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 Lai2, Han JinLin1 1 National Astronomical Observatories of China 2 Cornell University

Physical Image Ω k μ B Initial Radio Photon Magnetosphere Wave mode coupling Cyclotron absorption Faraday rotation effect Final polarization state？ Propagation effects Ω k μ 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 B Magnetosphere B*=108 G – 1015 G, dipole Relativistic streaming plasma along B field line N/NGJ ~ 10s – 1000s γ ~ 10s – 1000s

Some important propagation effects Cyclotron absorption Wave mode coupling (Wang, Lai & Han 2010, MNRAS; Beskin et al. 2009) Intrinsic Faraday Rotation effect in 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

Cyclotron Resonance/Absorption 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 = +

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.

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

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

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

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

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

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

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！

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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

k μ aligned k μ k μ inversely aligned μ k

PA evolution along the way for different parameters

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

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