A Quantitative, Topological Model of Reconnection and Flux Rope Formation in a Two‐Ribbon Flare

Abstract

We present a topological model for energy storage and subsequent release in a sheared arcade of either infinite or finite extent. This provides a quantitative picture of a twisted flux rope produced through reconnection in a two-ribbon flare. It quantifies relationships between the initial shear, the amount of flux reconnected and the total toroidal flux in the twisted rope. The model predicts reconnection occurring in a sequence which progresses upward even if the reconnection sites themselves do not move. While some of the field lines created through reconnection are shorter, and less sheared across the polarity inversion line, reconnection also produces a significant number of field lines with shear even greater than that imposed by the photospheric motion. The most highly sheared of these is the overlying flux rope. Since it is produced by a sequence of reconnections, the flux rope has twist far in excess of that introduced into the arcade through shear motions. The energy storage agrees well with previous calculations using the full equations of magnetohydrodynamics, and the agreement improves as the topology is defined using increasingly finer detail. This is the first comparative study of the application of a topological model to a continuous flux distribution. As such it demonstrates how the coarseness with which the photospheric flux distribution is partitioned affects the accuracy of prediction in topological models.

Estimation of Reconnection Flux Using Post-eruption Arcades and Its Relevance to Magnetic Clouds at 1 AU

“…We note that Hu et al (2014) considered only the Grad-Shafranov (GS) method of flux rope fitting rather than the force-free (FF) fitting we used. In Qiu et al's (2007) Table 4, all the poloidal flux values from the FF method were higher than those from the GS method -by a factor of ~1.6 on average. In our case, estimation of the poloidal flux was possible for 13 of the 21 events (Möstl 2014, private communication).…”

“…A number of investigations have identified a close connection between coronal mass ejections (CMEs) and the associated flares: (i) the CME acceleration is synchronized with the rise time of the associated flare (Zhang et al, 2001;Zhang and Dere, 2006;Gopalswamy et al, 2012), (ii) the CME kinetic energy and soft X-ray peak flux are correlated (Gopalswamy, 2009), (iii) the CME width is determined by the flare magnetic field (Moore, Sterling, and Suess 2007), (iv) flare reconnection (RC) and flux rope formation are related (Leamon et al, 2004;Longcope and Beveridge, 2007;Qiu et al, 2007;Hu et al, 2014), (v) the CME nose is directly above the flare location (Yashiro et al, 2008), and (vi) the high charge state of minor ions in interplanetary coronal mass ejections (ICMEs) is a consequence of the heated flare plasma entering into the CME flux rope during the eruption (Lepri et al, 2001;Reinard, 2008;Gopalswamy et al,, 2013). One of the key aspects of CMEs is their flux rope nature considered extensively from theory and observations (see e.g., Mouschovias and Poland 1978;Burlaga et al, 1981;Marubashi 1997;Gibson et al,, 2006;Linton and Moldwin 2009).…”

“…A number of investigations have also shown that the flare RC process results in the simultaneous formation of a post-eruption arcade (PEA) and a flux rope during solar eruptive events (Leamon et al, 2004;Longcope and Beveridge, 2007;Qiu et al, 2007;Hu et al, 2014). At present it is not fully understood whether CME flux ropes exist before eruption or formed during eruption.…”

“…The reality may be something in between: flux may be added to a pre-existing flux rope via flare RC (see e.g., Lin, Raymond, and van Ballegooijen, 2004). If the flux rope is formed due to reconnection, for each flare loop formed, the flux rope gets one turn, as explained in Longcope et al, 2007;Longcope and Beveridge (2007). The flare loops are rooted in the flare ribbons on either side of the polarity inversion line.…”

Multiwavelength observation of a large-scale flux rope eruption above a kinked small filament

“…Qiu et al (2007) quantitatively compared the total magnetic reconnection flux in the low corona (measured from flare ribbons) in the wake of CMEs and the magnetic flux in magnetic clouds, favoring the flux rope formation during magnetic reconnection. The model developed by Longcope & Beveridge (2007) also explains the flux rope formation by a sequence of magnetic reconnection above the polarity inversion line in a two-ribbon flare.…”