Safety first: Stability and dissipation of line-tied force-free flux tubes in magnetized coronae

TL;DR

This paper investigates the stability and energy dissipation of line-tied force-free magnetic flux tubes in astrophysical coronae, revealing how twist and system size influence kink instabilities and magnetic energy release.

Contribution

It provides a detailed analysis of how flux tube parameters affect stability and dissipation, introducing scalings for kink growth rates and minimum instability wavelengths.

Findings

Kink modes and dissipation occur for safety factor q less than approximately 1.

Higher-order modes cause less dissipation but can distort flux tubes.

Growth rate of kink instability scales with the cube of the flux tube's characteristic pitch.

Abstract

Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes ($m=1$) and efficient magnetic energy dissipation develop for plasma safety factors $q\lesssim 1$, where $q$ is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes ($m>1$) can distort equilibrium flux tubes for $q>1$ but induce significantly less dissipation. In our analysis, the characteristic pitch $\tilde{\mu}_0$ of flux tube field lines determines the growth rate ($\propto \tilde{\mu}_0^3$) and minimum wavelength of the kink instability ($\propto \tilde{\mu}_0^{-1}$). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given $\tilde{\mu}_0$. By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions.