It is well established that the development of the kink instability in coronal loops may play a crucial role in the dynamics of the solar corona. Indeed, a kinked magnetic flux tube experiences a disruption that could explain compact loop flares (Velli et al. 1997, Arber et al. 1999, Amari & Luciani 1999). It also releases, at the same time, a significant amount of magnetic energy that could contribute to heat the solar corona (Galsgaard & Nordlund 1997, Baty 2000 hereafter referred to as Paper I).
Of particular interest here, are solar loops having magnetic field lines that are locally twisted in the central region and carrying no net axial current (Lionello et al. 1998, Baty et al. 1998, Arber et al. 1999). This class of configurations would result from a vortex photospheric flow acting on an initially potential magnetic field and leading to a sequence of quasi-equilibria with a gradual build-up of the twist (Mikic et al. 1990). When the amount of twist injected in the loop exceeds a critical value, the configuration becomes kink unstable (Raadu 1972, Hood & Priest 1979, Einaudi et al. 1983). The early evolution of this instability then generates a high electric current concentration along the loop length (Baty 1997, Velli et al. 1997, Arber et al. 1999). When sufficiently large magnetic field gradients are created, the ensuing evolution becomes resistive with the occurrence of a magnetic reconnection process (Einaudi et al. 1997, Lionello et al. 1998, Arber et al. 1999, Paper I). In Paper I, we have obtained a steady-state reconnection of field lines consistent with results predicted by the well known two-dimensional Sweet-Parker model, in spite of the three-dimensional (3D) character of the process. We have also found that the system finally reaches a relaxed state of lower magnetic energy, releasing more than 50 percent of the free energy stored in the initial configuration.
In the present paper, we propose to examine in details the magnetic topology change that arises during the reconnection. Some aspects of this problem have been previously addressed in cylindrical geometry approximation (Bazdenkov & Sato 1998) and also in the true 3D geometry (Amari & Luciani 1999, 2000). An important result obtained in these studies is the splitting of the initial flux tube into two topologically distinct pieces. Indeed, Amari & Luciani (1999) have shown that the final state is a relaxed configuration consisting of two almost untwisted flux tubes confined by an overlaying arcade. Contrary to these papers where a photospheric flow is applied to the footpoints to continuously inject twist in the loop, we introduce an initial twisted configuration that is already kink unstable. Therefore, we focus on the topological change resulting from the non linear evolution of the kink instability alone, the whole evolution of the loop configuration with the photospheric flow effect being beyond the scope of the present paper. This is an important point in order to contribute to the understanding of the 3D reconnection phenomenon in the solar corona, that has begun to be studied only recently (Priest 1997 and references therein).
As in most of the previously mentioned references, we have carried out numerical simulations in the cylindrical geometry approximation. We have followed the non linear resistive evolution of a single magnetic equilibrium representative of an initially unstable coronal loop, using optimal values for the dissipation coefficients in our MHD evolution code, SCYL.
The paper is organized as follows. The physical and numerical loop models are presented in Sect. 2. The next section is devoted to the numerical resuls. Finally, a schematic description of the magnetic topology change is given and conclusions are drawn.
© European Southern Observatory (ESO) 2000
Online publication: July 27, 2000