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Astron. Astrophys. 337, L9-L12 (1998)

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1. Introduction

The heating of the solar corona and acceleration of the solar wind have a common origin related to magnetic fields (Hollweg 1986). Models of these processes prescribe the source of the heating and its power (c.f. Esser et al. 1997). The physical nature of the mechanism of the build-up and release of energy remains a problem, although a number of crucial insights have been made in the study of this problem. It has been suggested by many authors that the mechanism involves twisting of flux tubes by convective motions, reconnections inside the flux tubes, and reconnections of closed flux tubes with open ones (Sturrock, Uchida 1981, van Ballegooijen 1986, Parker 1990, Feldman et al. 1993, Berger 1994, Galsgard, Nordlund 1996, Shibata 1997). An interesting idea about the form of energy release has been put forward by Axford and McKenzie (1992) and recently developed by Tu and Marsch (1997) and Marsch and Tu (1997a,b). According to these authors, a source generates high-frequency ([FORMULA] Hz) Alfvén waves, that dissipate by ion-cyclotron-resonance damping in the inner corona and thus provide the energy for heating of the low corona and the pressure for initial acceleration of the solar wind. The origin of these waves was associated with small-scale magnetic activity (such as reconnections) in the chromospheric network but has not been discussed in any detail.

Here we suggest a specific mechanism for the generation of the high-frequency Alfvén waves by the magnetic activity. Our approach is based on the concept of the minimum state for a topologically complex field, introduced by Freedman and He (1991) and Berger (1993) (see the section below). We use the highly fragmented nature of the solar magnetic field and utilize the ideas of twisting of flux tubes by random motions and reconnections of closed magnetic loops with the open field. Although the energy basically comes from convective motions and associated magnetic fields, the topological constraints, imbedded here in the form of the minimum energy state, help us to understand what portion of the magnetic energy can be released.

The solar loops can release magnetic energy in two primary ways. First, the magnetic flux emerging to the solar surface may have a high level of topological complexity acquired from shear motions inside the convection zone (for observational support of this point see Leka et al. 1997) and lose the energy by relaxing toward the minimum state. Second, the already emerged flux tubes can be further entangled due to random photospheric shear motions and lose their energy and topological complexity due to reconnections inside the flux tubes (Sturrock, Uchida 1981, van Ballegooijen 1986, Berger 1994) and due to reconnections with open structures (Axford, McKenzie 1992, Feldman et al. 1993, Shibata 1997). We show that relaxation along the minimum state contributes to coronal heating-this gives a new interpretation to the well- known dynamic balance between the twisting of footpoints and reconnections. We argue that reconnections of closed loops (emerging to the solar surface and those in the minimum state) with the open field release energy in the form of high-frequency Alfvén waves. To estimate the power released in the relaxation and the wave power we identify the magnetic loops with the observed small-scale bipoles (ephemeral regions) emerging on the Sun and interacting with the open network magnetic field.

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© European Southern Observatory (ESO) 1998

Online publication: August 6, 1998