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Polarization in Interferometry


Ninth Synthesis Imaging Summer School

Socorro, June 15-22, 2004 

Polarization in Interferometry 

Steven T. Myers (NRAO-Socorro)


 

Polarization in interferometry 

  • Physics of Polarization
  • Interferometer Response to Polarization
  • Polarization Calibration & Observational Strategies
  • Polarization Data & Image Analysis
  • Astrophysics of Polarization
  • Examples
  • References: 
    • Synth Im. II lecture 6, also parts of 1, 3, 5, 32
    • ��Tools of Radio Astronomy�� Rohlfs & Wilson

Polarization in Interferometry – S. T. Myers

 

WARNING! 

  • Polarimetry is an exercise in bookkeeping!
    • many places to make sign errors!
    • many places with complex conjugation (or not)
    • possible different conventions (e.g. signs)
    • different conventions for notation!
    • lots of matrix multiplications
  • And be assured��
    • I��ve mixed notations (by stealing slides )
    • I��ve made sign errors  (I call it ��choice of convention�� )
    • I��ve probably made math errors 
    • I��ve probably made it too confusing by going into detail 
    • But �� persevere (and read up on it later) 
 

DON��T PANIC !


Polarization in Interferometry – S. T. Myers

 

Polarization Fundamentals


Polarization in Interferometry – S. T. Myers

 

Physics of polarization 

  • Maxwell��s Equations + Wave Equation
    • E•B=0  (perpendicular) ; Ez = Bz = 0 (transverse)
  • Electric Vector – 2 orthogonal independent waves:
    • Ex = E1 cos( k z – w t + d1 )         k = 2p / l
    • Ey = E2 cos( k z – w t + d2 )         w = 2p n
    • describes helical path on surface of a cylinder��
    • parameters E1, E2, d  = d1 - d2 define ellipse 
       
       
       
       

Polarization in Interferometry – S. T. Myers

 

The Polarization Ellipse 

  • Axes of ellipse Ea, Eb
    • S0 = E12 + E22 = Ea2 + Eb2       Poynting flux
    • d phase difference                t = k z – w t
    • Ex = Ea cos ( t + d ) = Ex cos y + Ey sin y
    • Eh = Eb sin ( t + d ) = -Ex sin y + Ey cos y
 
 

Rohlfs & Wilson


Polarization in Interferometry – S. T. Myers

 

The polarization ellipse continued�� 

  • Ellipticity and Orientation
    • E1 / E2 = tan a      tan 2y = - tan 2a cos d
    • Ea / Eb = tan c      sin 2c = sin 2a sin d
    • handedness  ( sin d > 0 or tan c > 0  right-handed)
 

Rohlfs & Wilson


Polarization in Interferometry – S. T. Myers

 

Polarization ellipse – special cases 

  • Linear polarization
    • d  = d1 - d2 = m p     m = 0, ��1, ��2, ��
    • ellipse becomes straight line
    • electric vector position angle y = a
  • Circular polarization
    • d  = ½ ( 1 + m ) p     m = 0, 1, ��2, ��
    • equation of circle Ex2 + Ey2 = E2
    • orthogonal linear components:
      • Ex = E cos t
      • Ey = ��E cos ( t - p/2 )
      • note quarter-wave delay between Ex and Ey !

Polarization in Interferometry – S. T. Myers

 

Orthogonal representation 

  • A monochromatic wave can be expressed as the superposition of two orthogonal linearly polarized waves
  • A arbitrary elliptically polarizated wave can also equally well be described as the superposition of two orthogonal circularly polarized waves!
  • We are free to choose the orthogonal basis for the representation of the polarization
  • NOTE: Monochromatic waves MUST be (fully) polarized – IT��S THE LAW!

