Multi-wavelength Pulsed Emission from Fermi Pulsars: Vela & Crab ——Annular Gap Model

1. Pulsar Physics and The Application of Pulsar Timing Multi-wavelength Pulsed Emission from Fermi Pulsars: Vela & Crab ——Annular Gap Model Du Y. J., Qiao G. J., Han, J. L., Lee K. J. & Xu R. X. 2010, MNRAS, 406, 2671-2677 Du Y. J., Han, J. L., Qiao G. J. & Chou C. K. 2011, ApJ, 731, 2 (Vela) Du Y. J. 2011, ApJ,to be submitted (Crab) Reporter: YuanJie Du (NAOC) Supervisor：JinLin Han (NAOC) GuoJun Qiao (PKU) RenXin Xu (PKU)

2. Overview Vela Fermi observations Crab multi-wavelength observations Other models Our work —— Vela （☻） Our work —— Crab Outline • Background • Annular Gap Model • Summary

3. Pulsar Emission Background — Pulsed Emission • Before 2008, only 7 γ-raypulsars were discovered. 3 candidates • After Fermi launching, about 100 γ-ray pulsars were discovered so far • γ-ray selected pulsars, • radio selected pulsars • millisecond pulsars. • Golden age for pulsar high energy emission studies: opportunity and challenge

4. Yong Pulsar MSP J0437-4715 J0218+4232 Background——Pulsar Emission Physics Emission Physical Picture Problems：Emission Region and Emission Mechanism Crab Vela Geminga

5. Background—Fermi telescope Fermi ： LAT and GBM • LAT: a pair conversion telescope • Large effective area: ~ 8000 cm2 • Large view of field: ~ 2.4 sr • Wide energy band: 0.02GeV to 300 GeV • High angular resolution: 0.6o for 1 GeV; 0.1o for 10 GeV • GBM: for gamma-ray burst (not discussed here)

6. LAT data reduction for pulse profile • Data collect (based on radio timing solution) • Data selection (Diffuse, 0.1－300GeV, 2o, zenith angle<105o) • Energy selection • Timing each photon → phase information (Tempo2 with Fermi plug-in) • Light curves plotting

7. P2 P1 P3 Du et al. 2011, ApJ, 731, 2 The Vela Pulsar • Two sharp peaks, P1 is narrower than P2 • P1/P2 varies with energy • A third peak (P3) in the bridge, the location and intensity shift with energy

8. GeV phase-averaged spectrum for Vela Hyper-exponential power law cut-off

9. Multi-wavelength observed light curves for Crab • Two peaks • Bridge • Phase-aligned

10. Kuiper et al. 2001, A&A, 378, 918 Fermi data Observations of phase-averaged spectrum and phase-resolved spectra for Crab

11. Observation hints • Vela: Two sharp γ-ray peaks with a large separation 0.42 ——high emission height ! • Vela: P1/P2 and P3 varying with energy ——single pole or two pole? • Vela & Crab: The “radio lag” problem needs to be solved self-consistently ——Outer Gap model? • Modelings of multi-waveband light curves and phase-resolved spectra are needed for the Crab pulsar ——The Annular Gap model

12. Other models Our work —— Vela （☻） Our work —— Crab Outline • Background • Annular Gap Model • Summary

13. High Energy Emission Models Outer Gap (Cheng) Polar Cap (Harding) Two-pole caustic (Dyks) Slot Gap (Harding) Annular Gap (Qiao) Two separatrix layer

14. Polar Cap Model for Vela Daugherty & Harding 1996 • Emission height: 2-3 Rns • Nearly aligned rotator: αvery small

15. Outer Gap Model for Vela Romani & Yadigaroglu 1995 • Both radio and γshown • γemission is from single pole, whereas radio comes from the other polar cap. Comments from Lommen et al. 2007 “Our results imply a connection between the radio and X-ray emission mechanisms for Velathat is not consistent with outer gap model… It is not clear how a correlation could exist between the radio and high energy regimes in these models”.

16. Caustics in water Two-pole caustic model for Vela Dyks & Rudak 2003 Static dipole field rmax< 0.95RLC

17. Yu, Fang & Jiang 2009 A REVISIT OF THE TWO-POLE CAUSTIC MODEL Fang & Zhang 2010, ApJ Retarded dipole field

18. Two-layer outer gap model （Wang, Takata, Cheng 2011, arXiv: 1102.4474） α=57◦，ζ=80◦

19. Annular Gap Model —— Our work • Vela (Fermi Gamma-ray studies) • Concepts & Methods • Light curve • Phase-averaged spectrum • Phase-resolved spectra • Crab (Multi-wavelength studies) • Light curve • Phase-averaged spectrum • Phase-resolved spectra

20. Annular Gap + Core Gap • The open field line region is divided into core gap and annular gap regions by the critical field line. • The annular gap radius is much larger for pulsars with short spin periods, and can be a excellent accelerator for pulsar γ-ray emission. Ruderman & Sutherland 1975

21. Electric field Pair production Primary particles and pairs Zhang, Qiao & Han 1997, 491, 891 • Primary particles are accelerated to ultra-relativistic energy with γ~ 107 by the induced acceleration electric field. • Three modes of pairs: CR, thermal ICS and resonant ICS. • Thermal ICS induced pairs usually have larger Lorentz factors up to γth~ 105 . • Radio emssion comes from pairs. High energy emission comes from primary particles.

