### Polarization in Astronomy 天文学中的偏振

```POLARIZATION
IN
ASTRONOMY

Cheng Zhao
2014/05/09
CONTENTS
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Introduction
Measurement
Mechanisms
Applications
References
INTRODUCTION
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Theory
Transverse electromagnetic waves.
Electric field  is the main component
interacting with matter, hence it is
used to describe polarization.
Polarization:
Asymmetry of the oscillation direction
INTRODUCTION

Classification
Basis: oscillation feature of
Facing the propagation direction of light, there are only two
polarization states (basis): linear polarization in x, y direction.
INTRODUCTION
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QM Description
=1
Photon
=0
Eigenvalue
of spin
gauge symmetry
Symbol
Helicity = ±ℏ
Helicity
Polarization state
m = -1
-ℏ
Left-handed
circular polarization
m = +1
+ℏ
Right-handed
circular polarization
Transformation with linear polarization basis
| = 1/ 2 (| +| )
| = −/ 2 (| − | )
INTRODUCTION
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Formalism
Stokes vector:  = (, , , )
Degree of polarization
I：intensity
Q, U：linear component
V：circular component
Natural light: P=0
Linear polarization: P=1
（For linear polarization V=0）
MEASUREMENT
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Polarizer – Sheet or Plate Polarizers
 Sheet polarizer
Aligned anisotropic crystals or polymers. Extinction ratio
(transmitted intensity for the polarizing direction over that for
the perpendicular direction) is typically about 100.
 Wire-grid polarizer
Conducting wires with spacing smaller than the
wavelength (From sub-millimeter to optical regime). Fairly
large extinction ratios, and applicable over large wavelength
ranges.
 Brewster window
A simple piece of glass. The only polarizer in far UV
regime. Extinction ratio mostly depends on the incidence
angle.
MEASUREMENT
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Polarizer – Polarizing Beam-Splitters
Keep all the incident light as output. The polarizer acts as a
beam-splitter.
 Cube beam-splitter with multilayer coating
Fairly large extinction ratios are obtained when there are
internal reflections at the Brewster angle.
 Birefringent crystals
The refractive index in the crystal is an anisotropic tensor.
Incident light that is not in the direction of the crystal axes will
be split into two beams with different linear polarization states
and speeds.
MEASUREMENT
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MEASUREMENT
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Retarder
Retard the phase of electric field. Manipulate polarization by
rotating the angle of linear polarization and thus converting
circular into linear polarization.
Quarter-wave and half-wave retarders
MEASUREMENT
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Retarder
MEASUREMENT
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Novel Components
Mostly owing to developments in the field of nanophotonics
and by the liquid crystal display and telecommunications
industries.
 Circular polarizer
Based on chiral nanostructures. [Gansel et al. 2009]
 Passive devices (theta cell)
Based on twisted nematic liquid crystals that locally
rotate the direction of linear polarization.
Many astronomical objects exhibit a centrosymmetric
linear polarization pattern around a central source. Such a
passive liquid crstal device aligns this pattern in one direction
so that only one Stokes parameter has to be measured. [Snik,
Frans, 2009]
MEASUREMENT
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Novel Components
 Polarization grating
Such a grating not only acts as a dispersion element, but
as a polarizing beam-splitter as well. This polarization grating
may replace the combination of a spectrograph and a
polarizer. [Packham et al. 2010]
 Polarization-maintaining (birefringment) fiber
Polarimetric versions of fiber-based integral field units.
[Lin and Versteegh 2006]
MEASUREMENT
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Detector
Similar as other astronomical instruments: low dark current,
high linearity, high dynamic range, small gain variations, etc.
Polarimetric noise levels should be smaller than photon
noise. Nonideal detector properties can create unwanted
polarization signals [Keller 1996]. Electron-multiplying CCD
(EMCCD) can reduce the influence of read-out noise.
Polarimetry often requires fast read-out rates, sometimes
>1 kHz. Single-pixel detectors like photomultiplying tubes
(PMT) and avalanche photodiodes (APD) can cope with this
speed. CCD and other 2D detectors are usually too slow.
MEASUREMENT
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Detector
 ZIMPOL (Zurich Imaging Polarimeter)
Shifting charges back and forth in synchrony with the
polarization modulation, without reading out. Developed for VLT
for the direct detection of extra solar-planets.
Advantage: images in two polarization sates are registered
practically simultaneously, no flat field problems. Atmosphric and
instrumental aberrations affecting both images are identical.
Disadvantage: The many charge transfers and asymmetries
of charge transfer limit the polarimetric performance.
MEASUREMENT
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Detector
 CMOS
Each pixel has a individual read-out capacitor [Keller, 2004].
However it may have high dark current.
MECHANISMS
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Scattering and Reflection – Theory
Fresnel equations describe the phase shift (electric
field) of the reflected light when light moves from a
medium into a second medium.
If the light is incident at the Brewster angle, the
reflection light is perfectly linearly polarized.
