Transcript Wave Propagation 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
Wave mode coupling
Cyclotron absorption
Faraday rotation effect
Ω
Final polarization
state？
Propagation effects
k
μ
Initial Radio Photon
B
• 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
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
B
Cyclotron Resonance/Absorption
e
ω′= eB/mc. r = rcr
•
RCP absorbed by electrons
LCP absorbed by positrons
B
scattered
E=
+
• Optical depth with γ >>1
circular polarization can be generated by the asymmetric cyclotron
absorption of electrons and positrons.
p
Wave Mode Coupling
• The evolution of two linear eigenmodes from adiabatic to nonadiabatic.
• 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
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.
Δk =Δnω/c
• 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
– 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
谢谢
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
观测事实
观测事实