On the transfer of line radiation in random magnetic fields

An analysis is made of the influence of a magnetic field of constant magnitude but with random orientations, described by the spherical coordinates θ and φ, on the polarization transfer in spectral lines. The assumption that the statistical properties of the field are determined by the one- and two-point probability densities P₁(x, θ, φ) and P₂(x₁, θ₁, φ₁; x₂, θ₂, φ₂) where x is the coordinate along the ray, implies that the variations of θ and φ can be considered as being due to a Markovian process in x. The expectation values of the Stokes parameters 〈Iγ〉, γ = 1, …4, are calculated functions of x or the optical depth τ. The formalism includes the limiting cases of infinite and zero correlation length. Assuming an artificial triplet and simple conditions, the results suggest that isotropic magnetic fields of the type considered have no influence on the polarization characteristics during the transfer.