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The paradox of solar polarization finally resolved by a French theory

29 août 2021

The paradox of the polarization of the sodium line from the Sun, which dated from 1997, has been resolved. The paradox arose from an observation by Stenflo & Keller in 1996, of persistent polarization, while theory predicted otherwise. Previous attempts to explain it required either an extreme reduction in the Sun’s magnetic field (which solar physicists thought unlikely) or changes in the physics of atom-photon interactions (which atomic physicists failed to observe). A recent article by Alsina-Ballester et al (2021) has just resolved the paradox, by new observations, and their interpretation with a more sophisticated atomic theory, taking into account complex interactions, previously neglected. Véronique Bommier’s theory of redistribution of polarized radiation in the presence of a magnetic field was created in 1997, for two-level atoms, and generalized to multi-level atoms in 2017.

The measurement of the magnetic field of the solar surface is made from the analysis of the light received from the sun, even by satellite. This magnetic field serves as a guide for charged and energetic particles, especially when they are ejected towards the Earth. Improving measurements is important for improving forecasting.

The light is absorbed then re-emitted by the atoms of the surface, and it is when the light is "in" the atoms that the magnetic field imprints its mark, its orientation, its strength too, by influencing and orienting the movement of electrons in the atom. This orientation is detected by analyzing the polarization of the light received. This phenomenon is scattering, and it is important, for the quantitative evaluation, to know if this scattering was "coherent in frequency" (between the absorbed photon and that re-emitted), or "incoherent in frequency" (without relation between them). These two types of scattering are possible and coexist.

Véronique Bommier was the first to develop a quantitative formalism of the contribution of these two types of scatterings and of their respective weight (what is called "redistribution"), in the presence of a magnetic field, based on the theory of the atom-radiation interaction in the formalism of the atomic density matrix taught by Prof. Claude Cohen-Tannoudji (CNRS Gold Medal 1996, Nobel Prize 1997). Véronique Bommier included coherent scattering, very important in Astrophysics, by pushing back then eliminating the Markov approximation (also called "short memory approximation" by C. Cohen-Tannoudji) in the theoretical description of the phenomenon of photon scattering by atoms.

She made a first publication of this work in 1997, which was widely used (118 citations), but concerns relatively simple atoms. It was not until 2016 that she completed the generalization to more complex atoms, such as sodium here concerned (because of its hyperfine structure). In 2017, she published a version adapted to the radiative transfer codes used by certain authors, who have now effectively integrated it into their code, and were then able to obtain an excellent agreement (cf Figure) between their observation and their theoretical model, taking into account the effect of the magnetic field.

This is the linear polarization of the D1 line of sodium (5896 Å) observed on the solar disk but near the limb. This linear polarization is formed by scattering, and the magnetic field can modify it. However, there had been an international debate since 1997 about the polarization of this line, because Jan Olof Stenflo and Christoph Keller had observed a clear "net" linear polarization (that is to say non-zero when one integrates over the entire profile of the line), while Quantum Mechanics (and the theory of V. Bommier) does not predict that. In an article in Nature in 1998, Egidio Landi Degl’Innocenti attributed this "net" polarization to the existence of an "atomic polarization", but this was incompatible with the solar magnetic fields as we know them, hence the term "paradox" attributed to this observation and this problem.

Ernest Alsina Ballester, Luca Belluzzi and Javier Trujillo Bueno have on the one hand redone the observation, and on the other hand calculated the theoretical curve using the theory of V. Bommier (2017). The excellent theory-observation agreement they obtain (cf Figure) proves, in itself, that this profile, which shows no "net" polarization, is the right one, which closes the paradox. This "net" polarization observed by Stenflo & Keller at Kitt Peak, and only there, has been attributed by V. Bommier (2020) to an instrumental effect of this telescope.

Figure : En noir : taux de polarisation linéaire observé près du bord du disque solaire dans la raie D1 du sodium. En bleu : taux de polarisation linéaire calculé par un modèle de transfert de rayonnement intégrant la théorie de Bommier (2017). La présence d’un champ magnétique de 15 G est intégrée. L’excellent accord théorie-observation prouve, en soi, que ce profil est le bon. Republié de E. Alsina Ballester, L. Belluzzi & J. Trujillo Bueno, 2021, Phys. Rev. Letters, 127, 081101.

References

V. Bommier « Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. V. The two-term atom »,
Astron. Astrophys., 2017, 607, A50

E. Alsina Ballester, L. Belluzzi, J. Trujillo Bueno, "Solving the Paradox of the Solar Sodium D1 Line Polarization", PhysRevLett., 2021, 127.081101

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