The Apparent Critical Decay Index at the Onset of Solar Prominence Eruptions

Abstract

A magnetic flux rope (MFR) embedded in a line-tied external magnetic field that decreases with height asz n is unstable to perturbations if the decay index of the field n is larger than a critical value. The onset of this instability, called torus instability, is one of the main mechanisms that can initiate coronal mass ejections. Since flux ropes often possess magnetic dips that can support prominence plasma, this is also a valuable mechanism to trigger prominence eruptions. Magnetohydrodynamic (MHD) simulations of the formation and/or emergence of MFRs suggest a critical value for the onset of the instability in the range [1.4−2]. However, detailed observations of prominences suggest a value in the range [0.9−1.1]. In this Letter, by using a set of MHD simulations, we show why the large discrepancy between models and observations is only apparent. Our simulations indeed show that the critical decay index at the onset of the eruption is =  n 1.4 0.1 when computed at the apex of the flux rope axis, while it is =  n 1.1 0.1 when it is computed at the altitude of the topmost part of the distribution of magnetic dips. The discrepancy only arises because weakly twisted curved flux ropes do not have dips up to the altitude of their axis.

The Causes of Quasi-homologous CMEs

“…Basically, n measures the run of the strapping field's confinement with height. Theoretical works predict the onset of torus instability when n is in the range of 1.5, 2.0 & Török 2006), while observations of eruptive prominences suggest a critical value n 1 (Filippov 2013; Su et al 2015).It is suggested that the former value is representative for the top of the flux rope axis, while the latter value is typical for the location of magnetic dips that hold the prominence material (Zuccarello et al 2016). Therefore, n 1, 1.5 = [] are used as critical decay index values for our analysis.…”

Expanding and Contracting Coronal Loops as Evidence of Vortex Flows Induced by Solar Eruptions

“…They exhibit a multitude of observed dynamic phenomena arising from release of energy stored within the pre-flare magnetic field (e.g., Fletcher et al 2011;Schmieder et al 2015). The destabilization of the magnetic field via the torus instability results in an eruption (e.g., Aulanier et al 2012;Zuccarello et al 2015Zuccarello et al , 2016, with the eruption driving other dynamic phenomena, such as slipping motion of flare loops and expansion/contraction behavior of the neighboring coronal loops (e.g., Janvier et al 2013;Dudík et al 2014Dudík et al , 2016. In this paper, we are concerned with the expansion/contraction behavior of closed coronal loops at the periphery of active regions with respect to the flare and/or eruption site.…”

On the Factors Determining the Eruptive Character of Solar Flares

“…In other words, a system becomes unstable when the overlying horizontal field strength decayes sufficiently fast. Based on magneto-hydrodynamic simulations involving different geometrical assumptions on the current channel mimicking the flux rope (e.g., Török & Kliem 2007;Fan & Gibson 2007;Démoulin & Aulanier 2010;Zuccarello et al 2015) and prominence observations (e.g., Zuccarello et al 2016), n crit is found in the range 1.0-2.0. Despite this extended range of critical values n crit = 1.5 is often used in observation-based studies that aim at assessing the likelihood of a CME to occur.…”