Resonance line polarization for arbitrary magnetic fields in optically thick media. 3: A generalization of the square root of epsilon law

E. Landi Degl'Innocenti , V. Bommier (1)

1 LESIA (UMR_8109) - Laboratoire d'études spatiales et d'instrumentation en astrophysique

The well-known 'square root of epsilon-law' -- one of the few exact analytical results in the theory of radiative transfer -- is generalized to the case of an isothermal, plane-parallel atmopshere in the presence of a magnetic field vector of arbitrary intensity and direction and in the presence of depolarizing collisions. A compact expression is found, relating the squares of the surface value of the upper level components of the atomic density matrix in the representation of the irreducible spherical tensors to the value of the constant Planck function. By taking the appropriate limits, the usual square root of epsilon-law for unpolarized radiation, and its generalization to resonance scattering polarization in a non-magnetic atmosphere (Ivanov 1990), are recovered as particular cases.

Mots clés: Isothermal Processes; Linear Polarization; Optical Thickness; Radiative Transfer; Resonance Scattering; Solar Atmosphere; Solar Magnetic Field; Sun; Analytic Functions; Integral Equations; Kernel Functions; Numerical Analysis

Domaines: Physique [physics]; Astrophysique [astro-ph]; Astrophysique stellaire et solaire [astro-ph.SR]

E. Landi Degl'Innocenti, V. Bommier. Resonance line polarization for arbitrary magnetic fields in optically thick media. 3: A generalization of the square root of epsilon law. Astronomy and Astrophysics - A&A, 1994, 284, pp.865-873. ⟨hal-02393382⟩