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

Columns and other structures of twisted magnetic field lines with footpoints anchored to a surface at both ends exist in several astrophysical scenarios. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and probably exist in other compact astrophysical objects, like highly magnetized neutron star magnetospheres and accretion disk coronae. Around the Sun, flux tubes have been studied for many years, with many theories on their stability and dynamics. Compact object magnetospheres have different conditions, with strong magnetic fields, small plasma densities, and often rigid surfaces for anchoring and displacing magnetic field lines. We study the stability of simplified flux-tube geometries under these conditions and estimate the dissipation of electromagnetic energy expected during their instability.

Research summary

The well-established plasma safety factor q can be used as an instability criterion for the so-called kink instability in force-free flux tubes. It measures the inverse of the number of magnetic field line windings per flux tube length. Instabilities occur for q<1, namely when sufficient windings occur.
For a given magnetic twist, the flux tube length determines the instability. Long enough flux tubes (q<1) will always become unstable. But even for shorter systems, with q>1, so-called fluting instabilities can develop. The kink instability dissipates significantly more energy than the fluting instability.
These findings can be combined with information about the surface motions installing the twist when applied to compact object magnetospheres. For example, deformations of the magnetar crust can shear a bundle of magnetic flux. It depends on the shear velocity if the respective bundle will become kink unstable (fast shear) or dissipate energy by fluting before the critical winding is installed (slow shear). Less dissipation may leave more free energy in the system that could be released during powerful magnetar X-ray bursts.

Visualizing science

Currents during the evolution of a selected flux tube (α = 1, p0 = 0.75, L/r0 = 8). This animation shows structures that are characteristic of the m = 2 (fluting) mode. Significant currents remain in the relaxed state.

Currents during the evolution of a selected flux tube (α = 1, p0 = 1.25, L/r0 = 10). This animation shows structures that are characteristic of the asymmetric m = 1 (kink) mode. Some currents remain in the relaxed state.

Currents during the evolution of a selected flux tube (α = 1, p0 = 0.75, L/r0 = 14). During the evolution structures that are characteristic of the asymmetric m = 1 (kink) mode as well as the m = 2 (fluting) mode arise. The m = 2 mode has shorter wavelengths than the m = 1 mode. In the relaxed state, some currents remain.

Collaborative results

Rugg, N., Mahlmann, J. F., & Spitkovsky, A. (2024). Safety first: Stability and dissipation of line-tied force-free flux tubes in magnetized coronae. The Astrophysical Journal, 966(2), 173, doi: 10.3847/1538-4357/ad3206.