Astron. Astrophys. 355, 781-788 (2000)

4. Conclusions

Our analysis of the center-to-limb behavior of the scattering polarization in the Na I D₁ and D₂ lines shows that the enigmatic and narrow polarization peaks in the line cores are not a property that is restricted to the limb region, but it is a property that dominates the relative profile shape even more as we move away from the limb towards disk center. The relative core to wing amplitude ratio increases substantially with limb distance. However, the ratio between the polarization amplitudes in the D₁ and D₂ line cores remains approximately independent of limb distance, which is more likely to happen if these two peaks have the same physical origin.

Such a common origin is not obvious, since it is generally believed that for the Ca I 4227 and Sr II 4078 Å lines, the core polarization peaks with their surrounding minima and wing maxima are due to partial redistribution effects in the formation of these lines (Rees & Saliba 1982; Saliba 1985). Such redistribution effects are however incapable of generating the polarization seen at the core of the Na I D₁ line, but a more "exotic" mechanism like that of Landi Degl'Innocenti (1998) involving optical pumping in combination with hyperfine structure splitting seems to be required. Such a mechanism however cannot work for the Ca I 4227 Å line, since its ground state is not polarizable (its quantum number ), and it has no hyperfine structure splitting (since calcium has zero nuclear spin). The appearance of the Na I D₂ profile shape is rather similar to that of the Ca I 4227 Å line, but our results here support the view that the underlying physical mechanism is more closely related to the mechanism that is responsible for the D₁ core peak rather than to partial redistribution physics.

As we move away from the limb, the observations of the scattering polarization become increasingly vulnerable to and affected by disturbances from the longitudinal Zeeman effect, which infiltrates the linear polarization measurements because of instrumental cross talk. Due to the ubiquitous nature of solar magnetic fields, such Zeeman-effect signals appear everywhere on the disk, but in the case of the Na I D₁ and D₂ lines they are much less prominent close to the limb. Still, even far from the limb, it is possible to identify these spurious spectral signatures and exclude from the analysis those portions along the slit where they occur. It is particularly remarkable to find that the pronounced core polarization peaks in the D₁ and D₂ lines survive practically unscathed even when they are surrounded by magnetic flux elements everywhere, regardless of how far from the solar limb we are.

In his theory that seeks to explain the core peaks in the D₁ and D₂ lines Landi Degl'Innocenti (1998) concludes that the peaks can sufficiently survive magnetic depolarization effects and have as large relative amplitudes as the observed ones only if the magnetic field strengths do not exceed 0.01 G, or if the field orientation is very nearly vertical. The observations show high and apparently undisturbed core polarization peaks in environments on the solar disk, where all over the adjacent surroundings we have signals from the longitudinal Zeeman effect that are signatures of strong magnetic fields (with field strengths on the order of 1 kG, as we know from other Zeeman-effect diagnostics of photospheric flux elements, cf. Stenflo 1994). It seems highly unlikely from the point of view of plasma physics that adjacent to these kG flux tubes, side by side, we would have magnetic fields that are weaker by more than 5 orders of magnitude, or that the field lines that fill the volume between the kG flux tubes can avoid being tilted by the dynamic forces of the turbulent motions. Although the theory of magnetoturbulence is not developed well enough to have much predictive power concerning the degree of intermittency, we feel that it is physically not credible that the turbulent amplification of the magnetic field could be so supressed that the field would not exceed 0.01 G, which is several orders of magnitude below the value that the field would have in the case of equipartition between the kinetic and magnetic energies, or that field line tilts could be prevented. An untilted or a superweak magnetic field with a large filling factor also appears to be ruled out by observations of Hanle depolarization in different spectral lines (Bianda et al. 1998a,b, 1999).

For these reasons we must conclude that we still do not have any acceptable theoretical explanation for the core polarization peaks in the Na I D₁ and D₂ lines. With our present work we have explored the center-to-limb variation of these polarized profiles in considerable quantitative detail. The established empirical relations may guide future theoretical efforts and provide detailed quantitative constraints on modelling attempts.

© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000
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