22. rN (0) Re (α,ψ) Central Emission height α,ψ rN (ψ) θnull (α,ψ) Gaussian distribution Gamma-ray Profile View angle Aberration retardation Project onto the sky 256 bins of φandζ I(φ0,ζ0) I(φ,ζ) Light curve modeling thread

23. Light Curve Modeling Steps (Vela) • Dividing polar cap • Projected intensity • Emissiom direction • Emission phase • Light curve

24. Core Gap Annular Gap Torus fitting ζ (Ng & Romani 2008) PA fitting α (Johnston 2005) β Step Ⅰ: Dividing polar cap • Magnetic inclination angle α: 70 deg • Viewing angle ζ: 64 deg • Critical field line θN (ψ) • Last open field line θP (ψ) • Footpoint in each open field line • 40 rings for both core and annular gap Dividing polar cap Projected intensity Emissiom direction Emission phase Light curve plotting

25. Dividing polar cap • Projected intensity • Emissiom direction • Emission phase • Light curve plotting Step Ⅱ：Projected intensity Two types of Gaaussian emission intensities are assumed, i.e., • A Gaussian distribution on a field line (parameter: κ,λ,σarc_AG,σarc_CG, ratio, I1, I2 , ICG) • Another Gaussian distribution between field lines with same magnetic azimuthal (ψ) (parameter: σpeak_AG,σpeak_CG) • Model parameters are different between core and annular gap.

26. Dividing polar cap • Projected intensity • Emissiom direction • Emission phase • Light curve plotting Step Ⅲ: Emission direction Emission direction of each emission spot nB in the magnetic frame Matrix Tα nspin in the spin frame Aberration nobserver = {nx, ny, nz} in the observer frame

27. Dividing polar cap • Projected intensity • Emissiom direction • Emission phase • Light curve plotting Step Ⅳ: Emission phase • “Retardation effect” is needed for the final photon emission phase φ. • A phase shift Δφret retardation is because of the photon flight time at a certain emission height. This leads to photon generated at higher height comes to the Earth earlier. • Finally, φ= φ0 -Δφret Wang et al. 2006

28. Dividing polar cap • Projected intensity • Emissiom direction • Emission phase • Light curve plotting Du et al. 2011, ApJ, 731, 2 Step Ⅴ: Light curve plotting • Observations (red solid lines in 256 bins) versus similations (thick black solid lines in 128 bins) in the framework of Annular + Core gap model. • P1 and P2 originate from the annular gap region. • P3 and bridge emission come from the core gap region

29. Du et al. 2011, ApJ, 731, 2 Radio lag • A radio lag ~0.13 is shown. • Radio emission originates from high altitude and narrow regions in the annular gap. • Single-pole annular and core gap model is favored for Vela.

30. Du et al. 2011, ApJ, 731, 2 Phase-averaged spectrum for Vela • 3 Components （P1、P2 and P3） • Emission position： P1: 0.62RLC, ψ=-110° P2: 0.75RLC, ψ=131° P3: 0.28RLC, ψ=-104° • 3 free parameters： γmin、 γmax、Ω • GeV emission is generated from Synchro-curvature radiation from primary particles and synchrotron radiation from secondaries (pairs)

31. P3 high-energy P3 low-energy Phase-resolved spectra Du et al. 2011, ApJ, 731, 2 P1 P2 • P1 and P2：located in AG region，larger pitch angle, synchrotron is important for < 1 GeV band • P3：located in CG region， pitch angle, CR dominated

32. Du et al. 2011, ApJ, 731, 2 Dependencies of flux and emission height Emission intensities are notuniform along an open field line. They are likely to have a gaussian distribution near the peak position.

33. Annular Gap Model —— Our work • Vela (Fermi Gamma-ray studies) • Concepts & Methods • Light curve • Phase-averaged spectrum • Phase-resolved spectra • Crab (Multi-wavelength studies) • Light curve • Phase-averaged spectrum • Phase-resolved spectra

34. Preliminary! Preliminary! Preliminary! AG multi-wavelength results for the Crab pulsar • Light curves • Phase-averaged spectrum • Phase-resolved spectra

35. Outer Gap for Crab Tang et al. 2008, ApJ, 676, 562

36. Harding et al. 2008, ApJ, 680, 1378 Slot Gap for Crab

37. Outer Gap for Crab Li & Zhang 2010, ApJ, 725, 2225 Phase-averaged spectrum Photon sky-map

38. Brief Introduction to the AG work Du et al. 2010, MNRAS, 406, 2671 • This is a fast work mainly focusing on the light curve simulations for millisecond and young pulsars. • Concepts and methods are announced in details for our annular gap model, although the results are rough.

39. 年轻脉冲星 Du et al. 2010, MNRAS, 406, 2671

40. 毫秒脉冲星 Du et al. 2010, MNRAS, 406, 2671 Fingerprints of pulsars!

41. Outline • Background • Annular Gap Model • Summary

42. Summary • Under our self-consistent annular gap model,multi-wavelength light curves and phase-averaged and phase-resolved spectra for the Vela pulsar and the Crab pulsar are well reproduced with comparison of the observations. • The features (spectra and light curves) of P3 for Vela are well described by our model. • Our model explains the radio lag problem for Vela and Crab, and they are different. • Existence of both annular and core gaps could be verified by the Vela pulsar and the Crab pulsar.

43. 路漫漫其修远兮 吾将上下而求索 谢谢各位老师和同学！ All rivers run into sea. Thanks!!!

46. Crab Vela

48. 补充材料 • MSP J0437-4715 • Crab

49. MSP J0437-4715 Both the simulated radio and γ-ray light curves for millisecond pulsar J0437-4715. The radio lag problem can be well solved by our model. One part of Poster for 38th Cospar conference in Bremen

50. Crab脉冲轮廓