1. Gamma-ray emission mechanism in pulsar magnetosphere – electrodynamics and models 徐佩君 清大天文所

2. Contents  Introduction  Models  My work  Summary

3. Observational motivation EGRET all sky survey (100MeV-10GeV) How the observed gamma-rays are emitted around the pulsars? Thompson et al. 1999

4. Plasma-filled magnetosphere Force free condition: Goldreich-Julian charge density

5. Accelerators Poisson’s equation: (one-dimensional) A super dynamo ! Harding 2000 NS

6. Models Polar cap Outer gap Hirotani & Shibata Cheng, Ho, & Ruderman Slot gap Polar cap … … Arons et al. Muslimov & Harding Ruderman & Sutherland … … Arons & Scharlemann

7. Polar cap  Sturrock(1971); Ruderman & Sutherland(1975)  Arons, Scharlemann, & Fawley(1977~)

8. Slot gap  Muslimov & Harding (2004) They explored the SG electrodynamics up to very high altitudes - A narrow region on the boundary of the open field lines developing above the polar cap The extended gap can explain the observed light curve well

9. Outer gap (geometrical)  Cheng, Ho, & Ruderman(1986)

10. Pulse profile Romani & Yadigaroglu 1995 Vela Observation Model Outer gap model can explain double peak light curve with bridge emission

11. However..  Vacuum gap is assumed to solve E ||  In the gap the number of primary charged particles is roughly given by Inconsistency Cheng, Ruderman & Zhang, 2000 0 Crab Inner boundary (E || =0;Φ=0) is at null surface

12. Extended gap Dyks & Rudak, 2003 An outer gap with inner boundary extended toward the stellar surface can explain the light curve well (off-pulse emission) Vela

13. Outer gap (electrodynamical)  Hirotani & Shibata e + and e - are accelerated by E || Relativistic e + /e - emit gamma-rays via synchrotron, curvature, and IC processes Gamma-rays collide with soft photons to materialize as pairs in the accelerator

14. Basic Equations  Poisson Equation  Particle Boltzmann Equations Stationary condition Electric force Curvature radiation reaction force

15. Basic Equations  Collision Terms  Gamma-Ray Boltzmann Equations The electrodynamical model connects these equations and solves Outer gap structure self-consistently Inverse Compton Scattering Pair production Curvature radiation

16. Computed spectrum Vela Hirotano et al. 2003

17. weaknesses of the present electrodynamical model  One-dimensional model (Thick gap)(Thick gap) (Hirotani & Shibata 1999~2004) - can not apply the Crab case (thin gap) - ignore the tarns-field structure  Two-dimensional model (Takata et al. 2004,2006) - do not solve pitch angle - only calculate the curvature radiation

18. Motivation Synchrotron radiation is important Information about the pitch angle of particles is needed Takata et al. 2004 Vela

19. Comparison between some outer gap models ModelRomani & Yadigaroglu (1995) Hirotani et al. (1999) Takata et al. (2004) Hirotani Pei-Chun Geometry3D1D2D Dynamics xooo Pitch-angle xxxo

20. My work Pair Production Poisson Equation Next step Future work

21. Some results s

22. Summary  It is believed that gamma-ray is emitted by relativistic charge particles accelerated in charge depletion region in pulsar magnetosphere.  Many models have been published to explain the observation. And there is no perfect one. We do not know which one is the answer.  We are trying to quantitatively solve two- dimensional electro-dynamical equations for a stationary pair-production cascade in pulsar magnetospheres.

23. Reference  Cheng, Ho, & Ruderman, 1986, ApJ, 300, 500  Cheng, Ruderman & Zhang, 2000, ApJ, 537, 964  Dyks & Rudak, 2003, ApJ, 598, 1201  Goldreich & Julian, 1969, ApJ, 157,869  Hirotani, Harding & Shibata, 2003, ApJ, 591, 334  Muslimov & Harding, 2004, ApJ, 606, 1143  Romani & Yadigaroglu, 1995, ApJ, 438, 314  Takata, Shibata &Hirotani, 2004, MNRAS, 348, 241

24. f: Vertical Size  In outer-gap model, the typical energies of the soft X-rays and the  -rays are completely determined by the vertical size and the horizontal extension of the outer gap  Soft X-ray photon:  Curvature  -ray photon evaluated at the half of the light cylinder:  Using pair production condition we obtain:   -ray luminosity

25. Basic Equations  Poisson Equation 2D form