A Titov-D\'emoulin Type Eruptive Event Generator for $\beta>0$ Plasmas

TL;DR

This paper introduces an analytical model for simulating eruptive solar events, incorporating finite plasma beta, and connects model parameters to observable CME properties, enhancing understanding of solar eruptions.

Contribution

The model extends the Titov-Demoulin framework by including finite plasma beta and provides explicit relations between model parameters and CME observational data.

Findings

Analytical solutions for magnetic fields in toroidal filaments.

Model describes equilibrium and eruption due to magnetic reconnection.

Connections established between model parameters and CME velocities and masses.

Abstract

We provide exact analytical solutions for the magnetic field produced by prescribed current distributions located inside a toroidal filament of finite thickness. The solutions are expressed in terms of toroidal functions which are modifications of the Legendre functions. In application to the MHD equilibrium of a twisted toroidal current loop in the solar corona, the Grad-Shafranov equation is decomposed into an analytic solution describing an equilibrium configuration against the pinch-effect from its own current and an approximate solution for an external strapping field to balance the hoop force. Our solutions can be employed in numerical simulations of coronal mass ejections. When superimposed on the background solar coronal magnetic field, the excess magnetic energy of the twisted current loop configuration can be made unstable by applying flux cancellation to reduce the strapping field. Such loss of stability accompanied by the formation of an expanding flux rope is typical for the Titov & D\'emoulin (1999) eruptive event generator. The main new features of the proposed model are: (i) The filament is filled with finite $\beta$ plasma with finite mass and energy, (ii) The model describes an equilibrium solution that will spontaneously erupt due to magnetic reconnection of the strapping magnetic field arcade, and (iii) There are analytic expressions connecting the model parameters to the asymptotic velocity and total mass of the resulting CME, providing a way to connect the simulated CME properties to multipoint coronograph observations.