Abstract
During eruptive solar flares and coronal mass ejections, a non-pot{\-}ential magnetic arcade with much excess magnetic energy goes unstable and reconnects. It produces a twisted erupting flux rope and leaves behind a sheared arcade of hot coronal loops. We suggest that: the twist of the erupting flux rope can be determined from conservation of magnetic flux and magnetic helicity and equipartition of magnetic helicity. It depends on the geometry of the initial pre-eruptive structure. Two cases are considered, in the first of which a flux rope is not present initially but is created during the eruption by the reconnection. In the second case, a flux rope is present under the arcade in the pre-eruptive state, and the effect of the eruption and reconnection is to add an amount of magnetic helicity that depends on the fluxes of the rope and arcade and the geometry.
Highlights
It was first suggested to be important in coronal heating, solar flares and coronal mass ejections by Heyvaerts and Priest (1984), who proposed that, when the stored magnetic helicity is too great, it may be ejected from the Sun in an erupting flux rope
We have set up a simple model for estimating the twist in erupting prominences, in association with eruptive two-ribbon flares and/or with coronal mass ejections
It is based on three simple assumptions, namely, conservation of magnetic flux, conservation of magnetic helicity and equipartition of magnetic helicity
Summary
The standard understanding of eruptive solar flares (e.g., Schmieder and Aulanier, 2012; Priest, 2014; Aulanier, 2014; Janvier, Aulanier, and Démoulin, 2015) is that excess magnetic energy and magnetic helicity build up until a threshold is reached at which point the magnetic configuration either goes unstable or loses equilibrium, either by breakout (Antiochos, DeVore, and Klimchuk, 1999; DeVore and Antiochos, 2008) or magnetic catastrophe (Démoulin and Priest, 1988; Priest and Forbes, 1990; Forbes and Isenberg, 1991; Lin and Forbes, 2000; Wang, Shen, and Lin, 2009) or kink instability (Hood and Priest, 1979) or by. Our aim in this paper is to determine two key observational consequences of the reconnection process, namely, the amount of magnetic helicity, and twist, in the erupting flux rope, and in the shear of the underlying flare loops. Have considered an alternative possibility, namely, preferential transfer of magnetic helicity to the flux rope during the reconnection, which would imply the flaring loops have vanishing self-helicity This seems less likely, because, the flare loops are generally seen as non-twisted structures, they are observed to be non-potential, since the low-lying loops appearing early in the flare possess more shear than the high-lying loops (Aulanier, Janvier, and Schmieder, 2012).
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