Magnetohydrodynamic waves and their stability status in solar spicules

Abstract

Aims. We investigate conditions under which magnetohydrodynamic waves propagating along spicules become unstable because of the Kelvin-Helmholtz instability. Methods. We employ the dispersion relations of normal modes (kink and sausage waves) derived from the linearised magnetohydrodynamic equations. We assume real wave numbers and complex angular wave frequencies, namely complex wave phase velocities. The dispersion relations are solved numerically at fixed input parameters and various flow velocities. Results. It is shown that the stability of the waves depends upon three parameters, the density contrast between spicules and their environment, the ratio of the background magnetic field outside to that inside spicules, and the value of the Alfven-Mach number (the ratio of the jet velocity to Alfven speed inside the spicules). At certain densities and magnetic fields, an instability of the Kelvin-Helmholtz type can arise if the Alfven-Mach number exceeds a critical value ‐ in our case it is equal to 12.6, which means that for an Alfven speed inside the spicules of 70 kms −1 the jet velocity should be larger than 882 kms −1 . Conclusions. It is found that only kink waves can become unstable, while the sausage ones are always unaffected by the Kelvin-Helmholtz instability.