Origin of pulsar orthogonal polarization modes Chen WANG P.F. WANG, Jinlin HAN National Astronomical Observatories, CAS FAST Pulsar Symposium 3, July 2-4, 2014, Shanghai, China

Outline Polarized Curvature Radiation in Pulsar Magnetosphere (with both emission and propagation). => naturally generate orthogonal polarization modes (OPM) Wang, Wang & Han, 2014 Distinguish orthogonal polarization modes of pulsar emission using spin axis and proper motion => constrain OPM model Wang 2014

Basic Physical Image of polarization evolution Pulsar magnetosphere 1) Rotating dipole 2) ±e plasma streaming along B field line 3) Lorentz factor of the plasma γ ~ 400； 4) Density of the plasma Ω k μ Propagation 1) O mode refraction 2) Adiabatic walking B Emission Curvature radiation 3

⊕ μ Ω B Two linear eigenmodes of wave in pulsar magentosphere k B O-mode X-mode ⊕ Ordinary mode (O-mode), n < 1 Extraordinary mode (X-mode), n ~ 1 The separation between the emission points of the O/X-mode waves Refraction of O-mode wave X O observer Ω μ X O B Observed O/X-mode components at given phase are incoherent !

Curvature Radiation Without co-rotation V0 // B V0 1/γcone 1/γcone 1/γ Classical model considered by Cheng & Ruderman 1979 B With co-rotation V // B V0 V B

Profiles with various impact angle Without co-rotation Emission beam Profiles with various impact angle Uniform Cone Core Patch 6

Profiles with various impact angle With co-rotation Emission beam Profiles with various impact angle Uniform Cone Core Patch 7

Conclusion for polarized curvature radiation in pulsar magnetosphere The O-mode refraction separate X and O-mode components. which cause: The observed X-mode and O-mode wave at given phase are emitted from incoherent region; The orthogonal mode happens naturally due to the change of the dominance of the two modes; X/O-mode components of CR have: almost the same magnitude without considering the co-rotation of plasma, which cause strong depolarization; very different distribution with co-rotation included, high LP can be observed. Refraction induced OPM perfers “O X O” modes sequence. May be checked by observation!

Distinguish orthogonal polarization modes of pulsar emission Orthogonal polarization mode for PSR B2020+28 Mean profile Polarization of single pulses V PA Which mode is it? O- or X-mode? L 90o PA 90o I Stinebring et al. (1984)

Rotating Vector Model O-mode X-mode Another well-known method to determine the spin axis depends on the linear polarization profile of radio emission. If the polarization profile could be described by rotating vector model, we can constrain the projected spin axis by the polarized angle in the center of the pulse. This has been attempted before for several times, but inconsistent results. The problem is polarization profile of most pulsars can not be cleanly described by RVM model, so they didn't have enough useful data with less uncertainty. For example, the map show a S-shape profile which can be well described by RVM, we can easily determine the polarization angle at the center of pulse. But most pulsars have profiles like this, it’s very hard to know where is the center of the pulse. O-mode X-mode

Two ways to constrain spin axis PWN of Vela: X-ray obs. Get spin axis directly by fitting the symmetric tori of PWNe around some young pulsars obtain spin axis of 15 pulsars by Ng & Romani 2004, 2007, 2008. Not avialable for normal pulsars without PWNe Using proper motion direction instead of spin axis according to spin-kick alignment Spin-kick alignment proved by Romani, Ng, Johnston, Wang, Noutsos et al. Proper motion measured by pulsar timing and interferometer obs. Brisken et al. 2002, 2003; Hobbs et al. 2005. Ng & Romani 2004 Spin-kick alignment of pulsars Noutsos et al. 2011

For 7 pulsars, O-mode dominate central intensity-peak region. (X O X) Mode distinguishment for 14 OPM-pulsars (with both believable PM and PA data) For 7 pulsars, O-mode dominate central intensity-peak region. (X O X) For 4 pulsars, X-mode dominate intensity-peak region. (O X O) For 3 pulsars, each mode dominates half profiles Polarization profiles comes from Johnston et al. 2005, 2007; Carr 2007; Han et al. 2009

Possible constrains on origin of OPM Refraction effect. O-X-O (4 pulsars) O mode refracted towards away from magnetic axis. Emission mechanism origin. Cheng & Ruderman 1979, X-O-X (7 pulsars) Central O-mode emission from parallel accelaration X-mode from curvature radiation dominates two wings Different OPM-pulsars may have different origin of OPM. PSR2020+28 X-mode O-mode X-mode

Summary Refraction of O-mode seperates the two eigenmodes and make them incoherent, which naturally causes OPM. X/O-mode components of curvature radiation have: almost the same magnitude without considering the co-rotation of plasma, which cause strong depolarization; very different distribution with co-rotation included, high LP can be observed. Modes sequence of OPM perfer “O X O” Polarization modes of 14 OPM-pulsars can be recognized by pulsar spin axis and/or proper motion. 4 of them agree with “O X O” modes sequence 7 of them are “X O X”, 3 of them are “X O”. Different OPM-pulsars may have different origin of OPM. Need more polarization and timing obs. to get PA and PM angle. 65m & FAST ???

