Scattering Polarization in the Solar Atmosphere

1
Scattering Polarizationin the Solar Atmosphere

• R. Casini
• High Altitude Observatory
• National Center for Atmospheric Research

2
Polarized Radiation

• Origin symmetry-breaking processes of the
  Atom-Photon interaction
• (e.g., anisotropic illumination, deterministic
  magnetic and/or electric fields, anisotropic
  collisions)

3
Polarized Radiation

• Description 4 independent parameters
• i) coherency matrix (a.k.a. polarization tensor )
• ii) Stokes parameters

Jones calculus
Mueller calculus
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Polarized Radiation

• Operational definition of Stokes parameters

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Polarized Radiation

• Polarized radiation tensors

6
Polarized Radiation

Example Unpolarized radiation from the quiet-sun
photosphere
Only two non-vanishing components
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Atomic Polarization

• Gas of atoms subject to
• Anisotropic and/or polarized illumination
• External fields
• Collisions

• Atomic system not in a pure state
• Population imbalances and quantum interferences
• between atomic levels

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Atomic Polarization

• Density operator
• Density matrix

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Atomic Polarization

• Irreducible spherical components of the density
  matrix
• If (e.g., Zeeman effect)
• Otherwise (e.g.,
  Paschen-Back effect, Stark effect)

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Atomic Polarization

• Example Multi-level atom
• Population
• Orientation
• Alignment

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Atomic Polarization

• Ex. 1 Positive orientation in a level
• Ex. 2 Positive alignment in a level
• Ex. 3 Orientation and alignment in a level

• Presence of net polarization in the re-emitted
  radiation
• (even in the absence of external fields)

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Time evolution of the system

• Liouvilles equation
• Evolution equation for expectation values

Atom
Radiation
?
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Resonance Scattering

• Atom-Photon interaction to 2nd order of
  perturbation

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Resonance Scattering

• Restriction Non-coherent scattering
• Scattering as the succession of
• 1st-order absorption and re-emission
• Complete Re-Distribution in frequency
• The atom loses memory of the incident photons,
• and the re-emitted photons are statistically
• re-distributed in frequency

Flat-Spectrum Approximation
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Resonance Scattering

• Restriction Non-coherent scattering
• Scattering as the succession of
• 1st-order absorption and re-emission
• Two-step solution
• Determine the excitation state of the atomic
  system consistently with the ambient radiation
  field (Statistical Equilibrium Problem)
• Calculate the scattered radiation consistently
  with the excitation state of the atomic system
  (Radiative Transfer Problem)

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Statistical Equilibrium

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Radiative Transfer

in stationary regime
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Resonance Scattering
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Resonance Scattering

• Difficulties
• The Statistical Equilibrium problem grows rapidly
  with the complexity of the atomic system (very
  large sparse matrices)
• Possible strategy weak-anisotropy approximation
• The Radiative Transfer problem requires the
  solution of a
• set of 4 coupled ODEs
• Possible strategy Diagonal Elements Lambda
  Operator (DELO)
• No guarantee of convergence of the
  self-consistency loop
• (maybe with the exception of the simplest atomic
  models,
• with appropriate initialization)
• Possible strategy ?????

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Atom 0-1
Classical analogy in the 3D harmonic oscillator
with forcing term
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Atom 0-1
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Atom 1-0
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Atom 1-0
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Atom 1-1
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Atom 1-1
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Atomic polarization and Radiative transfer
Homogeneous slab
0-1 or 1-0 w/o atomic pol. (Zeeman effect)
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Atomic polarization and Radiative transfer
0 1 2
Homogeneous slab
He I
10830 Å
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Atomic polarization and Radiative transfer
0 1 2
He I
Homogeneous slab
10830 Å
Trujillo Bueno et al., Nature 415, 403 (2002)
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Atomic polarization in Na I
F
?
3 2 1 0
?
2 1
D1
D2
2 1
? ? ?
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Atomic polarization in Na I
D2
F
?
3 2 1 0
?
2 1
5896 Å
D1
D2
D1
2 1
? ? ?
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Atomic polarization in Na I
F
?
3 2 1 0
?
2 1
2 1
? ? ?
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Alignment-to-Orientation transfer
F
?
3 2 1 0
When quantum interferences between FS and/or HFS
levels are important
?
2 1
2 1
? ? ?
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Atomic orientation in H I
HAO Advanced Stokes Polarimeter March 2003
THEMIS heliographic telescope September 2003
Spectro-polarimetric observations of Ha in solar
prominences (off the limb)
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Atomic orientation in H I
Spectro-polarimetric simulations with FS and HFS
THEMIS heliographic telescope September 2003
Maximum net circular polarization 1 order of
magnitude too small for typical prominence
fields (less than 100 G)
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Atomic orientation in H I
Catalytic effect of small electric fields on H
I atomic orientation
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vertical magnetic field, forward scattering
Catalytic effect of small electric fields on H
I atomic orientation
Ha
Inclinations of random-azimuth, 1 V cm-1 fields
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Conclusions

• Spectro-polarimetric observations reveal the
  complexity of the atomic processes underlying
  resonance scattering (atomic coherences, FS and
• HFS effects, magnetic and electric fields,
  alignment-to-orientation transfer)
• The local problem can already become numerically
  very intensive
• Points to focus on
• Improve speed in the construction of the
  Statistical Equilibrium matrix
• Invent new strategies to accelerate convergence
  of the iterative scheme for atoms of arbitrary
  complexity and general illumination conditions