辐射在脉冲星磁层中的传播效应

1. 2013年脉冲星天文学讲习班 2013.08.20 辐射在脉冲星磁层中的传播效应 国家天文台 王陈

2. Motivation – Circular polarization • Single sign & Sign reversal • Weak and strong Intrinsic emission mechanism Propagation effect Origin P.A. Lyne & Manchester (1988)

3. Motivation - Orthogonal mode emission V P.A. %L I Stinebring et al. (1984)

4. 脉冲星磁层中辐射的传播效应 波模耦合 回旋吸收 准切点效应 法拉第效应 最终偏振状态？ Ω 传播效应 k μ • 辐射高度 ~ a few - 100’s RNS . • 初始线偏振 O模： E // k-B plane X模： E ⊥ k-B plane B 磁层 • B*=108 G – 1015 G • 充满相对论流动的ee+等离子体（开放磁力线区域） 沿磁层流动N/NGJ ~ 10s – 1000s γ ~ 10s – 1000s

5. Outlines • Previous studies • Dispersion relation and natural wave modes in pulsar magnetosphere. • Some propagation effects • Our works • On some special propagation effects • Vacuum resonance (Wang, Lai & Han 2007) • Quasi-tangential effect (Wang & Lai 2009) • Wave mode coupling effect(Wang, Lai & Han 2010) • Intrinsic Faraday Rotation effect in pulsar magnetosphere (Wang, Han & Lai 2011) • Numerical simulations on Polarization profile changes due to all the propagation effects.(Wang, Lai & Han 2010) Conclusion

6. Previous studies • Dispersion relation and natural wave modes in pulsar magnetosphere.(Melrose & Stoneham 1977, Arons & Barnard 1986, von Hoensbroaech et al. 1998, Lyubaskii 1998, Melrose et al. 1999) • Special Propagation effects • Adiabatic Walking(Cheng & Ruderman 1979) • Wave mode coupling(or limiting-polarization effect)(Cheng & Ruderman 1979, Petrova 2000, 2006) • Circularization(Cheng & Ruderman 1979) • Refractive effect of O-mode(Melrose 1979, Allen & Melrose 1982, Barnard & Arons 1986, Lyubarskii & Petrova 1998, Weltevrede et al. 2003, Fussell & Luo 2004) • Cyclotron absorption(Luo & Melrose 2001, 2006, Fussell et al. 2003)

7. Dispersion relation and natural wave modes in pulsar magnetosphere B=∞ limit(Tsytovitch & Kaplan 1972; Arons & Barnard 1986) • Cyclotron frequency >> wave frequency • Don’t consider QED effect in dielectric tensor. Two natural wave modes • ordinary mode, or O-mode • extraordinary mode, or E-mode k B Polarized in k-B plane O-mode k B Polarized perpendicular to k-B plane E-mode In the real case, the two modes are elliptically polarized.

8. Dispersion relation and natural wave modes in pulsar magnetosphere B=∞ limit Dispersion relation of O-mode In the plasma rest frame In the lab frame

9. Propagation effects：Adiabatic walking 电场方向 垂直磁场方向 B⊥ E • The polarization direction followsB⊥ field in adiabatic condition • Make the final PA differentfrom the initial emission Adiabatic φPA φB Non-Adiabatic Adiabatic Condition

10. Refractive effect of O-mode (Melrose 1979, Allen & Melrose 1982, Barnard & Arons 1986, Lyubarskii & Petrova 1998, Weltevrede et al. 2003, Fussell & Luo 2004) • Only happens when wave frequency is close to proper plasma frequency, near the emission height. n is not so close to unity. • Refraction direction depends on the density gradient. • Can cause the separation of natural waves, => OPM phenomenon. (Melrose 1979, Allen & Melrose 1982) • Outward density decrease causes ray deviation away from magnetic axis, which may widen the emission beam width. (Lyubarskii & Petrova 1998) • The refraction induced wave mode coupling may cause CP with sign reversal (Petrova & Lyubarskii 2000)

11. B B Cyclotron Resonance/Absorption e p (Luo & Melrose 2001, 2006, Fussell et al. 2003) ω′= eB/mc. r = rcr • RCP absorbed by electrons LCP absorbed by positrons • Optical depth with γ >>1 circular polarization can be generated by the asymmetric cyclotron absorption of electrons and positrons. scattered + E =

12. 不对称的正负电子回旋吸收 对称的正负电子回旋吸收

13. A small summary to previous studies • Dispersion relation and natural wave modes in some simple approximations was analytically derived. • A few kinds of propagation effects were studied qualitatively (early years) and using numerical calculations (recent works). • Almost none of the previous studies has calculated the final polarization profiles with all of these propagation effects included in a self-consistent way within a single theoretical framework

