Equilibrium and catastrophe of coronal flux ropes in axisymmetrical magnetic field

Abstract

[1] Using a 2.5-dimensional, time-dependent ideal magnetohydrodynamic model in spherical coordinates, we present a numerical study of the property of magnetostatic equilibria associated with a coronal magnetic flux rope embedded in an axisymmetrical background magnetic field. The background field is potential (either closed or partly opened), a magnetic flux rope emerges out of the solar surface, and the resultant system is allowed to relax to equilibrium through numerical simulation. It is shown that the flux rope either sticks to the solar surface so that the whole magnetic configuration stays in equilibrium or escapes from the top of the computational domain, leading to the opening of the background field. Whether the rope remains attached to the solar surface or escapes to infinity depends on the magnetic energy of the system. The rope sticks to the solar surface when the magnetic energy of the system is less than a certain threshold, and it escapes otherwise. The threshold is slightly larger than the open limit, i.e., the magnetic energy of the corresponding fully opened field. The gravity, say, associated with the prominence mass, will raise the threshold by an amount that is approximately equal to the magnitude of the excess gravitational energy associated with the prominence. It implies that a catastrophe occurs when the magnetic energy of the system exceeds the threshold. The implication of such a catastrophe in coronal mass ejections is briefly discussed.

The Catastrophe of Coronal Magnetic Flux Ropes in CMEs

“…In terms of a 2.5-D flux rope model in spherical coordinates, Hu et al (2003) concluded that W c is slightly larger than W open , and the gravity associated with the prominence supported by the flux rope raises W c by an amount that is approximately equal to the magnitude of the excess gravitational energy associated with the prominence. Such a conclusion was further quantified by : W c exceeds W open by 8%.…”

“…In an extension of the flux rope model to spherical geometry, Hu et al (2003) found that a flux rope embedded in a bipolar background field also exhibits a catastrophic behavior with respect to Φ p or Φ t , which does not depend on whether the background field is partly-open or closed. The rope sticks to the solar surface in equilibrium below the catastrophic point, and escapes to infinity above.…”

“…Therefore, by itself, a catastrophe is sufficient to implement the eruption process associated with CMEs. Hu et al (2003) took an isothermal static corona as the background and obtained profiles of the geometrical parameters of the rope with height after catastrophe. The flux rope erupts at the Alfvén timescale that increases with height, leading to an initial sharp acceleration followed by a gradual deceleration.…”

A review of recent studies on coronal dynamics: Streamers, coronal mass ejections, and their interactions

“…Chen et al [93] managed to eliminate numerical reconnections across the CME current sheet and achieved numerical simulation of the flux rope eruption within the framework of ideal MHD. This is done by taking advantage of the fact that the magnetic flux function being a known constant along the current sheet [86]. This allows them to make a first-time quantitive comparison of energy releases for cases with and without magnetic reconnections.…”

“…In the former models, the pre-exisiting flux rope carries enough free energy driving the eruption. Both analytical rope models [24,85] and numerical rope models [29,86] have been developed under 2-D configuration. In these models, the rope system first evolves slowly with the boundary or the background conditions till a certain threshold is reached.…”