Polarization in Interferometry – S. T. Myers

 

Linear and Circular representations 

  • Orthogonal Linear representation:
    • Ex = Ea cos ( t + d ) = Ex cos y + Ey sin y
    • Eh = Eb sin ( t + d ) = -Ex sin y + Ey cos y
  • Orthogonal Circular representation: 
    • Ex = Ea cos ( t + d ) = ( Er + El ) cos ( t + d )
    • Eh = Eb sin ( t + d ) = ( Er - El ) cos ( t + d – p/2 )
    • Er = ½ ( Ea + Eb )
    • El = ½ ( Ea – Eb )

 


Polarization in Interferometry – S. T. Myers

 

The Poincare Sphere 

  • Treat 2y and 2c as longitude and latitude on sphere of radius S0
 

Rohlfs & Wilson


Polarization in Interferometry – S. T. Myers

 

Stokes parameters 

  • Spherical coordinates: radius I, axes Q, U, V
    • S0 = I = Ea2 + Eb2
    • S1 = Q = S0 cos 2c cos 2y
    • S2 = U = S0 cos 2c sin 2y
    • S3 = V = S0 sin 2c
  • Only 3 independent parameters:
    • S02 = S12 + S22 + S32
    • I2 = Q2 + U2 + V2
  • Stokes parameters I,Q,U,V
    • form complete description of wave polarization
    • NOTE: above true for monochromatic wave!

Polarization in Interferometry – S. T. Myers

 

Stokes parameters and polarization ellipse 

  • Spherical coordinates: radius I, axes Q, U, V
    • S0 = I = Ea2 + Eb2
    • S1 = Q = S0 cos 2c cos 2y
    • S2 = U = S0 cos 2c sin 2y
    • S3 = V = S0 sin 2c
  • In terms of the polarization ellipse:
    • S0 = I = E12 + E22
    • S1 = Q = E12 - E22
    • S2 = U = 2 E1 E2 cos d
    • S3 = V = 2 E1 E2 sin d

Polarization in Interferometry – S. T. Myers

 

Stokes parameters special cases 

  • Linear Polarization
    • S0 = I = E2 = S
    • S1 = Q = I cos 2y
    • S2 = U = I sin 2y
    • S3 = V = 0
  • Circular Polarization
    • S0 = I = S
    • S1 = Q = 0
    • S2 = U = 0
    • S3 = V = S (RCP) or –S (LCP)
 

Note: cycle in 180��


Polarization in Interferometry – S. T. Myers

 

Quasi-monochromatic waves 

  • Monochromatic waves are fully polarized
  • Observable waves (averaged over Dn/n << 1)
  • Analytic signals for x and y components:
    • Ex(t) = a1(t) e i(f1(t) – 2pnt)
    • Ey(t) = a2(t) e i(f2(t) – 2pnt)
    • actual components are the real parts Re Ex(t), Re Ey(t)
  • Stokes parameters
    • S0 = I = <a12> + <a22>
    • S1 = Q = <a12> – <a22>
    • S2 = U = 2 < a1 a2 cos d >
    • S3 = V = 2 < a1 a2 sin d >

 


Polarization in Interferometry – S. T. Myers

 

Stokes parameters and intensity measurements 

  • If phase of Ey is retarded by e relative to Ex , the electric vector in the orientation q is:
    • E(t; q, e) = Ex cos q + Ey eie sin q
  • Intensity measured for angle q:
    • I(q, e) = < E(t; q, e) E*(t; q, e) >
  • Can calculate Stokes parameters from 6 intensities:
    • S0 = I = I(0��,0) + I(90��,0)
    • S1 = Q = I(0��,0) + I(90��,0)
    • S2 = U = I(45��,0) – I(135��,0)
    • S3 = V = I(45��,p/2) – I(135��,p/2)
    • this can be done for single-dish (intensity) polarimetry!

