

5. Hybrid model(Dipole model+Superfluid) • Rotation energy loss rate: • Period derivative: • Assumptions: • Magnetic field: • Age: • Braking index: (n decreases with increased P)

6. Contrast between the two models

7. The observedkick velocities for Pulsars V(km/s) Number Percentage  100 71 75%  300 36 38%  500 14 15%  1000 5 5%

8. J Parity violation Jf  Ji p n n

9. Neutrino Jet Rocket Model If the neutron angular momentum is carried away mainly by neutrinos, the direction of emitted neutrinos with left hand spin must be opposite to the original neutron angular momentum , while the neutron itself will get a recoil along its angular momentum direction. On the contrary, If the neutron angular momentum is carried away mainly by the anti-neutrinos, the direction of the emitted anti-neutrinos with right hand spin must be the same as the original neutron angular momentum direction , while the neutron itself will get a recoil opposite to its angular momentum direction.

10. Formulae :Asymmetry factor

11. 72 Pulsars’ B12 and P0 • According to upwards models, we calculate 72 Pulsars’ B12 and P0 ,here we choose =3.0 to simplify solving the non-linear equations, and  closed 3 makes for acceleration. • For each pulsar, we choose least n0 make equation solved.

12. Calculation Results P0 min=0.000423s ( B12 =2.832, n0=950 V=2500km/s) B12 max=27.558 (P0 =0.00057s, n0=1115,V=252km/s ) 2) Hybrid Model can reduce magnetic field calculated by Dipole Model effectively. n0 max=1325 (B12=11.725,P0=0.000433s, V=1730km/s)

14. Statistics and Fit Correlation coefficient:0.882565

15. Physics Signification • The B12 is higher, that is said, the presupernova collapsed more fiercely, so the interior overfall is more disordered, it can be anticipated n0 is larger. • If P0 increased,because of angular momentum conversation law,we can draw same conclusion.

16. Conclusion and Discussion 1) Neutrino Jet Rocket Model is a gradual acceleration model, main accelerating period : P  0.5 s, Vmax  1000 km/s 3)Use the connection of B12-n0-P0, maybe solve the problem of high magnetic field and calculate more pulsars’ velocities etc. 4)More work should be done about making certain involved parameter more reasonably.

17. Thank you!