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

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1. Introduction

The linearly polarized solar spectrum that is produced by coherent scattering has a structural richness that is comparable to that of the intensity spectrum, but its appearance is entirely different, and the spectral structures are due to different physical processes (Stenflo & Keller 1996, 1997; Stenflo 1997). This spectrum, which has been referred to as the "second solar spectrum", provides us with a new window for diagnostics of the Sun. In the present paper we will explore the potential use of the second solar spectrum as a tool to diagnose magnetoturbulence on the Sun.

The physical process that provides novel and unique diagnostic possibilities is the Hanle effect, which can only be accessed through the second solar spectrum, since it is fundamentally a coherence phenomenon that can only occur when there is coherent scattering. Due to its richness in spectral features the second solar spectrum allows multiple-line diagnostics with combinations of many different spectral lines that have different sensitivities to the Hanle effect. This type of approach has proven extremely useful in the past for Zeeman-effect diagnostics to derive information on the "hidden" magnetic fine structure that exists on small scales beyond the spatial resolution limit (Stenflo 1973, 1994; Solanki 1993). With a differential approach much of the previous model dependence in the observations can be avoided, and one may develop semi-empirical models of the magnetic structures that are far more sophisticated and realistic than would otherwise be possible.

Diagnostic techniques based on the ordinary Zeeman effect however have a fundamental limitation: As the sign of the signal depends on the orientation of the magnetic field, the contributions from opposite polarities within the spatial resolution element cancel each other, such that to first order only the uncancelled portion gives a net signal that is available to Zeeman-effect diagnostics. There are two exceptions to this statement: (i) If the directional distribution of the field vectors is not isotropic, then there is not complete cancellation of the linear polarization due to the transverse Zeeman effect, and this can be used to constrain the distribution (Stenflo 1987). (ii) If the field-strength distributions for the two magnetic polarities are not identical, then the circular polarization of the longitudinal Zeeman effect can provide information on the subresolution fields if the Zeeman splitting is large enough, even when the opposite-polarity fluxes are perfectly balanced (Rüedi et al. 1992; Solanki 1993).

This limitation does not apply to the Hanle effect, which for mixed-polarity fields reduces the amount of scattering polarization from its maximum value in the absence of magnetic fields. The depolarization works with one sign, i.e., in one direction, regardless of the field polarity. This unique property was first used to constrain the strength of a volume-filling, turbulent photospheric magnetic field to be somewhere in the range 10-100 G (Stenflo 1982). With detailed numerical modelling of the polarized radiative transfer in the Sr I 4607 Å line Faurobert-Scholl (1993) and Faurobert-Scholl et al. (1995) could develop this approach into a more definite quantitative diagnostic tool and found that the turbulent field must be 10-30 G to fit the Sr I observations of Stenflo et al. (1980). Other areas where the Hanle effect has established its usefulness are diagnostics of solar prominences (Leroy et al. 1977; Sahal-Bréchot et al. 1977; Bommier 1980; Landi Degl'Innocenti 1982; Querfeld et al. 1985) and chromospheric magnetic canopies (Faurobert-Scholl 1992, 1994).

Interpretations that are based on observations of a single spectral line are however sensitive to the model used for the solar atmosphere and the atomic physics. As in Zeeman-effect diagnostics one can suppress such model dependence by using the differential rather than the absolute polarization effects, which are seen in combinations of lines with different sensitivities to the Hanle effect.

Our previous concept of solar magnetism (outside active regions) has been basically that of a 2-component atmosphere. Zeeman-effect diagnostics have shown that the major part of the net solar magnetic flux that is seen with a spatial resolution corresponding to a smearing window of one arcsec or larger originates in concentrated, intermittent kG "flux tubes", which occupy a tiny fraction of the photospheric volume, less than one percent in quiet solar regions. The remaining 99 % that appear more or less non-magnetic to Zeeman-effect diagnostics must (unless it is truly field free, which is hardly possible in the real physical world) contain some sort of tangled or turbulent magnetic field, since Zeeman-effect observations are almost "blind" to such a field if the magnetic polarities are mixed on a subresolution scale. If the mixing is only partial, or if the polarities are spatially partly resolved, e.g. in the case of the intranetwork fields, then Zeeman-effect diagnostics will of course still be useful.

The Hanle effect on the other hand is practically blind to the flux tube field, since this field has such a small filling factor, and the Hanle effect is insensitive to vertical magnetic fields when the illumination of the scattering particles is axially symmetric. Almost the entire contribution to the Hanle effect comes from the 99 % of the volume to which the ordinary Zeeman effect is almost blind. The Hanle and Zeeman effects therefore ideally complement each other.

Since the flux tube field strength has been found to have an almost unique value of about 1.5 kG in quiet network regions at the level in the solar atmosphere where the continuum around 5000 Å from the surrounding atmosphere is formed, it has been natural to believe that the turbulent, space-filling magnetic field should also have a unique field distribution with an rms field strength that is uniquely determined by the kinetic energy spectrum of the solar granulation. Accordingly it has been expected that the turbulent rms field strength should be nearly invariant with respect to time and location and therefore be a unique quantity that needs to be determined once and for all.

This view of solar magnetism was shaken when we in February 1996 started to record the same portions of the second solar spectrum in different regions on the Sun (at the same limb distance but at different position angles). We found to our surprise that the appearance of the spectral variations of the scattering polarization could change drastically from one spatial location to the next. While being able to rule out instrumental effects (including instrumental polarization), we know of no other solar causes than spatial variations of the magnetic-field effects across the solar disk. The discovery of these spatial variations appears to imply that the properties of the turbulent or tangled magnetic field are not invariant but that the turbulent field strength is a quantity that needs to be mapped.

In the present paper we present examples of these spatial variations and make an attempt to use the observed differential effects for combinations of lines in the second solar spectrum to explore the new diagnostic possibilities and to uncover problem areas. Our so far heuristic approach leads to quantitative estimates of the turbulent field strengths based on the differential Hanle effect without having to enter into radiative transfer calculations. We find that the turbulent field strength can easily vary by an order of magnitude. However, we cannot rule out that varying canopy-like fields also affect the interpretations.

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© European Southern Observatory (ESO) 1998

Online publication: November 24, 1997