For complex particles having
a preferred handedness (like
biology molecules), the
reflection light can be circularly
polarized.
MECHANISMS
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Scattering and Reflection – Sources
 Solar system bodies
Microphysical properties of small particles like dust
grains and atmospheric aerosols can only be unambiguously
determined using spectropolarimetry [Hansen and Travis,
1974], such as the small sulphuric acid cloud droplets in
Venus’atmosphere.
 Stellar ejecta and
circumstellar material
Disks, jets, (AGN) halo,
exoplanets, etc.
MECHANISMS
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Multiple Scatering – Theory
When aligned dust grains (by magnetic field) are
illuminated anisotropically and scatter this light, they
can also produce circular polarization.
MECHANISMS
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Multiple Scattering – Sources
 Interstellar dust aligned with the galactic magnetic field
Smallest dimension of nonspherical dust grains are
always aligned with the direction of the local magnetic field
[Hough, 2007]. Perfect for mapping and understanding the
galactic magnetic field structure.
 Dense molecule clouds
Star formation area, disks around young stars (protostar
disk and protoplanetary disk).
MECHANISMS
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Cyclotron and Synchrotron Radiation – Theory
Non-relativistic electron gyrates around a strong magnetic
field: cyclotron radiation. Linear polarization in the direction
perpendicular to the magnetic field; circular polarization
along the direction of the magnetic field.
For relativistic electron, the radiation is
polarized. Circular polarization is also
generated when the magnetic field has
a net component along the line of sight.
In extreme environments, synchrotron
MECHANISMS
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Cyclotron and Synchrotron Radiation – Sources
 AGN jets
 Neutron star
Study the structure of magnetic fields.
Jet of M87
Crab nebula
MECHANISMS
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Zeeman Effect – Theory
Magnetic field modifies the energy of the magnetic
sublevels of an atom (-μ·B), and splits the spectral lines.
According to the selection law of transition, Δm=0,±1.
For Δm=±1, angular momentum of the emergent photon
is ±ℏ (projection along the direction of the magnetic
field), corresponding to left-hand and right-hand
polarization respectively (σ polarization).
For Δm=0, the photon has no angular momentum
component along the magnetic field direction, and is
linearly polarized (π polarization).
MECHANISMS
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Zeeman Effect – Theory
Polarization state depends on the orientation of the
magnetic field with respect to the line of sight.
The emergent light can be red/blue-shifted by the strong
magnetic field.
Polarization due to Zeeman effect
MECHANISMS
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Zeeman Effect – Sources
 Sunspot
The magnetic field is fairly weak in this case.
 Large-scale and strong magnetic fields
Particularly applies to unresolved stars.
Surface magnetic field
of SU Aur obtained
through Zeeman effect
MECHANISMS
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Hanle Effect – Theory
When there is magnetic field along the line of sight, the
scattering linear polarization will precess around it, and
is mostly depolarized.
It is highly complementary to Zeeman effect: the
sensitive magnetic field strength is much smaller,
typically mG – 100G. Furthermore, Hanle effect can be
applied for mixed-polarity magnetic field [Trujillo Bueno,
2006 & 2009].
MECHANISMS
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Hanle Effect
Polarization by different directions of magnetic field
MECHANISMS
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Hanle Effect – Sources
 Sun (corona)
A standard tool in solar physics.
 Stellar atmosphere and stellar wind
Brightness and magnetic field
of a sunspot group
APPLICATIONS
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Application of Polarization in Astronomy
Bastien, Manset, et al., 2011,
Astronomical Polarimetry 2008: Science from Small to Large
Telescopes
APPLICATIONS
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Solar Physics & Space Physics

“天气”。
APPLICATIONS
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Star Formation and Circumstellar Disks

APPLICATIONS
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Stellar Evolution and Magnetic Stars
2005年后，通过光谱偏振测量，在一些低温度、低质量、充

APPLICATIONS
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Extrasolar Planet Detection

APPLICATIONS
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Interstellar Medium

APPLICATIONS
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Galaxies and AGN

APPLICATIONS
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Cosmology

CMB的偏振证实了早期宇宙密度的不均匀性（各向同性的入

REFERENCES
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Snik, Keller, 2013, Astronomical Polarimetry: Polarized Views of Stars
and Planets, Springer Science+Business Media Dordrecht, p.175
Bastien, Manset, et al., 2011, Astronomical Polarimetry 2008: Science
from Small to Large Telescopes

Schmid, Gisler et al., 2005, ZIMPOL/CHEOPS: a Polarimetric Imager for
the Direct Detection of Extra-solar Planets
Trujillo Bueno, 2009, Diagnostic methods based on scattering
polarization and the joint action of the Hanle and Zeeman effects
Raouafi, 2011, Coronal Polarization
Hough, 2007, New opportunities for astronomical polarimetry, J.
Quantit. Spectr. Rad. Transfer, 106, 122–132
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