1. Magnetic Field Decay and Core Temperature of Magnetars, Normal and MS pulsars Shuang-Nan Zhang 张双南 1 Yi Xie 谢祎 2 1. Institute of High Energy Physics 2. National Astronomical Observatories of China

2. 2/16 Evolutionary study of pulsars on p-pdot diagram Han, J.L, 1997, A&A B decay required?

3. 3/16 Indirect Evidence for B decay? Han, J.L. (1997): power-law decay with “gene”: t 0 ~B 0 dependence

4. 4/16 Direct Evidence for B Decay Best fits magnetars Normal pulsars ms pulsars Magnetars do not cross death line: normal radio pulsar mechanism works here? Consistent with recent detection of radio magnetars (talks by Manchester and Yuan in this meeting).

5. 5/16 P-Pdot or B-Age? Direct observables: But all tracks calculated using B-dipole radiation model, and indirect comparison with B-decay model. Derived quantities using B- dipole radiation model (OK if not overwhelmed by pulsar wind loss), but direct comparison with B-decay model. P Pdot

6. 6/16 Inclination angle decay? Magnetic-Dipole radiation model : Then the observed B-decay may be in fact an illusion of inclination angle decay (Faucher-Giguère & Kaspi 2006; Weltevrede & Johnston 2008). However, B-decay by 100 times for each kind of pulsars is difficult for inclination angle decay alone. –A better and more physical model required.

7. 7/16 B Decay Model: Heyl & Kulkarni, 1998, ApJL The dominant term

8. 8/16 ~ Constant Core Temperatures of NSs magnetars normal pulsars ms pulsars

9. 9/16 Best fits of real pulsars All observed P and Pdot paired randomly All observed P All observed Pdot General trend of the observed distributions!

10. 10/16 Each class of observed P and Pdot paired randomly Very similar to the observed distributions! Model for real pulsars

11. 11/16 Completely simulated data: Gaussian distributions Still very similar to the observed distributions! Model for real pulsars P (s) MσMσ 82-110.5 0.8 -160.2 0.0020.001-200.5 Input parameters

12. 12/16 Completely simulated data: Not a surprise! P (s) MσMσ 80.2-110.5 0.80.1-160.2 0.0020.0001-200.5 Model for real pulsars Simulated data follow model precisely! P=const  B-Dipole radiation: For each type of pulsars Ambipolar B-Decay model (T=const):

13. 13/16 Why is the Pdot so small for all pulsars? B-dipole radiation  –But why the observed Pdot is so small? Ambipolar diffusion B-decay with constant core temperature  –  P~constant  Pdot must be very small! This is a natural prediction of the above ambipolar diffusion B-decay model.

14. 14/16 Evidence for Hot Magnetars

15. 15/16 Evidence for Equilibrium between Heating & Cooling? ?

16. 16/16 Summary and Open Questions No magnetar cross the pulsar’s death line –Normal pulsar radiation mechanism? All NSs show clear evidence for B-deday –Agrees with ~constant T core ambipolar diffusion B- decay model well Heating by B-decay energy and NS cooling by neutrino and emission in ~equilibrium for all pulsars? The model naturally predicts very small Pdot as observed –Core temperature: Magnetars 2x10 8 K, Normal pulsars 2x10 7 K, ms pulsars 1x10 5 K Different populations at birth?