Polarization in Interferometry – S. T. Myers

 

Partial polarization 

  • The observable electric field need not be fully polarized as it is the superposition of monochromatic waves
  • On the Poincare sphere:
    • S02 �� S12 + S22 + S32
    • I2 �� Q2 + U2 + V2
  • Degree of polarization p :
    • p2 S02 = S12 + S22 + S32
    • p2 I2 = Q2 + U2 + V2

Polarization in Interferometry – S. T. Myers

 

Summary – Fundamentals 

  • Monochromatic waves are polarized
  • Expressible as 2 orthogonal independent transverse waves
    • elliptical cross-section  polarization ellipse
    • 3 independent parameters
    • choice of basis, e.g. linear or circular
  • Poincare sphere convenient representation
    • Stokes parameters I, Q, U, V
    • I intensity; Q,U linear polarization, V circular polarization
  • Quasi-monochromatic ��waves�� in reality
    • can be partially polarized
    • still represented by Stokes parameters

Polarization in Interferometry – S. T. Myers

 

Antenna & Interferometer Polarization


Polarization in Interferometry – S. T. Myers

 

Interferometer response to polarization 

  • Stokes parameter recap:
    • intensity I
    • fractional polarization       (p I)2 = Q2 + U2 + V2
    • linear polarization Q,U     (m I)2 = Q2 + U2
    • circular polarization V       (v I)2 = V2
  • Coordinate system dependence:
    • I independent
    • V depends on choice of ��handedness��
      • V > 0 for RCP
    • Q,U depend on choice of ��North�� (plus handedness)
      • Q ��points�� North, U 45 toward East
      • EVPA   F = ½ tan-1 (U/Q)    (North through East)

Polarization in Interferometry – S. T. Myers

 

Reflector antenna systems 

  • Reflections
    • turn RCP  LCP
    • E-field allowed only in plane of surface
  • Curvature of surfaces
    • introduce cross-polarization
    • effect increases with curvature (as f/D decreases)
  • Symmetry
    • on-axis systems see linear cross-polarization
    • off-axis feeds introduce asymmetries & R/L squint
  • Feedhorn & Polarizers
    • introduce further effects (e.g. ��leakage��)

 


Polarization in Interferometry – S. T. Myers

 

Optics – Cassegrain radio telescope  

  • Paraboloid illuminated by feedhorn:

Polarization in Interferometry – S. T. Myers

 

Optics – telescope response  

  • Reflections
    • turn RCP  LCP
    • E-field (currents) allowed only in plane of surface
  • ��Field distribution�� on aperture for E and B planes:
 

Cross-polarization

at 45�� 

No cross-polarization

on axes


Polarization in Interferometry – S. T. Myers

 

Polarization field pattern 

  • Cross-polarization
    • 4-lobed pattern
  • Off-axis feed system
    • perpendicular elliptical linear pol. beams
    • R and L beams diverge (beam squint)
  • See also:
    • ��Antennas�� lecture by P. Napier

Polarization in Interferometry – S. T. Myers

 

Feeds – Linear or Circular? 

  • The VLA uses a circular feedhorn design
    • plus (quarter-wave) polarizer to convert circular polarization from feed into linear polarization in rectangular waveguide
    • correlations will be between R and L from each antenna
      • RR RL LR RL form complete set of correlations
  • Linear feeds are also used
    • e.g. ATCA, ALMA (and possibly EVLA at 1.4 GHz)
    • no need for (lossy) polarizer!
    • correlations will be between X and Y from each antenna
      • XX XY YX YY form complete set of correlations
  • Optical aberrations are the same in these two cases
    • but different response to electronic (e.g. gain) effects

Polarization in Interferometry – S. T. Myers

 

Example – simulated VLA patterns 

  • EVLA Memo 58 ��Using Grasp8 to Study the VLA Beam�� W. Brisken

Polarization in Interferometry – S. T. Myers

 

Example – simulated VLA patterns 

  • EVLA Memo 58 ��Using Grasp8 to Study the VLA Beam�� W. Brisken
 

Linear Polarization 

Circular Polarization cuts in R & L


Polarization in Interferometry – S. T. Myers

 

Example – measured VLA patterns 

  • AIPS Memo 86 ��Widefield Polarization Correction of VLA Snapshot Images at 1.4 GHz�� W. Cotton (1994)
 

Circular Polarization 

Linear Polarization


Polarization in Interferometry – S. T. Myers

 

