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Astron. Astrophys. 317, 942-948 (1997)

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5. Conclusions

The continuum intensities of small-scale flux tubes averaged over the magnetic elements and the surrounding area is [FORMULA] % of the quiet Sun intensity, almost independently of the magnetic flux contained in the area of the spatial resolution element. There exists, however, a small tendency for lower intensities at sites with strong V signal.

The large macro-velocities of 1.5-3 km s-1 in the magnetized plasma, often adopted to fit Stokes V profiles from models to the observations, are not yet seen with the present resolution. The large width of the observed V profiles thus remains an unresolved puzzle and an important issue for further high spatial resolution observations. We note also, that, at sufficiently high spatial resolutions, the I profiles become very wide. This can partly be ascribed to magnetic splitting, but an additional, yet unspecified broadening mechanism also appears necessary for the I profiles (cf. Kneer et al. 1996).

The large fluctuation of the separation of the V extrema indicates a wide variety of the structure and dynamics of magnetic elements. This finding requires an explanation in terms of highly dynamic flux tubes interacting with the surrounding medium at all atmospheric and subphotospheric levels. Rüedi et al. (1992) found very different magnetic field strengths of 50-165 mT (at z = 0) in solar plages from infrared observations of low spatial resolution. Although they were able to reproduce the observed V profiles with static flux tube models, a macro-velocity of 2 km s-1 was still needed to cope with the width of the profiles, which is again uncomfortably large for static atmospheres. Kneer & Stolpe (1996) have suggested a picture of substructure on scales smaller than those presently resolved, with stochastic behaviours of both the magnetized plasma and the ambient gas. Similar interpretations have been presented by Domke & Pavlov (1979). Recent developments by Sánchez Almeida et al. (1996) of modeling the transfer of the Stokes vector in micro-structured magnetic elements imbedded in an intense flow field appear successful and promise a new view of small-scale magnetic structures in the solar atmosphere. A further fruitful route of investigation is the numerical modeling of small-scale magnetic field dynamics as done e.g. by Steiner et al. (1996). There, the large spatial and temporal variation of the (thermo-) dynamic and magnetic field parameters can possibly explain the rather small velocities [FORMULA] in the magnetic plasma when observed with high spatial resolution on the one hand, and the needs for V and I profile broadening in addition to Zeeman broadening on the other. In the framework of such models, very large separations of the V extrema, as found in the present investigation and in Amer & Kneer (1993) are the result of large velocity gradients along the line of sight, as occurring e.g. in shocks. In any case, our results emphasize that small-scale magnetic elements are dynamic structures which interact dynamically with their ambient medium.

Although it is laborious to perform the observations and the data analysis, and combinations of only a small number of spectral lines, 2 - 6, can be observed simultaneously with high spatial resolution at this state of the art, such observations are important in giving constraints on models of structure and dynamics in and around flux tubes. It is thus worthwhile to continue the effort.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998