Three‐dimensional magnetic reconnection without null points: 2. Application to twisted flux tubes

Abstract

Magnetic reconnection has traditionally been associated exclusively with the presence of magnetic null points or field lines tangential to a boundary. However, in many cases introducing a three‐dimensional perturbation in a two‐and‐half‐dimensional magnetic configuration implies the disappearance of separatrices. Faced with this structural instability of separatrices when going from two‐and‐half to three‐dimensional configurations, several approaches have been investigated to replace the topological ideas familiar in two‐dimensional, but no unanimity has yet emerged on the way reconnection should be defined. While it is true that the field line linkage is continous in three‐dimensional, we show here that extremely thin layers (called quasi‐separatrix layers (QSLs)) are present. In these layers the gradient of the mapping of field lines from one part of a boundary to another is very much larger than normal (by many orders of magnitude). Even for highly conductive media these extremely thin layers behave physically like separatrices. Thus reconnection without null points can occur in QSLs with a breakdown of ideal MHD and a change in connectivity of plasma elements. We have analyzed several twisted flux tube configurations, going progressively from two‐and‐half to three‐dimensional, showing that QSLs are structurally stable features (in contrast to separatrices). The relative thickness w of QSLs depends mainly on the maximum twist; typically, with two turns, w ≈ 10−6, while with four turns, w ≈ 10−12. In these twisted configurations the shape of the QSLs, at the intersection with the lower planar boundary, is typical of the two ribbons observed in two‐ribbon solar flares, confirming that the accompanying prominence eruption involves the reconnection of twisted magnetic structures. We conclude that reconnection occurs in three‐dimensional in thin layers or QSLs, which generalise the traditional separatrices (related only to magnetic null points or field lines tangential to the boundary).

Magnetic reconnection and energy release on the Sun and solar-like stars

“…in the concave-up parts under the flux rope axis plasma accumulates, leading to a fragmentation of the emerging flux rope (e.g., Magara 2004;Manchester et al 2004) which can only emerge through many smallscale reconnections (Pariat et al 2004). Nevertheless, characteristic magnetic patterns in emerging flux regions originating from the changing azimuthal component of a flux rope while crossing the photosphere, the so-called "magnetic tongues" (López-Fuentes et al 2000;Démoulin & Pariat 2008) indicate that there is an overall organization in the emerging flux tube, which is compatible with a global twist. Besides organised motion patterns random magnetic footpoint motions (shuffling) are considered important to entangle field lines leading to the formation of small-scale current sheets.…”

“…For detailed treatment of reconnection topologies see the book by Priest & Forbes (2000) and for a recent review see Démoulin (2007b). Along QSLs field line mapping is continuous but steep gradients are present (Démoulin et al 1996). Reconnection along QSLs also occurs in a continuous manner.…”

Three-dimensional magnetic reconnection and its application to solar flares

“…When thin enough, QSLs behave physically as separatrices even though there are no true mathematical discontinuities of the field line mapping. This generalisation to QSLs was introduced by the seminal works of Priest & Démoulin (1995) and Démoulin, Priest & Lonie (1996b). QSLs are defined as regions of space where the connectivity of the magnetic field is drastically changing, while remaining continuous in general.…”

“…Their straight part is associated with the low-lying coronal loop, while the round region is associated with the anchoring region of the twisted field lines. A zoom in the region shows a hook shape of the flux-rope anchoring region, where a higher twist corresponds to a higher number of swirls (adapted from Démoulin et al (1996b)). …”

“…Their traces on the lower boundary show a typical J-shape, with a straight part associated with low-lying coronal loops while the hook region of the J shape is associated with the anchoring region of the flux rope. In Démoulin et al (1996b), the authors investigated the morphology of the QSLs and especially the hook region: because the QSLs form a thin volume, that delimitates the frontier between differently connected field lines, this volume is also connected to the photospheric surface. Then, the more the magnetic field is twisted, the more complex the QSL photospheric footprint becomes: the QSL swirls around the flux rope as the twist of the structure increases (figure 5b).…”