Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...307..319i&link_type=abstract
Astronomy and Astrophysics, v.307, p.319
Astronomy and Astrophysics
Astrophysics
6
Stars: Atmospheres, Radiative Transfer, Polarization, Scattering
Scientific paper
The paper continues investigation of azimuth-averaged radiation fields in semi-infinite atmospheres with uniformly embedded sources of partially polarized radiation. It is assumed that the single scattering phase matrix is a superposition of the phase matrices of Rayleigh and isotropic scattering appearing with weights W and 1-W, respectively. Single scatttering is described by two parameters, the albedo λ_I_ and the depolarization parameter W. An analytical investigation is given of the properties of the Stokes matrix of the emergent radiation I(μ) which is essentially the Laplace transform of the source matrix S(τ). We show that I(μ) may be considered as a matrix generalization of the usual scalar H-function. The commonly used H-matrix is closely related, but not identical to I(μ). We argue that I(μ) has some advantages as compared with H(μ). Using linear and non-linear equations satisfied by I(μ), we find its asymptotic behavior for μ-{infinity}. This enabled us to get explicit expressions for S(τ) deep in the atmosphere. We show that the exact matrix equivalent of scalar conservative scattering is not the usual conservative Rayleigh scattering, but the biconservative scattering, i.e., scattering with λ_I_=1,λ_Q_=0.7Wλ_I_=1. Although it corresponds to W=10/7>1 and hence is `unphysical', biconservative scattering is, mathematically, an important limiting case with remarkable properties. The asymptotic theory of nearly biconservative scattering is developed. The matrices I(μ) and S(τ) which depend on two small parameters, 1-λ_I_ and 1-λ_Q_, are asymptotically expressed in terms of the corresponding parameter-free biconservative matrices. The final formulae are similar to well-known scalar expressions. The paradoxical conclusion is reached that the reason of qualitative differences in the overall structure of fields of polarized and unpolarized radiation in strongly scattering atmospheres is the weakness of cross-talk of the Stokes parameters I and Q.
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