Research output: Contribution to journal › Article › peer-review
Polarized line formation by resonance scattering : I. Basic formalism. / Ivanov, V. V.; Grachev, S. I.; Loskutov, V. M.
In: Astronomy and Astrophysics, Vol. 318, No. 1, 01.02.1997, p. 315-326.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Polarized line formation by resonance scattering
T2 - I. Basic formalism
AU - Ivanov, V. V.
AU - Grachev, S. I.
AU - Loskutov, V. M.
N1 - Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 1997/2/1
Y1 - 1997/2/1
N2 - The model two-level problem of non-LTE line formation in homogeneous plane atmospheres is reconsidered with the complete account of polarization arising in resonance scattering. We use the approximation of complete frequency redistribution (CFR) and restrict our discussion to the most important case of axially symmetric radiation fields in semi-infinite atmospheres. The primary sources are assumed to be partially polarized. The problem is reduced to the 2 × 2 matrix Wiener-Hopf integral equation for the matrix source function S(τ). The matrix kernel K1(τ) of the Λ-operator appearing in this equation is represented as a continuous superposition of exponentials. As we show in Paper II of the series, this enables one to develop a matrix version of the analytical theory which, on the one hand, is a generalization of the scalar CFR theory and, on the other, is the CFR version of the theory of multiple monochromatic Rayleigh scattering. As a preparatory step for this, we discuss in detail the properties of the kernel matrix K1(τ) and the dispersion matrix T(z). The latter is essentially the two-sided Laplace transform of K1(τ). We consider the asymptotic behavior of K1(τ) and T(z) for large τ and z, respectively. For the particular case of the Doppler profile the complete asymptotic expansions of these matrices are presented. These results are at the base of the theory presented in Paper II of the series.
AB - The model two-level problem of non-LTE line formation in homogeneous plane atmospheres is reconsidered with the complete account of polarization arising in resonance scattering. We use the approximation of complete frequency redistribution (CFR) and restrict our discussion to the most important case of axially symmetric radiation fields in semi-infinite atmospheres. The primary sources are assumed to be partially polarized. The problem is reduced to the 2 × 2 matrix Wiener-Hopf integral equation for the matrix source function S(τ). The matrix kernel K1(τ) of the Λ-operator appearing in this equation is represented as a continuous superposition of exponentials. As we show in Paper II of the series, this enables one to develop a matrix version of the analytical theory which, on the one hand, is a generalization of the scalar CFR theory and, on the other, is the CFR version of the theory of multiple monochromatic Rayleigh scattering. As a preparatory step for this, we discuss in detail the properties of the kernel matrix K1(τ) and the dispersion matrix T(z). The latter is essentially the two-sided Laplace transform of K1(τ). We consider the asymptotic behavior of K1(τ) and T(z) for large τ and z, respectively. For the particular case of the Doppler profile the complete asymptotic expansions of these matrices are presented. These results are at the base of the theory presented in Paper II of the series.
KW - Line: formation
KW - Polarization
KW - Radiative transfer
KW - Scattering
KW - Stars: atmosphere
KW - Sun: atmosphere
UR - http://www.scopus.com/inward/record.url?scp=0007171133&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0007171133
VL - 318
SP - 315
EP - 326
JO - ASTRONOMY & ASTROPHYSICS
JF - ASTRONOMY & ASTROPHYSICS
SN - 0004-6361
IS - 1
ER -
ID: 74196237