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Astron. Astrophys. 329, 319-328 (1998)

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5. Conclusions

Our discovery that spatially varying signatures of Hanle depolarization are common throughout the second solar spectrum has shattered the view that the turbulent magnetic field that fills the space (99 % of the photospheric volume) between the kG flux tubes has unique and invariant properties. The turbulent field strength is not only a function of height in the solar atmosphere - it is a quantity that needs to be mapped and followed in time.

Magnetographs or other Zeeman-effect diagnostics are "blind" to the turbulent fields, since the signals from the many opposite-polarity elements cancel within each spatial resolution element, or within the line-forming region along each line of sight. This is a basic motivation for trying to develop the Hanle effect into a standard diagnostic tool that would allow us to explore magnetoturbulence on the Sun in a parameter domain that is inaccessible by other methods.

The application of Hanle diagnostics on the solar disk is only possible with very sensitive polarimeters, and suitable systems have not been available in the past. With our ZIMPOL imaging polarimeter we have now reached a sensitivity that makes this domain of physics accessible for exploration and use. Ambiguities in the interpretation can be avoided by doing the observations for combinations of spectral lines with different sensitivities to the Hanle effect. We have shown examples of spectra in which the differential Hanle effect is directly seen. By comparing the appearances of the polarized spectra in different solar regions one can generally conclude by mere visual inspection which solar region has the larger turbulent field strength.

While it is possible to draw such qualitative conclusions from visual inspection without model calculations, we have in the present paper gone a step further and made an attempt to quantify these conclusions, by trying to calibrate the different lines for Hanle diagnostics such that the turbulent field strengths can be determined in units of G. This undertaking has been done in the form of a multi-line, multi-region observational program and an iterative least-squares inversion technique to fit the many free parameters of the problem to the observational constraints. Great care has been taken to condition the problem such that a solution can be obtained that is independent of the initial values used for the iteration. Such a unique convergence could indeed be found for the turbulent field strengths of the 8 solar regions studied, resulting in values ranging from 4 to 40 G for the various regions. These values are consistent with the results of Faurobert-Scholl (1993) and Faurobert-Scholl et al. (1995) from Hanle radiative transfer analysis of the single Sr I 4607 Å line, as well as with the range of field-strength values recently found by Bianda et al. (1997) from observations of Hanle depolarization in the Ca I 4227 Å line.

Our inversion "exercise" has revealed a number of problem areas that urgently need to be dealt with for further progress in this field. One particularly difficult problem is the interaction between the polarizing line and continuum opacities and the question of how to extract from the observed polarization what is due to the line alone, since it is only the line portion that is subject to the Hanle effect. This problem is connected with our inadequate understanding of the continuum polarization, which appears to be substantially larger near the limb than predicted by theoretical models. It is also directly dependent on the accurate positioning of the zero point of the polarization scale, which currently cannot be directly determined from the observations due to Stokes [FORMULA] instrumental cross talk. This effect could be minimized with telescopes that are nearly free from or compensated for instrumental polarization.

For the observational material that we have used for the present inversions we have checked in the 2-D spectral images that there were no significant variations of the polarization along the slit, before the 2-D spectra were contracted to 1-D spectra by spatial averaging. In other ZIMPOL I observations we have examples of spatially varying Hanle depolarization along the spectrograph slit. One such example is illustrated in Fig. 3. It shows how the polarization peak in the Doppler core of the Na I D2 line exhibits large spatial variations, while the polarization amplitudes in the line wings are practically constant, as expected from the frequency-redistribution theory for the Hanle effect (cf. Stenflo 1994). This confirms our interpretation that what we are seeing is really the Hanle effect at work.

[FIGURE] Fig. 3. Example of spatially varying Hanle depolarization along the spectrograph slit for the Na I D2 line. The upper panel shows the intensity I, while the lower panel shows the fractional linear polarization [FORMULA]. The slit was parallel to and 5 arcsec inside the solar limb at the position angle corresponding to geographical north. The recording was done with ZIMPOL I on 20 February, 1996, at the McMath-Pierce facility of NSO/Kitt Peak. While the polarization amplitude in the line core shows large spatial variations, the polarization maxima in the wings remain relatively constant. This is a characteristic property of the Hanle effect.

The very strong Na I D2 line is formed substantially higher in the atmosphere than the lines that we have used here for the inversion, so it is likely to be more affected by larger-scale, more ordered magnetic fields in the canopy region of the atmosphere (when observing close to the limb). This also applies to the strong Ca I 4227 Å line in the observations of Bianda et al. (1997), as has been shown by theoretical modelling (Faurobert-Scholl 1992, 1994). The canopy fields are different in nature from the turbulent fields, which are more relevant to the lower parts of the atmosphere. Therefore one has to be careful about the choice of combinations of spectral lines for differential Hanle diagnostics, since the different lines may not sample the same magnetic fields. It could well be that the canopy fields affect to varying degrees also the lines that we have selected here. The height variation of the field needs to be explored in the future. This will require more detailed radiative-transfer modelling of the differential effects in combinations of lines.

The initial magnetic-field models that we have been using are of course by necessity very heuristic and idealized, but as our understanding advances they can be progressively improved upon to higher levels of sophistication, similar to the increased physical realism in the modelling of solar magnetic flux tubes by Zeeman-effect diagnostics. Thus the classification of the magnetic field as being "turbulent", canopy-like, or in the form of flux tubes is a helpful aid for the present state of the art in Stokes inversion. It allows certain diagnostic regimes to be identified, while the "real" field is more complex. The turbulent fields are expected to occur over a continuous distribution of spatial scales. The microturbulent field that we have addressed here with the Hanle effect may well represent the small-scale end of the spectrum, while the large-scale regime is partly resolved in the form of the intranetwork fields. These intranetwork fields share the properties of flux tubes (by being intermittent) and turbulent fields (by having mixed polarities on small scales), and their field strengths are intermediate between the kG flux tubes in the network and the microturbulent field that is diagnosed with the Hanle effect (Solanki et al. 1996). Eventually the Zeeman and Hanle diagnostics will be combined in the development of a unified view of solar magnetism.

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© European Southern Observatory (ESO) 1998

Online publication: November 24, 1997