1. The Phase-Resolved Spectra of the Crab Pulsar Jianjun Jia Jan 3, 2006

2. Outline Review of the high energy pulsars Theoretical models The Crab pulsar Conclusions

3. Observations of high energy pulsars Light curves spectra

4. Theory of high energy pulsars Magnetic dipole approximation Geometry of the magnetic field lines The field lines can be traced by numerical calculations.

5. Geometry of the magnetic field lines footprints last closed field lines

6. Goldreich & Julian model

7. Outer gap model Global currents flow through the null charge surface results in large regions of charge depletion, which form the gaps in the magnetosphere. The gap extends from the null charge surface to the light cylinder. Parallel electric field is induced in the gap, which can accelerate the electrons to extremely relativistic speed. (CHR, 1986a,b)

8. Outer gap model e + e - pairs are accelerated to extremely relativistic velocity by the parallel electric field Relativistic pairs radiate high energy photons through curvature/ synchrotron /ICS mechanisms The high energy photons collide with the soft photons to materialize as e + e - pairs

9. The Crab Pulsar

10. Pulsation of the Crab pulsar energy dependant light curves phase bins

11. Modified structure of the outer gap The inner boundary of the outer gap is not located at the null charge surface, and can shift inwardly to the near surface region (~0.02R L ). (Hirotani, 2005) Thus, the azimuth extension can be larger than 180 0, and we get the radiation from both poles.

12. Radiation morphologies gap geometry emission from the gaps

13. Radiation morphologies relativistic aberration time of flight

14. Numerical results light curve emission projection

15. Phase-Resolved Spectra Synchrotron Self-Compton (SSC) mechanism e + e - pairs interact with the magnetic field to generate synchrotron photons high energy synchrotron photons interact with the field to generate relativistic pairs relativistic pairs collide with soft photons via ICS to emit high energy photons

16. Local properties of the magnetosphere Curvature radius Lorentz factor Curvature photon energy Magnetic field

17. Free parameters: pitch angle ( ) and beam solid angle ( ) trailing wing 1, bridge, leading wing 2: leading wing 1: peak 1: Peak 2: trailing wing 2: phase-averaged :

18. Phase-resolved spectra

19. Phase-averaged spectrum

20. Conclusions Inclination angle: Viewing angle: The phase-resolved spectra in the energy range from 100eV to 3GeV of the Crab pulsar can be fitted well. The photons beyond 1GeV may be the residual curvature photons emitted by the first generation pairs.

21. Thank you!