Stokes Profile Analysis and Vector Magnetic Fields. II. Formal Numerical Solutions of the Stokes Transfer Equations
Abstract
Two numerical methods for formal integration of the Stokes transfer equations for line formation in a strong magnetic field were tested by computing Stokes profiles for a Zeeman triplet in a MilneEddington model atmosphere, and for the anomalously split Ca II K line in a realistic solar model. The first method is a Feautrier (1964) type method, in which the equations are written in secondorder form and solved by finitedifferences. The second method is a new solution called DELO, in which an integral equation for the Stokes vector is formulated in terms of the lambda operator (LO) associated with the diagonal elements (DE) of the absorption matrix. It is shown that the DELO method is faster and more accurate than the Feautrier method, and that both methods are more efficient than the RungeKutta integration method.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1989
 DOI:
 10.1086/167364
 Bibcode:
 1989ApJ...339.1093R
 Keywords:

 Radiative Transfer;
 Solar Magnetic Field;
 Solar Spectra;
 Zeeman Effect;
 Calcium;
 Differential Equations;
 K Lines;
 Solar Atmosphere;
 Stokes Law Of Radiation;
 Thermodynamic Equilibrium;
 Solar Physics;
 LINE FORMATION;
 NUMERICAL METHODS;
 POLARIZATION;
 RADIATIVE TRANSFER;
 ZEEMAN EFFECT