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Wave Propagation Effects in Pulsar Magnetospheres

Pulsar Physics and The Application of Pulsar Timing May 11th, 2011. Wave Propagation Effects in Pulsar Magnetospheres. Chen Wang 1, 2 , Dong Lai 2 , Han JinLin 1. 1 National Astronomical Observatories of China 2 Cornell University. Physical Image. Wave mode coupling Cyclotron absorption

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Wave Propagation Effects in Pulsar Magnetospheres

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  1. Pulsar Physics and The Application of Pulsar Timing May 11th, 2011 Wave Propagation Effects in Pulsar Magnetospheres Chen Wang 1, 2, Dong Lai2, Han JinLin1 1 National Astronomical Observatories of China 2 Cornell University

  2. Physical Image Wave mode coupling Cyclotron absorption Faraday rotation effect Final polarization state？ Propagation effects Ω k μ B Initial Radio Photon • rem~ a few - 100’s RNS . • Initially O/X-mode O-mode： E // k-B plane X-mode： E ⊥ k-B plane Magnetosphere • B*=108 G – 1015 G, dipole • Relativistic streaming plasma along B field line N/NGJ ~ 10s – 1000s γ ~ 10s – 1000s

  3. Some important propagation effects • Cyclotron absorption • Wave mode coupling (Wang, Lai & Han 2010, MNRAS; Beskin et al. 2009) • Intrinsic Faraday Rotation effectin pulsar magnetosphere (Wang, Lai & Han 2011, to be submitted) • Refractive effect (Petrova 2006, MNRAS) • Vacuum resonance (Wang, Lai & Han 2007, MNRAS) • Quasi-tangential effect (Wang & Lai 2009, MNRAS) • Others

  4. B B Cyclotron Resonance/Absorption e p 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 =

  5. 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 by wave mode coupling.

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

  7. 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:

  8. 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

  9. Pair plasma case, where FR effect is negligible Pair plasma case，Ne ~ Np, Np–Ne = NGJ Cyclotron resonance wave mode coupling 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

  10. Pure electrons case, where FR effect is significant Pure electrons (+ions) case，N = Ne = 1000 NGJ Cyclotron resonance wave mode coupling 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

  11. Rotation Measure for the assumed pure electrons case • Subtract the influence to PA from other propagation effects • RM defined by Pulsar parameters：α=35，β=5，γ=100，η=1000，Bs=1e12G，P=1s，r_em=50Rs，Ψi=0

  12. Conclusion • The propagation effects in pulsar magnetospheres could modify both the intensity and the polarization states of the emission from inner magnetosphere • CP can be generated in wave mode coupling, which maybe the reason of the relation between PA profile and the sign of CP in Conal-Double pulsars. • 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 Thanks！

  13. 谢谢

  14. Simulation of wave evolution - 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 Plasma properties Determined by dielectric tensor Wave frequency Magnetic field

  15. k μ kμ aligned kμ inversely aligned μ k

  16. PA evolution along the way for different parameters

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

  18. 观测事实

  19. 观测事实

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