98. Observing and Modelling a Flux Rope in the Corona

Authors: Alexander James, Lucie Green, Gherardo Valori, and Lidia van Driel-Gesztelyi at MSSL UCL.

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To identify the mechanisms that initiate Coronal Mass Ejections (CMEs), we must first know what the magnetic structure of the solar corona is prior to eruptions. Measurements taken at 1 AU reveal that at least some — or perhaps all — interplanetary CMEs contain magnetic flux ropes: bundles of twisted magnetic field lines [1,2]. However, there is still debate regarding the pre-eruptive configuration of CMEs: do these flux ropes form before the onset of eruption [3], or after the onset of eruption of a sheared magnetic arcade [4,5]? In this work, we use a combination of EUV observations and magnetic field reconstruction to investigate the pre-eruptive configuration of a solar active region and to identify the mechanism that caused its eruption.

A Flux Rope in the Solar Corona

An interplanetary CME with a flux rope structure was identified in measurements from the Wind spacecraft at 1 AU and found to have originated from NOAA active region 11504 on 14 June 2012 [6]. At that time, the source active region was close to the centre of the Sun as viewed from the Solar Dynamics Observatory (SDO), meaning reliable measurements of the surface magnetic field in the active region were available.

During the two hours leading up to the eruption, an S-shaped plasma emission structure called a sigmoid was observed in the 131 Å extreme-ultraviolet (EUV) channel of SDO/AIA (Figure 1a). A sigmoid is a telltale signature of a magnetic field with at least one turn of twist along its length [7], suggesting that a flux rope was present in the active region during this time. The sigmoid appeared above a bright flaring arcade, indicating that the flux rope was forming high up in the corona via magnetic reconnection, a process that can change the local configuration of the magnetic field via the extremely small but finite resistivity of the coronal plasma. This is not the most common location where flux ropes are formed, but a number of other observations helped build the case that a flux rope may have formed high in the corona of the active region at least two hours before the eruption, including twin EUV footpoint dimmings, flare ribbons, radio emission, and spectroscopic composition data from Hinode/EIS [8].

Figure 1. a) A sigmoid (outlined by the red dashed line) above a flaring arcade in the 131 Å channel of SDO/AIA. b) The magnetic flux rope extrapolated from surface magnetic field measurements at 12:24 UT.

However, no single observation provides definitive proof that a flux rope was present. As a next step, a model of the active region magnetic field was produced by extrapolating the surface magnetic field measurements under the assumption that the coronal field is free from Lorentz forces (force-free). The extrapolated coronal field indeed contained a flux rope that extended high up in the corona and matched the observed sigmoid and footpoint signatures remarkably well (Figure 1b) [9].

With the validity of the extrapolated coronal magnetic field confirmed against observations, we could study it quantitatively. The decay index quantifies how rapidly the overlying stabilising field strength changes with height. In idealized theoretical models, a semi-toroidal flux rope would be unstable to expansion under the hoop force if the decay index is larger than ncrit=1.5 at its axis [10,11]. The extrapolation reveals that the flux rope lies in a region where the decay index is comparable to this threshold, meaning that the eruption of the flux rope is likely to have been driven by this so-called torus instability.

Table 1. Properties of the extrapolated flux rope. α is the force-free parameter. *Due to the asymmetry of the flux rope, three choices of axes were used to compute certain quantities.

As for how such a coronal flux rope was formed, we observed that several hours before the eruption, the active region contained two sets of J-shaped magnetic loops that underwent magnetic reconnection in the corona and transitioned to the flux rope and underlying flaring arcade. Magnetic flux emergence was ongoing in the active region during this time, and subsequently-emerging fragments of magnetic flux were seen to ‘orbit’ around pre-existing flux (see the movie in Figure 2). We argue that the footpoints of the observed J-shaped loops were rooted in these sunspot fragments that wrapped around each other, providing a triggering mechanism for the sheared coronal field to converge, reconnect, and build the flux rope in the corona.

Figure 2. Newly-emerging magnetic flux moves westward towards and then clockwise around the pre-existing leading sunspot in the active region. This 'orbital' motion wraps the legs of sheared coronal loops around each other, enabling magnetic reconnection in the corona.


In this case study, we observationally inferred the presence of a magnetic flux rope that formed in the solar corona at least 2 hours before its eruption. This scenario was confirmed with an observationally-constrained model of the active region, produced using the nonlinear force-free field extrapolation of surface magnetic field measurements. According to our analysis of the extrapolated coronal model, the eruption was driven by the torus instability. Finally, the observations suggest that the motion of newly-emerged magnetic flux in the photosphere enabled reconnection in the corona that built the flux rope.