Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope

TL;DR

This paper investigates the conditions leading to solar eruptions, demonstrating that magnetic catastrophe and torus instability are equivalent mechanisms initiating eruptions in a toroidal flux rope model.

Contribution

It shows that magnetic catastrophe and torus instability are fundamentally the same, occurring at the same point in the flux rope's equilibrium evolution.

Findings

Magnetic catastrophe occurs via loss of equilibrium in flux rope models.

Torus instability and catastrophe are shown to be equivalent.

Eruption onset conditions are identified in the parameter space.

Abstract

The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.