Generalized Rayleigh scattering. IV. Emergent radiation.

Details Generalized Rayleigh scattering. IV. Emergent radiation. Generalized Rayleigh scattering. IV. Emergent radiation.

Mar 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...307..332i&link_type=abstract

Astronomy and Astrophysics, v.307, p.332

Astronomy and Astrophysics

Astrophysics

4

Stars: Atmospheres, Radiative Transfer, Polarization, Scattering

Scientific paper

In standard problems of multiple Rayleigh and molecular scattering, the azimuth-independent component of the Stokes vector of the radiation emerging from homogeneous semi-infinite atmospheres can be expressed in terms of the 2x2 matrix I(μ). This matrix is a generalization of the scalar H-function to the matrix case proposed as an alternative to the commonly used H-matrix. Numerical data on I(μ) for μ{in}[0,{infinity}) are presented and discussed. They are found by iterative solution of the matrix equivalent of the alternative form of the non-linear H-equation. For conservative Rayleigh scattering, the matrix I(μ) is explicitly expressed in terms of Chandrasekhar's scalar H-functions H_l_(μ) and H_r_(μ). The numerical results show that for an atmosphere with uniformly distributed primary sources of partially polarized radiation, the matrix Eddington - Barbier relation holds: I(μ)=~S(τ=μ), where S(τ) is the matrix source function corresponding to this problem. In the preceding papers of the present series it was established that the matrix counterpart of the scalar conservative scatering is `biconservative' scattering. By this we mean scattering with λ_I_=λ_Q_=1, where λ_I_ is the usual albedo of single scattering and λ_Q_=0.7Wλ_I_; here W is the depolarization parameter. We show that, in case of biconservative scattering, the matrix version of the Eddington approximation can be formulated. For an atmosphere with uniformly distributed primary sources of unpolarized radiation, the dependence of the limb polarization on the parameters λ_I_ and λ_Q_ is investigated. The data on I-matrices are used also to discuss the center-to-limb variation of the degree of polarization δ(μ) of the radiation emerging from such an atmosphere. The notion of the λ-plane, i.e., the plane with the axes (λ_ I_,λ_I_), which was introduced in the first paper of the series, is used to elucidate the non-trivial dependence of the shape of the curve δ(μ) on λ_I_ and W.

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