2013年脉冲星天文学讲习班
2013.08.20
辐射在脉冲星磁层中的传播效应
国家天文台 王陈
Motivation – Circular polarization
• Single sign & Sign reversal
• Weak and strong
Origin
Intrinsic emission mechanism
Propagation effect
P.A.
Lyne & Manchester (1988)
Motivation - Orthogonal mode emission
V
P.A.
%L
I
Stinebring et al. (1984)
波
模
耦
合
脉冲星磁层中
辐射的传播效应
Ω
• 辐射高度 ~ a few - 100’s
RNS .
• 初始线偏振
回
旋
吸
收
准
切
点
效
应
法
拉
第
效
应
最终偏振
状态？
传播效应
k
μ
B
O模： E // k-B plane
X模： E ⊥ k-B plane
磁层
• B*=108 G – 1015 G
• 充满相对论流动的ee+等离
子体（开放磁力线区域）
沿磁层流动
N/NGJ ~ 10s – 1000s
γ ~ 10s – 1000s
Outlines
• Previous studies
– Dispersion relation and natural wave modes in pulsar
magnetosphere.
– Some propagation effects
• Our works
– On some special propagation effects
•
•
•
•
Vacuum resonance (Wang, Lai & Han 2007)
Quasi-tangential effect (Wang & Lai 2009)
Wave mode coupling effect (Wang, Lai & Han 2010)
Intrinsic Faraday Rotation effect in pulsar magnetosphere
(Wang, Han & Lai 2011)
– Numerical simulations on Polarization profile changes due to
all the propagation effects. (Wang, Lai & Han 2010)
Conclusion
Previous studies
• Dispersion relation and natural wave modes in pulsar
magnetosphere. (Melrose & Stoneham 1977, Arons & Barnard 1986,
von Hoensbroaech et al. 1998, Lyubaskii 1998, Melrose et al. 1999)
• Special Propagation effects
– Adiabatic Walking (Cheng & Ruderman 1979)
– Wave mode coupling (or limiting-polarization effect)
(Cheng & Ruderman 1979, Petrova 2000, 2006)
– Circularization (Cheng & Ruderman 1979)
– Refractive effect of O-mode
(Melrose 1979, Allen & Melrose 1982, Barnard & Arons 1986, Lyubarskii &
Petrova 1998, Weltevrede et al. 2003, Fussell & Luo 2004)
– Cyclotron absorption (Luo & Melrose 2001, 2006, Fussell et al. 2003)
Dispersion relation and natural wave modes in pulsar
magnetosphere
B=∞ limit (Tsytovitch & Kaplan 1972; Arons & Barnard 1986)
–
–
Cyclotron frequency >> wave frequency
Don’t consider QED effect in dielectric tensor.
k
B
Two natural wave modes
–
ordinary mode, or O-mode
Polarized in k-B
plane
O-mode
k
B
–
extraordinary mode, or E-mode
Polarized
perpendicular to
k-B plane
E-mode
In the real case, the two modes are elliptically polarized.
Dispersion relation and natural wave modes in pulsar
magnetosphere
B=∞ limit
Dispersion relation of O-mode
In the plasma rest frame
In the lab frame
Propagation effects：Adiabatic walking
φB
Adiabatic
Condition
• Make the final PA different
from the initial emission
Adiabatic
φPA
B⊥
NonAdiabatic
• The polarization direction follows
B⊥ field in adiabatic condition
垂直磁场 电场
方向
方向
E
Refractive effect of O-mode
(Melrose 1979, Allen & Melrose 1982, Barnard & Arons 1986, Lyubarskii &
Petrova 1998, Weltevrede et al. 2003, Fussell & Luo 2004)
• Only happens when wave frequency is close to proper plasma frequency, near
the emission height. n is not so close to unity.
• Refraction direction depends on the
density gradient.
• Can cause the separation of natural
waves,
=> OPM phenomenon.
(Melrose 1979, Allen & Melrose 1982)
• Outward density decrease causes ray
deviation away from magnetic axis,
which may widen the emission beam
width. (Lyubarskii & Petrova 1998)
• The refraction induced wave mode
coupling may cause CP with sign
reversal (Petrova & Lyubarskii 2000)
B
Cyclotron Resonance/Absorption
B
e
(Luo & Melrose 2001, 2006, Fussell et al. 2003)
ω′= eB/mc. r = rcr
•
RCP absorbed by electrons
LCP absorbed by positrons
scattered
E=
+
• Optical depth with γ >>1
circular polarization can be generated by the asymmetric cyclotron
absorption of electrons and positrons.
p
对称的正负电子回旋吸收
不对称的正负电子回旋吸收
A small summary to previous studies
• Dispersion relation and natural wave modes in some simple
approximations was analytically derived.