Example – measured VLA patterns 

  • frequency dependence of polarization beam :

Polarization in Interferometry – S. T. Myers

 

Beyond optics – waveguides & receivers  

  • Response of polarizers
    • convert R & L to X & Y in waveguide
    • purity and orthogonality errors
  • Other elements in signal path:
    • Sub-reflector & Feedhorn
      • symmetry & orientation
    • Ortho-mode transducers (OMT)
      • split orthogonal modes into waveguide
    • Polarizers
      • retard one mode by quarter-wave to convert LP  CP
      • frequency dependent!
    • Amplifiers
      • separate chains for R and L signals

Polarization in Interferometry – S. T. Myers

 

Back to the Measurement Equation 

  • Polarization effects in the signal chain appear as error terms in the Measurement Equation
    • e.g.  ��Calibration�� lecture, G. Moellenbrock:
 
      • F = ionospheric Faraday rotation
      • T = tropospheric effects
      • P = parallactic angle
      • E = antenna voltage pattern
      • D = polarization leakage
      • G = electronic gain
      • B = bandpass response
 

Antenna i 

Baseline ij (outer product)


Polarization in Interferometry – S. T. Myers

 

Ionospheric Faraday Rotation, F 

  • Birefringency due to magnetic field in ionospheric plasma
    • also present in radio sources! 
       
       
       
       
       
       
       

Polarization in Interferometry – S. T. Myers

 

Ionospheric Faraday Rotation, F 

  • The ionosphere is birefringent; one hand of circular polarization is delayed w.r.t. the other, introducing a phase shift:
    • Rotates the linear polarization position angle 
       
    • More important at longer wavelengths:
    • More important at solar maximum and at sunrise/sunset, when ionosphere is most active 
       
    • Watch for direction dependence (in-beam)
    • See ��Low Frequency Interferometry�� (C. Brogan)

Polarization in Interferometry – S. T. Myers

 

Parallactic Angle, P 

  • Orientation of sky in telescope��s field of view
    • Constant for equatorial telescopes
    • Varies for alt-az-mounted telescopes:
    • Rotates the position angle of linearly polarized radiation (c.f. F
       
       
       
    • defined per antenna (often same over array) 
       
    • P modulation can be used to aid in calibration

Polarization in Interferometry – S. T. Myers

 

Parallactic Angle, P 

  • Parallactic angle versus hour angle at VLA :
    • fastest swing for source passing through zenith

Polarization in Interferometry – S. T. Myers

 

Polarization Leakage, D 

  • Polarizer is not ideal, so orthogonal polarizations not perfectly isolated
    • Well-designed systems have d < 1-5%
    • A geometric property of the antenna, feed & polarizer design
      • frequency dependent (e.g. quarter-wave at center n)
      • direction dependent (in beam) due to antenna
    • For R,L systems
      • parallel hands affected as d•Q + d•U , so only important at high dynamic range (because Q,U~d, typically)
      • cross-hands affected as d•I so almost always important
 

Leakage of q into p

(e.g. L into R)


Polarization in Interferometry – S. T. Myers

 

Coherency vector and correlations 

  • Coherency vector:
    • e.g. for circularly polarized feeds: 
       
       
       

Polarization in Interferometry – S. T. Myers

 

Coherency vector and Stokes vector 

  • Example: circular polarization (e.g. VLA)
  • Example: linear polarization (e.g. ATCA) 
     
     
     
     

Polarization in Interferometry – S. T. Myers

 

Visibilities and Stokes parameters 

  • Convolution of sky with measurement effects:
  • e.g. with (polarized) beam E : 
     
     
     
     
    • imaging involves inverse transforming these 
       
       
       
 

Instrumental

effects, including

��beam�� E(l,m) 

coordinate transformation

to Stokes parameters 
 

(I, Q, U, V)


Polarization in Interferometry – S. T. Myers

 

Example: RL basis 

  • Combining E, etc. (no D), expanding P,S:
 

2c for co-located

array 

0 for co-located

array


Polarization in Interferometry – S. T. Myers

 

Example: RL basis imaging 

  • Parenthetical Note:
    • can make a pseudo-I image by gridding RR+LL on the Fourier half-plane and inverting to a real image
    • can make a pseudo-V image by gridding RR-LL on the Fourier half-plane and inverting to real image
    • can make a pseudo-(Q+iU) image by gridding RL to the full Fourier plane (with LR as the conjugate) and inverting to a complex image
    • does not require having full polarization RR,RL,LR,LL for every visibility
  • More on imaging ( & deconvolution ) tomorrow!

