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Astron. Astrophys. 325, 1199-1212 (1997)

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1. Introduction

Waves in solar magnetic flux tubes (FTs) are of interest for a variety of reasons. For example, it is well established that they play an important role in channeling the energy from the convection zone to the chromosphere (e.g. Herbold et al., 1984, Choudhuri et al., 1993a, b) and may transport a significant fraction of the energy needed to heat the corona (e.g. Hollweg, 1991, Choudhuri et al., 1993b). A detailed knowledge of FT wave modes is therefore important for an understanding of heating mechanisms.

FT waves are predicted by theory to exist in different modes, with longitudinal (sausage) and transversal (kink and torsional) oscillations being the most important in thin flux tubes. In contrast to the well developed theory (e.g. Defouw, 1976; Roberts & Webb, 1978; Spruit, 1982; Thomas, 1985; Roberts, 1986, 1990; Ryutova, 1990; Ulmschneider et al., 1991; Ferriz Mas et al., 1989; Zhugzhda, 1996, see Roberts & Ulmschneider, 1996, for a review), FT waves are not always easy to observe. Excepted are sunspots, the largest flux tubes, which have been observed to harbour running penumbral waves (Zirin & Stein, 1972; Giovanelli, 1972), magneto-atmospheric modes (Lites, 1992) and probably Alfvénic surface modes (Ulrich, 1996). The difficulty of spatially resolving small FTs forming plages and the network (the FT radii of about [FORMULA] km lie below the spatial resolution limit of most observations) has hindered the direct detection of their wave modes. Nevertheless, various observers have reported oscillatory motions in small FTs, mainly longitudinal tube modes at a period of 5 minutes (e.g. Giovanelli et al., 1978; Deubner, 1991; Fleck & Deubner, 1991; cf. Roberts, 1983), although recently evidence for shorter period waves was also found (Volkmer et al., 1995). Note that polarization measurements may yield information on magnetic structures smaller than the spatial resolution limit.

There are only few studies that attempt to bridge the gap between theory and observations, i.e. which use theory to predict the detailed signature of various wave modes. Such predictions are required to find new techniques for observing the waves and improving estimates of the energy flux transported be them. Simulations of line profiles disturbed by longitudinal waves have been presented by Rammacher & Ulmschneider (1989) and Rammacher (1991) for Mg ii k and Ca ii K and by Solanki & Roberts (1992) for Stokes I and V profiles of photospheric lines. For other FT wave modes only Steiner et al. (1995, 1996) have presented and discussed line profiles formed in the presence of kinked flux slabs. Their 2-D MHD simulations incorporate considerable physical realism. In the present paper we consider the polarimetric signature of kink waves in thin FTs on the basis of a simpler and less realistic model than Steiner et al. (1995, 1996). On the other hand, our approach allows us to study a whole grid of wave and line parameters. This paper may thus be considered to be an extension of the work of Solanki & Roberts (1992) on the longitudinal tube mode to the kink mode, as well as complementary to the approach taken by Steiner et al. (1995, 1996).

In the context of chromospheric and coronal heating kink waves are of greater interest than longitudinal tube waves: The kink mode has a much lower cut-off frequency, so that propagating kink waves are more likely to be excited by granular buffeting than longitudinal tube waves (Spruit, 1981). The importance of rapid foot points motion of FTs as efficient excitors of kink modes above their cut-off frequency has been pointed out by Choudhuri et al. (1993a). The tilts and shifts produced in isolated FTs by such buffeting are demonstrated dramatically by the 2-D simulations of Steiner et al. (1994). Another interesting aspect of kink waves is that they do not suffer from radiative damping, nor do they shock in the chromospheric layers. They may thus be interesting for coronal heating (Spruit, 1981; Hollweg, 1991). Kink modes may, nevertheless, also be important for chromospheric heating through their non-linear coupling with longitudinal modes (Ulmschneider et al., 1991). These shock and dissipate very efficiently in the chromospheric layers.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998