• A few kinds of propagation effects were studied qualitatively
(early years) and using numerical calculations (recent works).
• Almost none of the previous studies has calculated the final
polarization profiles with all of these propagation effects included
in a self-consistent way within a single theoretical framework
Our works
• Wave and modes amplitude evolution equation
• On some special propagation effects
–
–
–
–
Vacuum resonance (Wang, Lai & Han 2007)
Wave mode coupling (Wang, Lai & Han 2010)
Quasi-tangential effect (Wang & Lai 2009)
Intrinsic Faraday Rotation in magnetosphere
(Wang, Han & Lai 2011)
• Numerical calculations on Polarization profile
changes considering all the propagation effects.
(Wang, Lai & Han 2010)
Wave evolution equation
 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
Determined by
dielectric tensor
Wave frequency
Plasma properties
Magnetic field
Mode amplitude evolution equation
Y
y
Two elliptically polarized modes in the
lab frame
The ellipticity of the modes,
o
o
0 or 90 : linearly polarized;
E+
o
The orientation of the modes, dominated by B field
Mode amplitude evolution equation
i
Adiabatic
Condition
x
E-
45 : circularly polarized
i
B⊥
X
Our works on propagation effects
• Vacuum resonance
(Wang & Lai 2007, MNRAS)
• Wave mode coupling
(Wang, Lai & Han 2010, MNRAS)
• Quasi-tangential effect
(Wang & Lai 2009, MNRAS)
• Intrinsic Faraday Rotation effect in pulsar
magnetosphere
(Wang, Han & Lai 2011, MNRAS)
Vacuum resonance
(the competition between plasma and QED effect)
• X-ray band, Vacuum polarization (or QED effect) dominates the dispersion relation
• Radio band, plasma effect dominates
Where is the boundary?
What happens in the boundary regime
QED dominated
plasma dominated
Vacuum resonance
The two effects “cancled” with each other
1. Correction to dielectric tensor
2. Inverse permeability tensor
Wave modes with QED effect
• “Avoid mode crossing” occurs, the two modes (O-mode & E-mode)
coupled.
 define two new modes:
“＋” mode
“－” mode.
O-mode
X-mode
X-mode
O-mode
Mode conversion due to vacuum resonance
plasma
dominated
Vacuum
Resonance
QED
dominated
Helicity unchanged
O-mode
X-mode
X-mode
O-mode
Results on Vacuum resonance
• If mode evolution across vacuum resonance is adiabatic, mode
conversion (from O to X-mode or reversal) occurs.
• Location in dipole B field
• vacuum resonance can occur for sufficiently high frequencies and strong
surface magnetic fields.
=> high-frequency radio emission from the transient magnetar AXP XTE
J1810−197 (Camilo et al. 2006, 2007; Kramer et al. 2007).
• optical radiation emitted from the NS surface or near vicinity may
experience the vacuum resonance
Our works on propagation effects
• Vacuum resonance
(Wang & Lai 2007, MNRAS)
• Wave mode coupling
(Wang, Lai & Han 2010, MNRAS)
• Quasi-tangential effect
(Wang & Lai 2009, MNRAS)
• Intrinsic Faraday Rotation effect in pulsar
magnetosphere
(Wang, Han & Lai 2011, MNRAS)
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 because of 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:
Our works on propagation effects
• Vacuum resonance
(Wang & Lai 2007, MNRAS)
• Wave mode coupling
(Wang, Lai & Han 2010, MNRAS)
• Quasi-tangential effect
(Wang & Lai 2009, MNRAS)
• Intrinsic Faraday Rotation effect in pulsar
magnetosphere
(Wang, Han & Lai 2011, MNRAS)
Quasi-Tangential Effect
• Tangential and Quasi-Tangential point
k
B
k is in the magnetic field line plane, there
is a tangential point where θkB =0 and B⊥
change 180o suddenly 。
Bt
B⊥
k
k is not in the magnetic field line plane,
B⊥
Bt
B
there is a quasi-tangential point where θkB
reaches its minimum value (not 0) and B⊥
change 180o continuely.