Polarization in Interferometry – S. T. Myers

 

Leakage revisited�� 

  • Primary on-axis effect is ��leakage�� of one polarization into the measurement of the other (e.g. R  L)
    • but, direction dependence due to polarization beam!
  • Customary to factor out on-axis leakage into D and put direction dependence in ��beam��
    • example: expand RL basis with on-axis leakage
    • similarly for XY basis 
       
       
       
       

Polarization in Interferometry – S. T. Myers

 

Example: RL basis leakage 

  • In full detail:
 

��true�� signal 

1st order:

D•I into P 

2nd order:

D•P into I 

2nd order:

D2•I into I 

3rd order:

D2•P* into P


Polarization in Interferometry – S. T. Myers

 

Example: Linearized response 

  • Dropping terms in d2, dQ, dU, dV (and expanding G)
    • warning: using linear order can limit dynamic range! 
       
       
       
       
       
       
       
       
       
       

Polarization in Interferometry – S. T. Myers

 

Summary – polarization interferometry 

  • Choice of basis: CP or LP feeds
  • Follow the Measurement Equation
    • ionospheric Faraday rotation F at low frequency
    • parallactic angle P for coordinate transformation to Stokes
    • ��leakage�� D varies with n and over beam (mix with E)
  • Leakage
    • use full (all orders) D solver when possible
    • linear approximation OK for low dynamic range

 


Polarization in Interferometry – S. T. Myers

 

Polarization Calibration

& Observation


Polarization in Interferometry – S. T. Myers

 

So you want to make a polarization map��


Polarization in Interferometry – S. T. Myers

 

Strategies for polarization observations 

  • Follow general calibration procedure (last lecture)
    • will need to determine leakage D (if not known)
    • often will determine G and D together (iteratively)
    • procedure depends on basis and available calibrators
  • Observations of polarized sources
    • follow usual rules for sensitivity, uv coverage, etc.
    • remember polarization fraction is usually low! (few %)
    • if goal is to map E-vectors, remember to calculate noise in F= ½  tan-1 U/Q
    • watch for gain errors in V (for CP) or Q,U (for LP)
    • for wide-field high-dynamic range observations, will need to correct for polarized primary beam (during imaging)

Polarization in Interferometry – S. T. Myers

 

Strategies for leakage calibration 

  • Need a bright calibrator!  Effects are low level��
    • determine gains G ( mostly from parallel hands)
    • use cross-hands (mostly) to determine leakage
    • general ME D solver (e.g. aips++) uses all info
  • Calibrator is unpolarized
    • leakage directly determined (ratio to I model), but only to an overall constant
    • need way to fix phase p-q (ie. R-L phase difference), e.g. using another calibrator with known EVPA
  • Calibrator of known polarization
    • leakage can be directly determined (for I,Q,U,V model)
    • unknown p-q phase can be determined (from U/Q etc.)

