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Astron. Astrophys. 342, 854-862 (1999)

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1. Introduction

In recent years, there has been increasing interest, in both theoretical work and observations, in the study of magnetic topology in terms of separatrices and separators. A separatrix is the singular surface that divides topologically distinct magnetic fluxes into different cells, and the intersection between two separatrices is the separator. In a realistic active region, the presence of separatrices and/or separators is expected, since the mixture of opposite magnetic polarities readily produces the separatrices in three dimensional geometry (Baum & Bratenahl 1980). Under the frozen-in condition, current sheets can be created at separatrices by photospheric motions or flux emergence (e.g. Machado et al. 1983; Vekstein, Priest, & Amari 1991). As the strong current gets concentrated in a thin layer, resistive instability may occur which triggers reconnection. When this happens, magnetic field lines of distinct connectivity cells exchange their topological link at the separator and the free energy stored in the current sheet is rapidly released (Priest 1982; Priest & Forbes 1990; Aly & Amari 1997). The energy release may not be confined to the localized area where the flare is initiated by the current sheet dissipation but could cover an extended region bounded by the separatrices in a highly sheared magnetic field configuration (Hénoux & Somov 1987; Low & Wolfson 1988). Indeed, this is a favorable scenario to explain the observations that the H[FORMULA] flare brightenings are often seen to occur simultaneously at different sites over a global active region (Gorbachev & Somov 1988, 1989; Mandrini et al. 1991, 1993, 1995; Démoulin et al. 1993, 1994a; Van Driel et al. 1994; Bagalá et al. 1995). In these studies, the sites of flare brightening are found at the intersection of the separatrices with the chromosphere and associated with each other by magnetic field lines in the region around the separator. Such observation lends a strong support to the idea that energy release in solar flares takes place via reconnection at either the separator region or separatrices.

In a 2D field, magnetic topology is studied in terms of discontinuities of the field-line linkage, so the location of separatrices can be easily found. In the 3D case, however, field discontinuities are usually referred to as null points or quasi-singular lines associated with the global property of the magnetic topology in a complex way (Seehafer 1986; Lau 1993). This is why, to date, only a handful numbers of approaches are developed to explore the correlation between the flare and the magnetic topology. A convenient way called source method (SM) has been devised by Démoulin et al. (1992) to describe the 3D field by simulating the observed photospheric magnetograms with charges or dipoles. The connectivity of the field lines is then defined by grouping the sources which produce the field lines. With this method, however, one may lose the accuracy in recovering the real magnetic field which can be achieved by today's computing methods. A generalization of the idea of separatrices and separators leads to the introduction of quasi-separatrix-layers (QSLs; Démoulin et al. 1996). It can be applied to the 3D field extrapolated from the photospheric information while the strict restriction set for the case of separators is not necessary. Yet another different way was proposed by Wang & Wang (1996) to search for the singular points in a 2D field. By tracing the transverse field features, they can display the magnetic lanes separating the magnetic lines of distinct connectivities. The method enables to investigate the properties of the extrapolated magnetic field in the plane parallel to the photosphere for a specific model such as potential or force-free field model (e.g. Nakagawa & Raadu 1972; Chiu & Hilton 1977; Sakurai 1981; Wu et al. 1990; Yan et al. 1991), and illustrate the spatial correlation between the flares and the X-points (or saddle points) and magnetic lanes (Wang & Wang 1996; Wang 1997).

In this paper, we shall give a realistic diagnosis to 2D singular points in the observed transverse field in AR 7321 on October 27, 1991. In Sect. 2 some reasons are presented to prove that 2D observed field can be used to trace magnetic topology in certain conditions. In Sect. 3 observations and data reductions are introduced. In Sect. 4 the distinctive singular features in the observed field are explored in comparison with those in modeling field, and these features are further compared with the flare morphology in H[FORMULA] and SXR in order to understand the heating mechanism of flaring loops in the corona. Finally, we come to the conclusion in Sect. 5.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999