Twisted versus braided magnetic flux ropes in coronal geometry

Abstract

Aims. Sigmoidal structures in the solar corona are commonly associated with magnetic flux ropes whose magnetic field lines are twisted about a mutual axis. Their dynamical evolution is well studied, with sufficient twisting leading to large-scale rotation (writhing) and vertical expansion, possibly leading to ejection. Here, we investigate the behaviour of flux ropes whose field lines have more complex entangled/braided configurations. Our hypothesis is that this internal structure will inhibit the large-scale morphological changes. Additionally, we investigate the influence of the background field within which the rope is embedded. Methods. A technique for generating tubular magnetic fields with arbitrary axial geometry and internal structure, introduced in part I of this study, provides the initial conditions for resistive-MHD simulations. The tubular fields are embedded in a linear force-free background, and we consider various internal structures for the tubular field, including both twisted and braided topologies. These embedded flux ropes are then evolved using a 3D MHD code. Results. Firstly, in a background where twisted flux ropes evolve through the expected non-linear writhing and vertical expansion, we find that flux ropes with sufficiently braided/entangled interiors show no such large-scale changes. Secondly, embedding a twisted flux rope in a background field with a sigmoidal inversion line leads to eventual reversal of the large-scale rotation. Thirdly, in some cases a braided flux rope splits due to reconnection into two twisted flux ropes of opposing chirality -a phenomenon previously observed in cylindrical configurations. Conclusions. Sufficiently complex entanglement of the magnetic field lines within a flux rope can suppress large-scale morphological changes of its axis, with magnetic energy reduced instead through reconnection and expansion. The structure of the background magnetic field can significantly affect the changing morphology of a flux rope.

The emergence of braided magnetic fields

“…To study emergence, we must place a particular form for the magnetic field in the solar interior and apply a perturbation to allow it to emerge. Before presenting the models that we will consider in this study, we now briefly review the technique for creating magnetic flux tubes with arbitrary axial geometry introduced in Prior and Yeates (2016a).…”

“…A further embellishment of this process is to select a finite number of curves r i from the original tube T and to create smaller tubular fields surrounding each curve r i . In this way, a pigtail braided field with a sigmoidal axis was created in Prior and Yeates (2016a) (an example is shown later in figure 3). A second approach to increasing the complexity of the field is to define fields which partly overlap, creating a composite field with more complex internal topology.…”

“…This is used in what follows to develop a version of the braided field used in Yeates et al (2010), Wilmot-Smith et al (2011), Yeates et al (2015). The technical details of the process by which this field is interpolated onto a Cartesian grid are discussed in Prior and Yeates (2016a).…”

“…These results were recreated using flux ropes with realistic coronal morphology in Prior and Yeates (2016b). Since the Alfvén travel time in our model solar interior is much longer than the typical coronal value, we will pay close attention to whether the entanglement survives the emergence process.…”

“…In contrast to the B4 braid, however, the only significant current structure will be between the tubes rather than in the interior. In Prior and Yeates (2016b) it was found that this meant the disentanglement of the field through reconnection is far less efficient. Once again we will pay attention to how well the pigtail structure survives the emergence process in what follows.…”