14. Our works • Wave and modes amplitude evolution equation • On some special propagation effects • Vacuum resonance (Wang, Lai & Han 2007) • Wave mode coupling (Wang, Lai & Han 2010) • Quasi-tangential effect (Wang & Lai 2009) • Intrinsic Faraday Rotation in magnetosphere (Wang, Han & Lai 2011) • Numerical calculations on Polarization profile changes considering all the propagation effects.(Wang, Lai & Han 2010)

15. Wave evolution equation • Some propagation effects have not analytic solutions. • Different effects are coupled and not easy to be separated. => numerical ray integrations is necessary. • Wave evolution equation Determined by dielectric tensor Wave frequency Plasma properties Magnetic field

16. Mode amplitude evolution equation Y y B⊥ Two elliptically polarized modes in the lab frame x E+ E- The ellipticity of the modes, 0o or 90o : linearly polarized; 45o : circularly polarized X The orientation of the modes, dominated by B field Mode amplitude evolution equation i i Adiabatic Condition

17. Our works on propagation effects • Vacuum resonance(Wang & Lai 2007, MNRAS) • Wave mode coupling(Wang, Lai & Han 2010, MNRAS) • Quasi-tangential effect (Wang & Lai 2009, MNRAS) • Intrinsic Faraday Rotation effect in pulsar magnetosphere (Wang, Han & Lai 2011, MNRAS)

18. Vacuum resonance (the competition between plasma and QED effect) • X-ray band, Vacuum polarization (or QED effect) dominates the dispersion relation • Radio band, plasma effect dominates Where is the boundary? What happens in the boundary regime QED dominated plasma dominated Vacuum resonance The two effects “cancled” with each other 1. Correction to dielectric tensor 2. Inverse permeability tensor

19. Wave modes with QED effect • “Avoid mode crossing” occurs, the two modes (O-mode & E-mode) coupled. define two new modes: “＋” mode “－” mode. O-mode X-mode X-mode O-mode

20. plasma dominated Vacuum Resonance QED dominated Mode conversion due to vacuum resonance Helicity unchanged O-mode X-mode X-mode O-mode

21. Results on Vacuum resonance • If mode evolution across vacuum resonance is adiabatic, mode conversion (from O to X-mode or reversal) occurs. • Location in dipole B field • vacuum resonance can occur for sufficiently high frequencies and strong surface magnetic fields. => high-frequency radio emission from the transient magnetar AXP XTE J1810−197 (Camilo et al. 2006, 2007; Kramer et al. 2007). • optical radiation emitted from the NS surface or near vicinity may experience the vacuum resonance

22. Our works on propagation effects • Vacuum resonance (Wang & Lai 2007, MNRAS) • Wave mode coupling(Wang, Lai & Han 2010, MNRAS) • Quasi-tangential effect (Wang & Lai 2009, MNRAS) • Intrinsic Faraday Rotation effect in pulsar magnetosphere (Wang, Han & Lai 2011, MNRAS)

23. Wave Mode Coupling • The evolution of two linear eigenmodes from adiabatic to non-adiabatic. • rpl - polarization limiting radius, defined by • r << rpl, adiabatic mode evolution • r >> rpl, non-adiabatic mode evolution • Before WMC, PA follows the B field line plane After WMC, the polarization states are frozen • Circular polarization generated because of mode coupling.

24. Cyclotron absorption Single Photon evolution along the ray CP generated by wave mode coupling

25. An Interesting Application for WMC PA increase  V < 0 PA decrease  V > 0 • Conal-double pulsars, Can be explained easily by wave mode coupling effect CP generated by Wave mode coupling:

26. Our works on propagation effects • Vacuum resonance (Wang & Lai 2007, MNRAS) • Wave mode coupling(Wang, Lai & Han 2010, MNRAS) • Quasi-tangential effect(Wang & Lai 2009, MNRAS) • Intrinsic Faraday Rotation effect in pulsar magnetosphere (Wang, Han & Lai 2011, MNRAS)

27. k k B B Bt Bt Quasi-Tangential Effect • Tangential and Quasi-Tangential point B⊥ k isin the magnetic field line plane, there is a tangential point whereθkB =0 and B⊥ change 180o suddenly 。 B⊥ k is notin the magnetic field line plane, there is a quasi-tangential point whereθkB reaches its minimum value (not 0) and B⊥ change 180o continuely. Wang & Lai 2009, MNRAS

