Linearly Circularly or Elliptically Polarized Light n a

Linearly, Circularly, or Elliptically Polarized Light n (a) Linearly Polarized Light Oriented along the x axis Oriented along the y axis Orientation of 45 o from the x axis Orientation of 30 o from the x axis Fig. Presentation of linearly polarized with various orientations

n Circularly Polarized Light Orthogonal components with equal amplitudes & 90 o relative phase shift Clockwise Fig. Presentation of right circularly polarized with various orientations

Elliptical polarization • Linear + circular polarization = elliptical polarization

Proof of eq 1 <pf> # Proof of eq 2 <pf> #

Stokes Parameters n Elements of the Stokes Vector … (1) , where … (2) … (3) … (4) rcp In this case: Time-independent electric vector

Stokes parameters The Stokes parameters can be arranged in a Stokes vector: • Linear polarization • Circular polarization • Fully polarized light • Partially polarized light • Unpolarized light Polarization of Light: Basics to Instruments

不同成分：源于何处？ 辐射束亮度不均匀 脉冲星的辐射束模型 • Komesaroff (1970)+Backer (1976): Cone + Core： 1, 2, 3 peaks! • Rankin (1993): Core + cone + outer cone: 1, 2, 3, 4, 5 peaks! • Lyne & Machester (1998): Patchy beam: any number of peaks! a b c d e c a d e 乔老师画的Rankin的模型 Rankin自己画的辐射束模型: Patchy beam!

Cone-Core模型和patch模型

Observer Angle

脉冲整体宽度W与辐射束ρ W • W与α和β以及ρ有关！ • ρ与周期 P 有关: 转轴 Gould 1994, Rankin 1990, Rankin 1993, Kramer et al. 1994, Gil et al. 1993 Kramer et al. (1998) Lyne & Manchester 1998 Kramer et al. 1998 磁轴 天球面

脉冲轮廓的成分：高斯拟合 Kramer 199 Phillips & Wolsczcan (199

脉冲轮廓多个成分的Cone-Core理解 Gangadhara & Gupta (2001, Ap. J)

脉冲轮廓随频率变化: Radius-Frequency mapping • Pulse width generally increases with decreasing frequency. Thorsett 1991 Phillips & Wolsczcan (1992) • Consistent with ‘magnetic-pole’ model for pulse emission. • Lower frequencies are emitted at higher altitudes.

脉冲轮廓的偏振特征：观测 Lyne & Manchester (1988) P. A. Stokes I Linear Stokes V

脉冲轮廓的偏振特征：S 曲线 Rotating Vector model: Radhakrishnan & Cooke Vela Pulsar (1969) α β

Core与cone相对位移 可以产生PA jumps

脉冲星偏振随频率变化 圆偏振： Han et al. (1998, MNRAS); You & Han (2006, Ch. JAA)

Crewford et al. (2001, AJ) 1. 4 GHz Hi. P~Edot相关 von Hoensbroech et al. 1998, A&A 4. 9 GHz Han et al. (2009, Ap. JS) 774 MHz 408 MHz

Crab脉冲星的偏振 1. 424 GHz 4. 885 GHz

PSR J 0437 -4715的偏振轮廓 Navarro et al. (1997) Binary MSP： • P = 5. 75 ms • Pb = 5. 74 d • 至少 7个峰！ (Pulse truncated at 20% of peak) • PA曲线复杂 • PA有正交跳变 Linear Qiao et al. (2002)建议: ICS模型产生： Core+ cone+ outer_cone+ Outer_outer_cone! Circular 极冠内的多成分+磁层传播效应 1433 MHz

毫秒脉冲星的偏振轮廓观测 Han et al. (2009, Ap. JS) Manchester & Han (2004 Ap. J) Ord et al. (2004 MNRAS)

毫秒脉冲星的偏振轮廓观测 α~90° ; β~0° Ord et al. (2004 MNRAS) Stair et al. (1999, Ap. JS) Manchester & Han (2004 Ap. J)