## An operator perturbation method for polarized line transfer## III. Applications to the Hanle effect in 1D media
^{1} Laboratoire G.D. Cassini (CNRS, UMR 6529), Observatoire
de la Côte d'Azur, BP 4229, F-06304 Nice Cedex 4, France^{2} Indian Institute of Astrophysics, Bangalore 560034,
India
In this paper we present an Approximate Lambda Iteration method to treat the Hanle effect (resonance scattering in the presence of a weak magnetic field) for lines formed with complete frequency redistribution. The Hanle effect is maximum in the line core and goes to zero in the line wings. Referred to as PALI-H, this method is an extension to non-axisymmetric radiative transfer problems of the PALI method presented in Faurobert-Scholl et al. (1997), hereafter referred to as Paper I. It makes use of a Fourier decomposition of the radiation field with respect to the azimuthal angle which is somewhat more general than the decomposition introduced in Faurobert-Scholl (1991, hereafter referred to as FS91). The starting point of the method is a vector integral equation for a six-component source vector representing the non-axisymmetric polarized radiation field. As in Paper I, the Approximate Lambda operator is a block diagonal matrix. The convergence rate of the PALI-H method is independent of the polarization rate and hence of the strength and direction of the magnetic field. Also this method is more reliable than the perturbation method used in FS91. The PALI-H method can handle any type of depth-dependent magnetic field. Here it is used to examine the dependence of the six-component source vector on the co-latitude, azimuthal angle and strength of the magnetic field. The dependence of the surface polarization on the direction of the line-of-sight and on the magnetic field is illustrated with polarization diagrams showing versus at line center. The analysis of the results show that the full six-dimension problem can be approximated by a two-component modified resonance polarization problem, producing errors of at most 20 % on the surface polarization at line center.
## Contents- 1. Introduction
- 2. Basic equations
- 2.1. Polarized line radiative transfer equation
- 2.2. The azimuthal Fourier expansion method
- 2.3. Fourier coefficients of the Hanle phase matrix
- 2.4. Fourier expansion of the Stokes source vector
**S** - 2.5. Factorization of the Fourier source vector
- 2.5.1. The irreducible mean intensity J
- 2.5.2. The matrices and
- 2.5.3. Primary source term
- 2.5.4. The matrix
- 2.5.5. The matrix
- 3. The irreducible transfer equation
- 4. The numerical method of solution
- 5. Properties of the irreducible vectors and
- 6. The polarization diagrams
- 6.1. Dependence on the radiation field co-latitude
- 6.2. Dependence on the magnetic field co-latitude
- 6.3. Polarization diagram for a depth dependent azimuth
- 6.4. Dependence on the magnetic field strength parameter
- 6.5. The two-parameter polarization diagrams
- 6.6. A fast method of generating the polarization diagrams
- 7. Concluding remarks
- Acknowledgements
- References
© European Southern Observatory (ESO) 1998 Online publication: March 23, 1998 |