Critical decay index at the onset of solar eruptions

TL;DR

This study uses MHD simulations to determine the critical decay index range triggering solar eruptions, finding it consistent across different active region evolutions and aligning with the current-wire model despite complex effects.

Contribution

It demonstrates that the critical decay index range for eruption onset is robust against variations in photospheric dynamics and flux rope profiles, confirming the current-wire model predictions.

Findings

Critical decay index range is [1.3-1.5] for eruptions.

The critical range is unaffected by pre-eruptive photospheric evolution.

Results align with the current-wire model despite complex effects.

Abstract

Magnetic flux ropes are topological structures consisting of twisted magnetic field lines that globally wrap around an axis. The torus instability model predicts that a magnetic flux rope of major radius $R$ undergoes an eruption when its axis reaches a location where the decay index $-d(\ln B_{ex})/d(\ln R)$ of the ambient magnetic field $B_{ex}$ is larger than a critical value. In the current-wire model, the critical value depends on the thickness and time-evolution of the current channel. We use magneto-hydrodynamic (MHD) simulations to investigate if the critical value of the decay index at the onset of the eruption is affected by the magnetic flux rope's internal current profile and/or by the particular pre-eruptive photospheric dynamics. The evolution of an asymmetric, bipolar active region is driven by applying different classes of photospheric motions. We find that the critical value of the decay index at the onset of the eruption is not significantly affected by either the pre-eruptive photospheric evolution of the active region or by the resulting different magnetic flux ropes. As in the case of the current-wire model, we find that there is a `critical range' $ [1.3-1.5]$, rather than a `critical value' for the onset of the torus instability. This range is in good agreement with the predictions of the current-wire model, despite the inclusion of line-tying effects and the occurrence of tether-cutting magnetic reconnection.