Polarization in Interferometry – S. T. Myers

 

Other strategies 

  • Calibrator of unknown polarization
    • solve for model IQUV and D simultaneously or iteratively
    • need good parallactic angle coverage to modulate sky and instrumental signals
      • in instrument basis, sky signal modulated by ei2c
  • With a very bright strongly polarized calibrator
    • can solve for leakages and polarization per baseline
    • can solve for leakages using parallel hands!
  • With no calibrator
    • hope it averages down over parallactic angle
    • transfer D from a similar observation
      • usually possible for several days, better than nothing!
      • need observations at same frequency

Polarization in Interferometry – S. T. Myers

 

Finding polarization calibrators 

  • Standard sources
    • planets (unpolarized if unresolved)
    • 3C286, 3C48, 3C147 (known IQU, stable)
    • sources monitored (e.g. by VLA)
    • other bright sources (bootstrap)
 

http://www.vla.nrao.edu/astro/calib/polar/


Polarization in Interferometry – S. T. Myers

 

Example: D-term calibration 

  • D-term calibration effect on RL visibilities :

Polarization in Interferometry – S. T. Myers

 

Example: D-term calibration 

  • D-term calibration effect in image plane :
 

Bad D-term solution 

Good D-term solution


Polarization in Interferometry – S. T. Myers

 

Example: ��standard�� procedure for CP feeds


Polarization in Interferometry – S. T. Myers

 

Example: ��standard�� procedure for LP feeds


Polarization in Interferometry – S. T. Myers

 

Special Issues 

  • Low frequency – ionospheric Faraday rotation
    • important for 2 GHz and below (sometimes higher too)
    • l2 dependence (separate out using multi-frequency obs.)
    • depends on time of day and solar activity (& observatory location)
    • external calibration using zenith TEC (plus gradient?)
    • self-calibration possible (e.g. with snapshots)

Polarization in Interferometry – S. T. Myers

 

Special issues – continued�� 

  • VLBI polarimetry
    • follows same principles
    • will have different parallactic angle at each station!
    • can have heterogeneous feed geometry (e.g. CP & LP)
    • harder to find sources with known polarization
      • calibrators resolved!
      • transfer EVPA from monitoring program
 
 

2200+420


Polarization in Interferometry – S. T. Myers

 

Subtleties �� 

  • Antenna-based D solutions
    • closure quantities  undetermined parameters
    • different for parallel and cross-hands
    • e.g. can add d to R and d* to L
    • need for reference antenna to align and transfer D solutions
  • Parallel hands
    • are D solutions from cross-hands appropriate here?
    • what happens in full D solution (weighting issues?)

Polarization in Interferometry – S. T. Myers

 

Special Issues – observing circular polarization 

  • Observing circular polarization V is straightforward with LP feeds (from Re and Im of cross-hands)
  • With CP feeds:
    • gain variations can masquerade as (time-variable) V signal
      • helps to switch signal paths through back-end electronics
    • R vs. L beam squint introduces spurious V signal
      • limited by pointing accuracy
    • requires careful calibration
      • relative R and L gains critical
      • average over calibrators (be careful of intrinsic V)
    • VLBI somewhat easier
      • different systematics at stations help to average out

Polarization in Interferometry – S. T. Myers

 

Special Issues – wide field polarimetry 

  • Actually an imaging & deconvolution issue
    • assume polarized beam D��•E is known
    • see EVLA Memo 62 ��Full Primary Beam Stokes IQUV Imaging�� T. Cornwell (2003)
  • Deal with direction-dependent effects
    • beam squint (R,L) or beam ellipticity (X,Y)
    • primary beam
  • Iterative scheme (e.g. CLEAN)
    • implemented in aips++
    • see lectures by Bhatnagar & Cornwell

Polarization in Interferometry – S. T. Myers

 

Example: wide field polarimetry 

      • Simulated array of point sources
 

No beam correction 

1D beam + squint 

Full 2D beam


Polarization in Interferometry – S. T. Myers

 

Example: wide field polarimetry continued�� 

      • Simulated Hydra A image
 

Model 

Errors 1D sym.beam 

Errors full beam 

Panels:    I     Q

                U    V


Polarization in Interferometry – S. T. Myers

 

Summary – Observing & Calibration 

  • Follow normal calibration procedure (previous lecture)
  • Need bright calibrator for leakage D calibration
    • best calibrator has strong known polarization
    • unpolarized sources also useful
  • Parallactic angle coverage useful
    • necessary for unknown calibrator polarization
  • Need to determine unknown p-q phase
    • CP feeds need EVPA calibrator for R-L phase
    • if system stable, can transfer from other observations
  • Special Issues
    • observing CP difficult with CP feeds
    • wide-field polarization imaging (needed for EVLA & ALMA)

