Critical decay index for eruptions of ‘short’ filaments

Abstract

Model of a partial current-carrying torus loop anchored to the photosphere is analysed. Conditions of the catastrophic loss of equilibrium are considered and corresponding value of the critical decay index of external magnetic field is found. Taking into account line-tying conditions leads to non-monotonous dependence of the critical decay index on the height of the apex and length of the flux rope (its endpoints separation). For relatively short flux ropes, the critical decay index is significantly lower than unity, which is in contrast to widespread models with the typical critical decay index above unity. The steep decrease of the critical index with height at low heights is due to the sharp increase of the curvature of the flux-rope axis that transforms from a nearly straight line to a crescent.

Radiative Magnetohydrodynamic Simulation of the Confined Eruption of a Magnetic Flux Rope: Unveiling the Driving and Constraining Forces

“…For example, for a large aspect-ratio current tube undergoing a self-similar expansion, torus instability is usually thought to be satisfied theoretically when the decay index at its axis reaches 1 (for straight current tubes) or 1.5 (for semicircular ones). However, taking the factors such as the morphology of the flux rope , the line-tied effect (Isenberg & Forbes 2007;Filippov 2021), the photospheric evolution (Zuccarello et al 2015), and the role of gravity (Jenkins et al 2019) into consideration, there may be a critical range rather than a universal critical value for the onset of torus instability. Meanwhile, due to the lack of in situ observations, the local decay index at the position of the flux rope relies greatly on the way to choose its observational indicators (Zuccarello et al 2016;Sarkar et al 2019;Rees-Crockford et al 2020).…”