The Hanle Effect in 1D, 2D and 3D

  • Rafael Manso Sainz
  • Javier Trujillo Bueno
Part of the Astrophysics and Space Science Library book series (ASSL, volume 243)


This paper addresses the problem of scattering line polarization and the Hanle effect in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) media for the case of a two-level model atom without lower-level polarization and assuming complete frequency redistribution. The theoretical framework chosen for its formulation is the QED theory of Landi Degl’Innocenti (1983), which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. The self-consistent values of these density-matrix elements is to be determined by solving jointly the kinetic and radiative transfer equations for the Stokes parameters. We show how to achieve this by generalizing to Non-LTE polarization transfer the Jacobi-based ALI method of Olson et al. (1986) and the iterative schemes based on Gauss-Seidel iteration of Trujillo Bueno and Fabiani Bendicho (1995). These methods essentially maintain the simplicity of the A—iteration method, but their convergence rate is extremely high. Finally, some 1D and 2D model calculations are presented that illustrate the effect of horizontal atmospheric inhomogeneities on magnetic and non-magnetic resonance line polarization signals.

Key words

polarization magnetic fields radiative transfer scattering solar: atmosphere stars: atmospheres methods: numerical 


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  1. Auer, L. H., Fabiani Bendicho, P. and Trujillo Bueno, J. (1994), Astron. Astrophys., 292, 599ADSGoogle Scholar
  2. Bommier, V., Sahal-Bréchot (1978), Astron. Astrophys., 69, 57ADSGoogle Scholar
  3. Faurobert-Scholl, M., Frisch, H., Nagendra, K.N. (1997), Astron. Astrophys., 322, 896ADSGoogle Scholar
  4. Hanle, W. (1924), Z. Phys., 30, 93ADSCrossRefGoogle Scholar
  5. Landi Degl’Innocenti, E. (1983), Solar Phys., 85, 3CrossRefGoogle Scholar
  6. Landi Degl’Innocenti, E. (1984), Solar Phys., 91, 1Google Scholar
  7. Landi Degl’Innocenti, E. (1985), Solar Phys., 102, 1ADSCrossRefGoogle Scholar
  8. Landi Degl’Innocenti, E., Bommier, V., Sahal-Bréchot, S. (1990), Astron. Astrophys., 235, 459ADSGoogle Scholar
  9. Manso Sainz, R., Trujillo Bueno, J. (1999), Astrophys. J., submittedGoogle Scholar
  10. Messiah, A., (1969), Quantum Mechanics, Dunod, ParisGoogle Scholar
  11. Mihalas, D. (1978) Stellar Atmospheres. W.H. Freeman, San Francisco.Google Scholar
  12. Nagendra, K.N., Frisch, H., Faurobert-Scholl, M. (1998), Astron. Astrophys., 332, 610ADSGoogle Scholar
  13. Olson, G. L., Auer, L. H., & Buchler, J. R. (1986), J. Quant. Spectrosc. Radiat. Transfer, 35, 431ADSCrossRefGoogle Scholar
  14. Sánchez Almeida, J. (1999), These Proceedings in K.N. Nagendra, J.O. Stenflo (eds.), Solar Polarization, Proc. 2nd SPW, Kluwer, Dordrecht, (in this Volume)Google Scholar
  15. Stenflo, J.O. (1994) Solar Magnetic Fields. Polarized Radiation Diagnostics. Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
  16. Trujillo Bueno, J. (1999), in K.N. Nagendra, J.O. Stenflo (eds.), Solar Polarization, Proc. 2nd SPW, Kluwer, Dordrecht, (in this Volume)Google Scholar
  17. Trujillo Bueno, J., Fabiani Bendicho, P. (1995), Astrophys. J., 455, 646ADSCrossRefGoogle Scholar
  18. Trujillo Bueno, J., Manso Sainz, R. (1999), Astrophys. J., 516, in pressGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Rafael Manso Sainz
    • 1
  • Javier Trujillo Bueno
    • 1
  1. 1.Instituto de Astrofísica de CanariasLa Laguna, TenerifeSpain

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