1. 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

2. 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

3. 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

4. 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 = +

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

7. 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:

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 aligned k μ
k μ 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