 


Polarization in Interferometry – S. T. Myers

 

Polarization data analysis 

  • Making polarization images
    • follow general rules for imaging & deconvolution
    • image & deconvolve in I, Q, U, V (e.g. CLEAN, MEM)
    • note: Q, U, V will be positive and negative
    • in absence of CP, V image can be used as check
    • joint deconvolution (e.g. aips++, wide-field)
  • Polarization vector plots
    • use ��electric vector position angle�� (EVPA) calibrator to set angle (e.g. R-L phase difference)
    • F = ½ tan-1 U/Q for E vectors ( B vectors �� E )
    • plot E vectors with length given by p
  • Faraday rotation: determine DF vs. l2

Polarization in Interferometry – S. T. Myers

 

Polarization Astrophysics


Polarization in Interferometry – S. T. Myers

 

Astrophysical mechanisms for polarization 

  • Magnetic fields
    • synchrotron radiation  LP (small amount of CP)
    • Zeeman effect  CP
    • Faraday rotation (of background polarization)
    • dust grains in magnetic field
    • maser emission
  • Electron scattering
    • incident radiation with quadrupole
    • e.g. Cosmic Microwave Background
  • and more��

Polarization in Interferometry – S. T. Myers

 

Astrophysical sources with polarization 

  • Magnetic objects
    • active galactic nuclei (AGN) (accretion disks, MHD jets, lobes)
    • protostars (disks, jets, masers)
    • clusters of galaxies IGM
    • galaxy ISM
    • compact objects (pulsars, magnetars)
    • planetary magnetospheres
    • the Sun and other (active) stars
    • the early Universe (primordial magnetic fields???)
  • Other objects
    • Cosmic Microwave Background (thermal)
  • Polarization levels
    • usually low (<1% to 5-10% typically)

Polarization in Interferometry – S. T. Myers

 

Example: 3C31 

  • VLA @ 8.4 GHz
  • E-vectors
  • Laing (1996)
 

3 kpc


Polarization in Interferometry – S. T. Myers

 

Example: Cygnus A 

  • VLA @ 8.5 GHz   B-vectors    Perley & Carilli (1996)
 

10 kpc


Polarization in Interferometry – S. T. Myers

 

Example: Blazar Jets 

  • VLBA @ 5 GHz             Attridge et al. (1999)
 

1055+018


Polarization in Interferometry – S. T. Myers

 

Example: the ISM of M51 

Neininger (1992)


Polarization in Interferometry – S. T. Myers

 

Example: Zeeman effect


Polarization in Interferometry – S. T. Myers

 

Example: Zeeman in M17 


Zeeman Blos: colors (Brogan & Troland 2001)  Polarization Bperp: lines (Dotson 1996

Color: optical from the Digitized Sky Survey                  Thick contours: radio continuum from Brogan & Troland (2001)                                       Thin contours: 13CO from Wilson et al. (1999) 


Polarization in Interferometry – S. T. Myers

 

Example: Faraday Rotation 

  • VLBA
  • Taylor et al. 1998
  • intrinsic vs. galactic
 

  15   12       8 GHz


Polarization in Interferometry – S. T. Myers

 

Example: more Faraday rotation 

    • See review of ��Cluster Magnetic Fields�� by Carilli & Taylor 2002 (ARAA)

Polarization in Interferometry – S. T. Myers

 

Example: Galactic Faraday Rotation 

  • Mapping galactic magnetic fields with FR
 

Han, Manchester, & Qiao (1999)

Han et al. (2002) 

Filled: positive RM   Open: negative RM


Polarization in Interferometry – S. T. Myers

 

Example: Stellar SiO Masers 

  • R Aqr
  • VLBA @ 43 GHz
  • Boboltz et al. 1998

Polarization in Interferometry – S. T. Myers

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