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Wave Propagation Effects in Pulsar MagnetospheresWave Propagation Effects in Pulsar Magnetospheres
Chen Wang Chen Wang 1, 21, 2, Dong Lai, Dong Lai22, Han JinLin, Han JinLin11
1 National Astronomical Observatories of China
2 Cornell University
Pulsar Physics and The Application of Pulsar Timing
May 11th, 2011
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Initial Radio Photon Initial Radio Photon • rremem ~ a few - 100’s R~ a few - 100’s RNS NS ..
• Initially O/X-modeInitially O/X-mode
O-modeO-mode : : E // k-B planeE // k-B plane
X-modeX-mode : : E E ⊥⊥ k-B plane k-B plane Magnetosphere• B*=108 G – 1015 G, dipole• Relativistic streaming plasma along B field line
N/NGJ ~ 10s – 1000s γ ~ 10s – 1000s
Final polarization Final polarization statestate ??
Ω
μ k
B
Propagation effects
Physical Physical ImageImage
Wave mode coupling
Cyclotron absorption
Faraday rotation effect
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Some important propagation effects
• Cyclotron absorptionCyclotron absorption
• Wave mode couplingWave mode coupling (Wang, Lai & Han 2010, MNRAS; Beskin et al. 2009)(Wang, Lai & Han 2010, MNRAS; Beskin et al. 2009)
• Intrinsic Faraday Intrinsic Faraday Rotation effect effect in pulsar magnetospherein pulsar magnetosphere (Wang, Lai & Han 2011, to be submitted)(Wang, Lai & Han 2011, to be submitted)
• Refractive effect Refractive effect (Petrova 2006, MNRAS)(Petrova 2006, MNRAS)
• Vacuum resonance Vacuum resonance (Wang, Lai & Han 2007, MNRAS)(Wang, Lai & Han 2007, MNRAS)
• Quasi-tangential effect Quasi-tangential effect (Wang & Lai 2009, MNRAS)(Wang & Lai 2009, MNRAS)
• OthersOthers
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ω′= eB/mc. ω′= eB/mc. r r = = rrcrcr
• RCP absorbed by electrons RCP absorbed by electrons LCP absorbed by positronsLCP absorbed by positrons
• Optical depth with Optical depth with γ >>1γ >>1
circular polarization can be generated by the asymmetric cyclotron circular polarization can be generated by the asymmetric cyclotron
absorption of electrons and positrons.absorption of electrons and positrons.
B
+E =
scattered
eCyclotron Resonance/AbsorptionCyclotron Resonance/Absorption
B
p
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Wave Mode CouplingWave Mode Coupling
• The evolution of two linear eigenmodes from adiabatic to non-The evolution of two linear eigenmodes from adiabatic to non-adiabatic.adiabatic.
• rrplpl - polarization limiting radius, defined by - polarization limiting radius, defined by – r << rr << rplpl , adiabatic mode evolution, adiabatic mode evolution– r >> rr >> rplpl , non-adiabatic mode evolution, non-adiabatic mode evolution
• Before WMC, PA follows the B field line plane Before WMC, PA follows the B field line plane After WMC, the polarization states are frozen After WMC, the polarization states are frozen
• Circular polarization generated by wave mode coupling.Circular polarization generated by wave mode coupling.
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Single Photon evolution along the ray
CP generated by wave mode coupling
Cyclotron absorption
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An Interesting Application for WMC An Interesting Application for WMC
• Conal-double pulsars,
PA increase PA increase V < 0V < 0 PA decrease PA decrease V > 0V > 0
Can be explained easily by wave mode coupling effect
CP generated by Wave mode coupling:
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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
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Pair plasma casePair plasma case ,, Ne ~ Np, Np–Ne = NNe ~ Np, Np–Ne = NGJGJ
Pair plasma case, where FR effect is negligible
wave mode coupling
Cyclotron resonance
LP
CP
FR effect negligible
Pulsar parameters : α=35 , β=5 , γ=100 , η=100 , Np-Ne=NGJ , Bs=1e12G , P=1s , r_em=50Rs , Ψi=0
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Pure electrons (+ions) casePure electrons (+ions) case ,, N = Ne = 1000 NN = Ne = 1000 NGJGJ
wave mode coupling
Cyclotron resonance
LP
CP
FR effect significant
Pulsar parameters : α=35 , β=5 , γ=100 , η=1000 , N=Ne , Bs=1e12G , P=1s , r_em=50Rs , Ψi=0
Pure electrons case, where FR effect is significant
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• Subtract the influence to PA from other propagation effects
Rotation Measure for the assumed pure electrons case
• RM defined by
Pulsar parameters : α=35 , β=5 , γ=100 , η=1000 , Bs=1e12G , P=1s , r_em=50Rs , Ψi=0
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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
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谢谢谢谢
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Simulation of wave evolutionSimulation of wave evolution
=> numerical ray integrations=> numerical ray integrations is necessary. is necessary.• Wave evolution equationWave evolution equation
Determined by dielectric tensor
- Some propagation effects have not analytic solutions.- Different effects are coupled and not easy to be separated.
Plasma properties
Wave frequency
Magnetic field
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k μ aligned
μ
k
k μ inversely aligned
k
μ
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PA evolution along the way for different parameters
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Phased resolved RM profile
Pulsar parameters : α=35 , γ=100 , η=1000 , Bs=5e12G , P=1s, r_em=50Rs
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观测事实
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观测事实