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 & D2 lines: convergence. (arXiv:2007.08226v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Bommier_V/0/1/0/all/0/1">V. Bommier</a>
This paper presents a numerical application of a self-consistent theory of
partial redistribution in non-LTE conditions, developed in previous papers of
the series. The code was described in a previous paper of this series. However,
in that previous paper (number IV of the series), the numerical results were
unrealistic. The present paper presents an approximation, which was able to
restore the reliability of the outgoing polarization profiles. The convergence
of the results is also proved. It is demonstrated that the step increment
decreases like 1/N^a, with a > 1, so that the results series behaves like a
Riemann series, which is absolutely convergent. However, 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 dimensioned model atmospheres. However, it is time
consuming for lines having an hyperfine structure as the Na I D lines are. The
net linear polarization observed in Na I D1 with the 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 Na I D2 line center, with
respect to the present calculation result, where the magnetic field is not
accounted for, when the Hanle effect acts as a depolarizing effect in the
Second Solar Spectrum. The observed linear polarization excess is found of the
same order of magnitude 0.1% in both line centers, which is also comparable to
the instrumental polarization compensation level of this experiment.
This paper presents a numerical application of a self-consistent theory of
partial redistribution in non-LTE conditions, developed in previous papers of
the series. The code was described in a previous paper of this series. However,
in that previous paper (number IV of the series), the numerical results were
unrealistic. The present paper presents an approximation, which was able to
restore the reliability of the outgoing polarization profiles. The convergence
of the results is also proved. It is demonstrated that the step increment
decreases like 1/N^a, with a > 1, so that the results series behaves like a
Riemann series, which is absolutely convergent. However, 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 dimensioned model atmospheres. However, it is time
consuming for lines having an hyperfine structure as the Na I D lines are. The
net linear polarization observed in Na I D1 with the 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 Na I D2 line center, with
respect to the present calculation result, where the magnetic field is not
accounted for, when the Hanle effect acts as a depolarizing effect in the
Second Solar Spectrum. The observed linear polarization excess is found of the
same order of magnitude 0.1% in both line centers, which is also comparable to
the instrumental polarization compensation level of this experiment.
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