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

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

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

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

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.

Single Photon evolution along the ray

CP generated by wave mode coupling

Cyclotron absorption

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:

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 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

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

• 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

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

谢谢谢谢

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

k μ aligned

μ

k

k μ inversely aligned

k

μ

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