年轻脉冲星星风云X-ray观测 部分PWN为环状结构 可以直接确定自转轴方向 Crab Vela PArot PArot 部分PWN为环状结构 可以直接确定自转轴方向 B0531+21 B0540-69 J1833-1034 J0205+6449 J2229+6114 B1509-58 J1124-5916 J1930+1852 Kargaltsev & Pavlov 2008 B0833-45 J2021+3651 B1706-44 B1800-21

Mode distinguishment for 3 young pulsars Both spin axis and well-calibrated polarization position angle curve is needed

普通脉冲星：spin-kick趋于一致 利用偏振曲线最陡处PA0代替spin，统计PA0v的分布 Wang et al. 2006 Johnston et al. 2005

讨论 利用自行与PA最陡处偏振位置角之差（PA0v）辨别模式的前提： 下一步工作：获得更大的PA0v样本。 Spin-kick趋于一致。是否可靠？ 年老的脉冲星可能不一致 部分年轻或正常脉冲星也有可能不一致。 传播效应对PA曲线垂直方向影响不大。基本可靠! 确定PA曲线最陡处的位置。对基本符合RVM描述的S型比较容易。但是对S曲线不完整的比较勉强！ 下一步工作：获得更大的PA0v样本。 偏振观测与校准 多波段偏振观测 自行观测数据，长期timing或者VLBI观测获得。 下一步工作：正交模式的起源。正在进行中…

总结 利用年轻脉冲星星风云X-ray观测得到的自转轴方向可以辨别偏振模式，但是个数太少。 根据spin-kick的一致性，可以利用自行方位与PA最陡处偏振位置角之差（PA0v）来辨别偏振模式 PA0v ~ 0 o 为O-mode PA0v ~ 90 o为X-mode 应用： 利用PA0v辨别了12颗脉冲星的正交模式，发现 8颗脉冲星 X-mode位于leading side 4颗脉冲星 O-mode位于leading side 利用PA0v辨别了4颗conal-double PSRs 的偏振模式，有3颗是O-mode。 需要更多的校准好的偏振数据以及自行数据进行下一步统计研究。

Cheng & Ruderman 1979 curvature dominate Bunching dominate

星风云的详细结构

Vela 脉冲星星风云的结构 G. G. Pavlov et. al. ApJ. 591:1157 C. -Y. Ng ApJ Vela 脉冲星星风云的结构 G. G. Pavlov et. al. ApJ. 591:1157 C.-Y. Ng ApJ.601:479 (FITTING PWN TORI) Chandra ACIS-S3 image of Vela PWN：(1) Vela pulsar, (2) inner arc, (3) outer arc, (4) inner jet, (5) counter jet, (6) shell, (7) outer jet.

考虑spin-kick的一致性，可以用自行代替自转轴方向 判断自行方向角PAv与PA最陡处PA0的差值PA0v PA0v ~ 0 o => O-mode PA0v ~ 90 o => X-mode X-mode Two Vela-like PSRs X-mode PAv PAv X-mode

O-mode X-mode 应用PA0v辨别正交模式 B1929+10 B0736-40 PAv O-mode X-mode

B1237+25 B1857-26 X-mode O-mode X-mode O-mode PAv

PAv X-mode O-mode? O-mode X-mode X-mode B0835-41 B0450-18 X-mode

8颗脉冲星 X-mode位于leading side B0355+54 J1735-0724 X-mode X-mode O-mode PAv O-mode 8颗脉冲星 X-mode位于leading side

J0953+0755 J1453-6413 X-mode O-mode PAv O-mode O-mode X-mode

4颗脉冲星 O-mode位于leading side 8颗脉冲星 X-mode位于leading side J1645-0317 J1709-1640 PAv X-mode O-mode O-mode X-mode 4颗脉冲星 O-mode位于leading side 8颗脉冲星 X-mode位于leading side

Conal-Double PSRs 中PA与V的关系 Conal-double pulsars, PA increase  V < 0 PA decrease  V > 0 PAv Han et al. 1998, You et al. 2006 可以利用磁层中的波模耦合传播效应来很好的解释 波模耦合产生的圆偏振依赖于PA的变化趋势 要求：Conal-Double PSRs的偏振辐射都是O-mode！ 可以用PA0v来检验是否为O-mode

4颗conal-double PSRs有PA0v 3 颗为 O-mode, 1颗为 X-mode