Line Formation Theory for the Multiterm Atom with Hyperfine Structure in a Magnetic Field

Abstract

Within the framework of the quantum theory of polarized line formation, in the limit of complete frequency redistribution and of the collisionless regime, we derive explicit formulae describing the statistical equilibrium and the radiative emission of a multiterm atom with hyperfine structure, in the presence of an external magnetic field. The formulae we obtained for the radiative rates of the statistical equilibrium equations and for the radiative coefficients of the transfer equation for polarized radiation can be applied to investigate the formation of spectral lines for which both fine-structure and hyperfine-structure effects are important (e.g., the D1 and D2 lines of Na i in the solar atmosphere).

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit

“…The polarization profile of D1 is found globally antisymmetric. No net linear polarization is obtained in D1, as obtained by Casini & Manso Sainz (2005) and Landi degl'Innocenti (1998); this is in contrast to the observations by Stenflo (1996), Stenflo & Keller (1997), Stenflo et al (2000) and in agreement with the observations of Bommier & Molodij (2002). Further investigation is envisaged concerning the effect of a line-of-sight atomic velocity gradient as a possible source of profile antisymmetry breaking.…”

“…A qualitative but good agreement is visible in line centers with the observations for D1 and D2, except that the net linear polarization peak in D1 is not retrieved. As obtained by Casini & Manso Sainz (2005) and Landi degl'Innocenti (1998), D1 is globally antisymmetrical without any net linear polarization. Interestingly, a sharp structure appears in the very center of D1 that is very analogous to what was observed by Bommier & Molodij (2002, Figs.…”

“…From the theoretical point of view, Casini & Manso Sainz (2005) took all the coherences and interferences into account, but this was for an optically thin model (single scattering) and no global net linear polarization resulted in D1. On the other hand, Landi degl'Innocenti (1998) successfully reproduced the observed spectrum from a metalevel-based theory, except for the net linear polarization peak in D1.…”

Radiative transfer withJ-state interference in a two-term atom

“…As the figure shows, PRD along with the effects of J-state interference can indeed generate Q/I signals near the centers of multiplet components with W 2 = 0, but these signatures have an anti-symmetric shape with a zero crossing at the exact line center. These antisymmetric polarization signals can also be produced at the 1/2 → 1/2 → 1/2 transition using CRD (see Trujillo Bueno et al 2002;Casini & Manso Sainz 2005, where also the role of hyperfine structure and lower term polarization are investigated).…”

Coherence structure of D1 scattering

“…Among the wealth of previously unknown polarization features, the symmetric polarization peak in the core of the well-known Na i D 1 line at 5896Å was immediately recognized as enigmatic (Stenflo & Keller 1996, because the D 1 transition was believed to be intrinsically unpolarizable. Numerous attempts have been made to explain the observed D 1 behavior (as documented in greater detail in Stenflo et al 2000a,b) in terms of optical pumping of the hyperfine structure levels of the ground state or as caused by the spectral structuring of the solar D 1 radiation, but they have all failed either because the predicted amplitude has been much too small, or because the predicted polarization profile has been anti-symmetric rather than having the observed symmetric shape (Landi Degl'Innocenti 1998;Trujillo Bueno et al 2002;Casini et al 2002;Kerkeni & Bommier 2002;Klement & Stenflo 2003;Casini & Manso Sainz 2005;Belluzzi & Trujillo Bueno 2013).…”