1. Study on polarization of high- energy photons from the Crab pulsar 〇 J. Takata (TIARA-NTHU/ASIAA,Taiwan) H.-K. Chang (NTH Univ., Taiwan) K.S. Cheng (HK Univ., Hong-Kong) TIARA: Theoretical Institute Advanced Research in Astrophysics ASIAA: Academia Sinica Institute of Astronomy and Astrophysics NTHU : National Tsing Hua University

2. Contents 1. Introduction 2. Synchrotron model for the Crab pulsar 3. Results 4. Discussion 5. Summary & Conclusion

3. 1, Introduction; Gamma-ray pulsar Vela Crab Where and how are the particles accelerated and the gamma-rays radiated in the pulsar magnetosphere?

4. Gamma-ray emission models 1, Introduction Pulsar as a huge electric dynamo Particle acceleration ( ) via electric field (E||) parallel to magnetic field line in gap, where Gamma-ray emissions (~a few GeV) via curvature process Last open line

5. Rotation phase Emission direction =particle motion direction -aberration -time delay Outer gap & Caustic Polar cap Viewing angle Double peak light curve 1, Introduction Polar cap Caustic Outer gap

6. Why polarization? Polarization data will play an important role to discriminate the various models Polarization measurement will increase (2 times) number of observed parameter; polarization position angle (P.A.) swing and polarization degree (P.D.) So far, Crab optical data is available. In future, Compton telescope will measure in MeV-bands for the Crab pulse. 1, Introduction

7. Crab optical data 40% Smith et al 1988 Kanbach et al 2004 Observation -fast swing P.A. through peaks -constant P.A. in off-pulse phase -min. in P.D. at both peaks -~40% of max. in P.D. Polarization degree (P.D.) Position angle (P.A.) Intensity 1, Introduction bridgeoff pulse

8. Cheng, Ruderman & Zhang (2000) model for Crab pulsar Synchrotron and inverse-Compton process of secondary pair produces photons in wide energy bands (optical to GeV). Outer gap C.R. S.R. We examine the polarization characteristics predicted by the synchrotron model 2,previous studies Expected Synchrotron phase-ave. spec. 1MeV 1eV

9. 3 polarizations *Synchrotron radiation Projected B on the skey observer Polarization characteristics are described by Stokes parameters, I, Q, U,V -Linearly Degree of polarization -Position angle of polarization plane

10. 3 Synchrotron emission model Emission direction (particle motion direction) =edge of cone with Acceleration Observed electric vector of EM wave with aberration effect gyration

11. Model; Stokes parameters At each point and at each radiation ….. 1, linearly polarized radiation at 2,Stokes parameters 3, Intensity (projected rotation axis on the sky) 3,synchrotron model

12. Viewing angle Phase 90 Observed P.D. and P.A. after collecting photons Collecting of photons Fig. Emission position projected on plane for the outer gap model

13. Fig., predicted Crab spectrum by KS2000 Emissivity & model parameters Model,Outer gap model - Cheng, Ruderman & Zhang (2000) -Emission region starting from null charge surface Model parameters Emission region is upper surface of the gap

14. 4,Results; Outer gap model Fast P.A. swing at both peaks and in bridge phase. Maximum in P.D. (~60%) near both peaks 1eV 300eV100keV P.D. 10% 60% 40° 0 - 40° P.A. 1.5 phase A

15. Maximum in P.D. near the peaks P.A. P.D. A P1P2 80

16. 4, Results; Crab data.Vs. model results 40 ％ P.D. P.A. 60 % *Model explains observed features of 1, Fast swing at both peaks, 2, relatively constant at bridge 4, relatively small P.D. But, it is difficult to explain 1,pattern of P.D. 2,off pulse emission 1.5 phase

17. 5, Discussion What the observation indicates? Observation may indicate that present model is very simple …. 1, gap geometry -outer gap will extending inside of the null surface 2, only outward emission by the outgoing particles, -inward emission via ingoing particles may be observed 3, constant power low index (p=2) of particle distribution, -more realistic particle distribution may be important, 4 rotating dipole field? Crab optical data will reflect more detail structure of pulsar magnetosphere.

18. In fact, outer gap will start from insider of the null charge surface No currents ! Bound. of vacuum gap （ ρ=0) J max =0.4 0.3 null surface Height Radius in units of light radius 0.2 J max =0.3 5, Discussion; Outer gap geometry Current Takata et al. (2004, 2006)

19. Inward emission 90° Outward emission Modified emission map 5, Discussion;

20. Electric field Field-aligned electric fields Distance along field line in units of light radius null surface Vacuum gap J max =0.4 J max =0.3 5, Discussion;

21. Expected light curve Outward emission Inward emission 90° 5, Discussion;

22. 6,Summary The polarization characteristics by the synchrotron emission, which is favor for Crab spectrum, were calculated with traditional outer gap model. -Model explains observed small value of P.D. and the constant of P.A. at bridge -Predicted pattern of P.D. is problematic. None of the present models was able to explain both of P.A. and P.D. for Crab optical data. The light curves with the outer gap starting from near the stellar surface have multi peaks.

23. P.A. at bridge / off pulse phase B Ω

24. Dipole field Rotating dipole field 0 deg 90 deg 270 deg 0.1 P.A.

25. Outer gap Caustic model Curvature radiation Synchrotron radiation Which one more similar to observation?

27. Gamma-ray emission models Polar cap Caustic Outer gap

28. 3 polarizations of Curvature Vs. Synchrotron * Curvature radiation *Synchrotron radiation Projected B on the skey

29. Fig., predicted Crab spectrum by KS2000 Emissivity & model parameters Model1,Outer gap model - Cheng, Ruderman & Zhang (2000) -Emission region starting from null charge surface Model 2Model 2,Caustic model -emission region starting from stellar surface -constant emissivisity Model parameters Emission region is upper surface of the gap

30. 4, Results; Caustic model Caustic model explains off pulse emission of Crab pulsar 1,Maximum in P.D. (~15%) at peak or trailing of peaks 2,P.A. at off pulse … -relatively constant -similar value with bridge phase 15% Off pulse bridge P.D. P.A. A 0

31. Previous studies (Dyks et al. 2004) Curvature emission model predicts -high Polarization degree (P.D) -large P.A. swing at off- pulse phase 2,previous studies There are no curvature emission model for the Crab spectrum Intensity Position angle (P.A.) Polarization degree (P.D.) Polar cap Caustic Outer gap Data 40%80%

32. Observed polarization plane with aberration effect * No aberration effect * With aberration effect