Wang & Lai 2009, MNRAS
Ω
μ
k
Hot spot
X-ray
emissoin
B
Quasi-tangential
point (a few RNS)
Sketch Map of the model evolution across QT point
Polarization State after QT effect for the X-ray emission from
polar cap region（Initially 100% O-mode LP）
Wt
Wang & Lai 2009, MNRAS
Polarization intensity (Q) changes due to Quasi-tangential effect
（total intensity does not change)
Wang & Lai 2009, MNRAS
The phase evolution of the modification of linear polarization by the QT effect,
B_surf = 10^13G
B_surf = 10^14G
Conclusion for the QT effect:
• the QT effect will have at most modest effect on the observed X-ray
polarization signals from magnetized NSs.
=> linear polarization is weakened, LP profiles will be modified.
Our works on propagation effects
• Vacuum resonance
(Wang & Lai 2007, MNRAS)
• Wave mode coupling
(Wang, Lai & Han 2010, MNRAS)
• Quasi-tangential effect
(Wang & Lai 2009, MNRAS)
• Intrinsic Faraday Rotation effect in pulsar
magnetosphere
(Wang, Han & Lai 2011, MNRAS)
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
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 case，N = Ne = 1000 NGJ
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
k μ aligned
k
μ
k μ inversely aligned
μ
k
Phased resolved RM profile
Pulsar parameters：α=35，γ=100，η=1000，Bs=5e12G，P=1s，r_em=50Rs
Results on Intrinsic Faraday rotation effect
• 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
• The intrinsic RM for mainpulse and interpulse should be opposite sign.
Which may be checked in precise RM observations.
Our works
• Wave and modes amplitude evolution equation
• On some special propagation effects
–
–
–
–
Vacuum resonance (Wang, Lai & Han 2007)
Wave mode coupling (Wang, Lai & Han 2010)
Quasi-tangential effect (Wang & Lai 2009)
Intrinsic Faraday Rotation in magnetosphere
(Wang, Han & Lai 2011)
• Numerical calculations on Polarization profile
changes considering all the propagation effects.
(Wang, Lai & Han 2010)
Numerical calculations on Polarization profile changes
considering all the propagation effects. (Wang, Lai & Han 2010)
• Wave evolution equation
Assumptions:
•
•
•
•
•
Photon emitted along the tangential direction of local B field
Initially 100% linearly polarized, (generally O-mode).
Single gamma (cold plasma)
Uniformly distributed plasma in the open field line region.
all emissions are from the same height
Solid line (red):
Dashed line (blue):
Dotted line (green):
经过磁层传播效应后的偏振轮廓
（一个例子，回旋吸收和波模耦合主导）
回旋吸收各相位不同
波模耦合产生足够强的圆偏振
偏振位置角曲线移动很大
正交模式现象?
2D
polarization
profiles
Possible examples in observation: orthogonal modes
总结
传播效应对辐射尤其偏振有很大影响
作用波段
总强度
线偏振
圆偏振
备注
绝热行走
Radio ～ X-ray
无
有
无
影响偏振位置角
波模耦合
Radio ～ X-ray
无
有
有
产生圆偏振
回旋吸收
Radio ～ X-ray
有
有
有
吸收辐射
O模折射
Radio
无
有
有
分离2种波模
准切点效应
Radio ～ X-ray
无
有
无
影响偏振谱
圆化效应
Radio
无
有
有
产生圆偏振
真空极化效应
Radio ～ X-ray
无
有
无
可能导致正交模式
法拉第效应
Radio
无
有
无
产生本征RM
总结
• 很多脉冲星偏振观测现象可以由传播效应来解
释。
– 锥双峰脉冲星中圆偏振的起源
– 部分正交模式现象
• 需要更详细模型下的理论计算
• 需要更多的与观测的结合
谢谢！
谢谢
观测事实
观测事实
Ω
μ
k
绝热行走使
各处偏振一致
Hot spot
辐射区
B
刚出大气层时热斑各
处偏振不一致
中子星整个表面各处
准切点效应对X-ray
线偏振度的影响
QT效应影响区域
QT效应影响区域
PA evolution along the way for different parameters
Dielectric tensor in pulsar magnetosphere
Basic parameters:
• density.
Using the Goldreich–Julian number density as a fiducial value
and
• Lorentz factor.
here we consider cold plasma case with single
• cyclotron frequency and plasma frequency.
define
Dielectric tensor for an streaming electron-positron plasma
•
Particle (electron and position) motion equation
•
Current density
•
Dielectric tensor
Conductivity
tensor
Wave modes in magnetosphere: dielectric tensor
Dielectric tensor caused by plasma effect
z′
B
Coordinate system
x′y′z′
with
k
θ
x′
Dielectric tensor corrections due to Vacuum Polarization
(QED effect)
1. Correction to dielectric tensor
2. Inverse permeability tensor
For
and
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