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 Zeeman effect Circular polarization Linear polarization • 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

4. Polarized Radiation For al/4retarder  • Operational definition of Stokes parameters

5. Polarized Radiation Irreducible spherical tensors transformation conjugation • Polarized radiation tensors

6. Polarized Radiation Example:Unpolarized radiation from the quiet-sun photosphere Only two non-vanishing components:

7. 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

8. Atomic Polarization Atomic eigenstates or some other complete basis • Density operator • Density matrix

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

10. Atomic Polarization Example: Multi-level atom • Population: • Orientation: • Alignment:

11. Atomic Polarization Ex. 1: Positive orientationin a level Ex. 2: Positive alignmentin a level Ex. 3: Orientation and alignmentin a level • Presence of netpolarization in the re-emitted radiation (even in the absence of external fields)

12. Time evolution of the system Perturbative expansion • Liouville’s equation • Evolution equation for expectation values Atom Radiation 

13. Resonance Scattering 1st order  2nd order  • Atom-Photon interaction to 2nd order of perturbation

14. 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

15. 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)

16. Statistical Equilibrium functions of the incident radiation

17. Radiative Transfer Absorbtion matrix Function of Stimulation matrix Function of Emission vector Function of in stationary regime

18. Resonance Scattering Self-consistency loop (L-iteration) non-LTE of the 2nd kind

19. 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: ?????

20. Atom 0-1 Classical analogy in the 3D harmonic oscillator with forcing term

21. Atom 0-1

22. Atom 1-0 • Hanle effect of the lower level • Non-linear dependence on

23. Atom 1-0

24. Atom 1-1

25. Atom 1-1

26. Atomic polarization and Radiative transfer 0-1 with atomic pol. 1-0 with atomic pol. Homogeneous slab 0-1 or 1-0 w/o atomic pol. (Zeeman effect)

27. Atomic polarization and Radiative transfer 0 1 2 Homogeneous slab He I 10830 Å

28. Atomic polarization and Radiative transfer 0 1 2 He I Homogeneous slab 10830 Å Trujillo Bueno et al., Nature 415, 403 (2002)

29. Atomic polarization in Na I F  3 2 1 0  2 1 D2 D1 2 1   

30. Atomic polarization in Na I D2 F  3 2 1 0  2 1 5896 Å D2 D1 D1 2 1   

31. Atomic polarization in Na I F  3 2 1 0  2 1 2 1   

32. Alignment-to-Orientation transfer diagonal depolarization K-K coupling alignment-to-orientation F  3 2 1 0 When quantum interferences between FS and/or HFS levels are important  2 1 2 1   

33. 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)

34. 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)

35. Atomic orientation in H I  Enhanced net circular polarization in Ha Catalytic effect of small electric fields on H I atomic orientation

36.  present also for isotropic electric fields IsotropicEfield Only B Prominence B fields w/o HFS with HFS vertical magnetic field, forward scattering Catalytic effect of small electric fields on H I atomic orientation Ha Inclinations of random-azimuth, 1 V cm-1fields

37. 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