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

VI. Application to the second solar spectrum of the Na I D1 and D2 lines: convergence

LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92190 Meudon, France
e-mail: V.Bommier@obspm.fr

Received: 11 May 2020
Accepted: 12 October 2020

Abstract

Context. This paper presents a numerical application of a self-consistent theory of partial redistribution in nonlocal thermodynamical equilibrium conditions, developed in previous papers of the series.

Aims. The code was described in IV of this series. However, in that previous paper, the numerical results were unrealistic. The present paper presents an approximation able to restore the reliability of the outgoing polarization profiles.

Methods. The convergence of the results is also proved. It is demonstrated that the step increment decreases like 1/N^α, with α >  1.

Results. Thanks to these additions, the results series behaves like a Riemann series, which is absolutely convergent. However, convergence is not fully reached in line wings within the allocated computing time. Development of efficient acceleration methods would be desirable for future work.

Conclusions. Agreement between the computed and observed linear polarization profiles remains qualitative only. The discrepancy is assigned to the plane parallel atmosphere model, which is insufficient to describe the chromosphere, where these lines are formed. As all the integrals are numerical in the code, it could probably be adapted to more realistic and higher dimensional model atmospheres. However, this is time consuming for lines with a hyperfine structure, as in the Na I D lines. The net linear polarization observed in Na I D₁ with the Zürich Imaging Polarimeter ZIMPOL mounted on the McMath-Pierce telescope at Kitt Peak is not confirmed by the present calculations and could be an artefact of instrumental polarization. The presence of instrumental polarization could be confirmed by the higher linear polarization degree observed by this instrument in the Na I D₂ line center with respect to the present calculation result where the magnetic field is not accounted for. At this precise point, the Hanle effect acts as a depolarizing effect in the second solar spectrum. The observed linear polarization excess is found to be of the same order of magnitude in both line centers, namely 0.1%, which is also comparable to the instrumental polarization compensation level of this experiment.