Kelvin-Helmholtz instability of kink waves in photospheric twisted flux tubes

TL;DR

This study examines how kink waves in twisted photospheric flux tubes become Kelvin-Helmholtz unstable due to specific conditions involving magnetic twist, density contrast, and flow velocity, using numerical solutions of dispersion relations.

Contribution

It provides a detailed analysis of the stability conditions for kink waves in twisted flux tubes, highlighting the influence of magnetic twist and flow speed on Kelvin-Helmholtz instability thresholds.

Findings

Kelvin-Helmholtz instability occurs at certain density and twist parameters.

Critical flow speeds depend on magnetic twist and external magnetic field strength.

Weak external magnetic fields slightly lower the instability threshold.

Abstract

We investigate conditions under which kink magnetohydrodynamic waves propagating along photospheric uniformly twisted flux tubes with axial mass flows become unstable as a consequence of the Kelvin-Helmholtz instability. We employed the dispersion relations of kink waves derived from the linearised magnetohydrodynamic equations. We assumed real wave numbers and complex angular wave frequencies, namely complex wave phase velocities. The dispersion relations were solved numerically at fixed input parameters and several mass flow velocities. We show that the stability of the waves depends upon four parameters, the density contrast between the flux tube and its environment, the ratio of the background magnetic fields in the two media, the twist of the magnetic field lines inside the tube, and the value of the Alfven-Mach number (the ratio of the jet velocity to Alfv\'en speed inside the flux tube). At certain densities and magnetic field twists, an instability of the Kelvin-Helmholtz type of kink (m = 1) mode can arise if the Alfven-Mach number exceeds a critical value. The observed mass flows may trigger the Kelvin-Helmholtz instability of the kink (m = 1) mode in weakly twisted photospheric magnetic flux tubes at critical Alfven-Mach numbers lower that those in untwisted tubes if the magnetic field twist lies in the range 0.36--0.4 and the flow speed exceeds a critical value. A weak external magnetic field (with a ratio to the magnetic field inside the tube in the range 0.1--0.5) slightly increases that critical value.