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Astron. Astrophys. 345, 986-998 (1999)

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1. Introduction

The details of the chromospheric and coronal heating processes have been the subject of long and intense study. Among others, a variety of processes have been proposed in which MHD waves in small magnetic flux tubes channel the energy flux from below into the chromosphere and still higher layers (see the reviews by Narain & Ulmschneider 1990, 1996). One aspect of the investigation into these processes deals with the generation of flux-tube waves by turbulent motions in the outer convection zone. For example, Ulmschneider & Musielak (1998) investigated the generation of longitudinal tube waves, Huang et al. (1995) the generation of kink waves, while Anton (1989) studied the interaction between vortical flows and flux tubes, a process which gives rise to torsional waves. Another aspect has to do with the transport of kinetic energy through the photosphere by MHD-waves (e.g. Webb & Roberts 1980, Ziegler & Ulmschneider 1997a,b). The final aspect is the dissipation of the wave energy, e.g. by shock waves in the chromospheric layers in the case of longitudinal tube waves (e.g. Herbold et al. 1985, Fawzy et al. 1998) or through such mechanisms as mode coupling (e.g. Zähringer & Ulmschneider 1987), phase mixing (e.g. Nakariakov et al. 1997) and resonant absorption (e.g. Poedts et al. 1994) in the case of Alfvénic wave modes.

Observational evidence for the contribution of flux-tube waves to chromospheric or coronal heating is difficult to obtain and correspondingly poor (however, see Venkatakrishnan 1993). One possibility is to try to observe the propagating waves in the photosphere by means of polarization measurements. The problem with this approach is that little is known about the expected signature of such waves, in particular of the torsional Alfvén waves. The aim of the current paper is to provide some of the missing information. We use a simple model of torsional waves propagating along flux tubes to predict their signature in the polarized radiation of Zeeman-split lines.

Our model relies on the assumption that the flux tubes are small in diameter. This is thought to be satisfied for most flux tubes forming the solar magnetic network and active region plages. Consequently, the large variety of flux-tube modes (Roberts & Ulmschneider 1996) reduces to three (Spruit 1982), a compressible longitudinal ("sausage" mode) and two incompressible transverse modes (kink and torsional waves). The polarization signature of sausage modes has been investigated at solar disc centre by Solanki & Roberts (1992), that of kink waves by Ploner & Solanki (1997) at various positions on the disc. This paper is consequently dedicated to torsional waves. Other investigations that use theory in order to predict the influence of wave-like dynamic phenomena in flux tubes on spectral lines have been carried out by, e.g., Rammacher & Ulmschneider (1989), Rammacher (1991) and Steiner et al. (1995, 1996), but none of them considers torsional waves. In addition, techniques of polarimetric measurements are rapidly improving (e.g. Povel 1995, Gandorfer & Povel 1997), in particular for the observation of dynamic phenomena (Solanki 1996, Ulrich 1996, Martínez Pillet et al. 1997, cf. Frutiger & Solanki 1998) giving a certain timeliness to investigations like the present one.

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© European Southern Observatory (ESO) 1999

Online publication: April 28, 1999