The equilibrium shape of slender flux tubes in a linear force-free magnetic field

Abstract

In this paper we extend previous work of Browning and Priest (1984, 1986) by studying the equilibrium path of twisted and untwisted thin flux tubes in a stratified, isothermal atmosphere using as the ambient field a linear force-free field. When an untwisted flux tube is considered, we find that shearing the magnetic arcade provides a different form to change the parameter λ which characterizes the external atmosphere, but at the same time this introduces a limitation in the width allowed for the external arcade. Also, the critical width found for the different analytical cases considered is always greater than one arch of the ambient arcade which prevents an eruption inside the arcade. In the case of twisted flux tubes, an analytical solution can be found for the critical λ _c , which separates regimes of strong and weak gravity, and the shape of the flux tube is now dependent on β, a parameter which represents the magnetic field enhancement of the loop at the photosphere.