28. Ω k μ Hot spot X-ray emissoin B Quasi-tangential point (a few RNS)

29. Sketch Map of the model evolution across QT point

31. Polarization State after QT effect for the X-ray emission from polar cap region（Initially 100% O-mode LP） Wt Wang & Lai 2009, MNRAS

32. Polarization intensity (Q) changes due to Quasi-tangential effect（total intensity does not change) Wang & Lai 2009, MNRAS

33. The phase evolution of the modification of linear polarization by the QT effect, B_surf = 10^13G B_surf = 10^14G • Conclusion for the QT effect: • the QT effect will have at most modest effect on the observed X-ray polarization signals from magnetized NSs. • => linear polarization is weakened, LP profiles will be modified.

34. Our works on propagation effects • Vacuum resonance (Wang & Lai 2007, MNRAS) • Wave mode coupling(Wang, Lai & Han 2010, MNRAS) • Quasi-tangential effect (Wang & Lai 2009, MNRAS) • Intrinsic Faraday Rotation effect in pulsarmagnetosphere (Wang, Han & Lai 2011, MNRAS)

35. Intrinsic Faraday Rotation in pulsar magnetosphere • Faraday rotation effect : two natural circular polarized modes have different phase velocities. • FR of Pulsars in ISM (non-relativistic electrons, B~uG) is used to measure interstellar B field. • RM = RM_ISM + RM_PSR • Pulsar Magnetosphere • Strong B field • relativistic streaming plasma Δk =Δnω/c • Natural modes are linear polarized in inner magnetosphere and circularly polarized in outer magnetosphere • Δk no longer prop. to λ^2

36. Pair plasma case, where FR effect is negligible Pair plasma case，Ne ~ Np, Np–Ne = NGJ LP FR effect negligible CP Pulsar parameters：α=35，β=5，γ=100，η=100，Np-Ne=NGJ，Bs=1e12G，P=1s，r_em=50Rs，Ψi=0

37. Pure electrons case, where FR effect is significant Pure electrons case，N = Ne = 1000 NGJ LP FR effect significant CP Pulsar parameters：α=35，β=5，γ=100，η=1000，N=Ne，Bs=1e12G，P=1s，r_em=50Rs，Ψi=0

38. k μ kμ aligned kμ inversely aligned μ k

39. Phased resolved RM profile Pulsar parameters：α=35，γ=100，η=1000，Bs=5e12G，P=1s，r_em=50Rs

40. Results on Intrinsic Faraday rotation effect • For symmetric pair plasma case (e.g. Goldreich-Julian model), intrinsic Faraday rotation in pulsar magnetosphere is negligible • Only for the assumed highly asymmetric plasma (e.g., a electrons-ions streams with Ne >> NGJ), FR maybe significant. FR angle is proportional to λ^~0.5, not 2 • The intrinsic RM for mainpulse and interpulse should be opposite sign. Which may be checked in precise RM observations.

41. Our works • Wave and modes amplitude evolution equation • On some special propagation effects • Vacuum resonance (Wang, Lai & Han 2007) • Wave mode coupling (Wang, Lai & Han 2010) • Quasi-tangential effect (Wang & Lai 2009) • Intrinsic Faraday Rotation in magnetosphere (Wang, Han & Lai 2011) • Numerical calculations on Polarization profile changes considering all the propagation effects.(Wang, Lai & Han 2010)

42. Numerical calculations on Polarization profile changes considering all the propagation effects.(Wang, Lai & Han 2010) • Wave evolution equation Assumptions: • Photon emitted along the tangential direction of local B field • Initially 100% linearly polarized, (generally O-mode). • Single gamma (cold plasma) • Uniformly distributed plasma in the open field line region. • all emissions are from the same height

43. Solid line (red): Dashed line (blue): Dotted line (green):

44. 经过磁层传播效应后的偏振轮廓（一个例子，回旋吸收和波模耦合主导）经过磁层传播效应后的偏振轮廓（一个例子，回旋吸收和波模耦合主导） 回旋吸收各相位不同 波模耦合产生足够强的圆偏振 偏振位置角曲线移动很大 正交模式现象?

45. 2D polarization profiles

46. Possible examples in observation: orthogonal modes

47. 总结 传播效应对辐射尤其偏振有很大影响

48. 总结 • 很多脉冲星偏振观测现象可以由传播效应来解释。 • 锥双峰脉冲星中圆偏振的起源 • 部分正交模式现象 • 需要更详细模型下的理论计算 • 需要更多的与观测的结合

49. 谢谢！

50. 谢谢