Kink instability of triangular jets in the solar atmosphere

Abstract

Context. It is known that hydrodynamic triangular jets (i.e. the jet with maximal velocity at its axis, which linearly decreases at both sides) are unstable to anti-symmetric kink perturbations. The inclusion of the magnetic field may lead to the stabilisation of the jets. Jets and complex magnetic fields are ubiquitous in the solar atmosphere, which suggests the possibility of the kink instability in certain cases. Aims. The aim of the paper is to study the kink instability of triangular jets sandwiched between magnetic tubes (or slabs) and its possible connection to observed properties of the jets in the solar atmosphere. Methods. A dispersion equation governing the kink perturbations is obtained through matching of analytical solutions at the jet boundaries. The equation is solved analytically and numerically for different parameters of jets and surrounding plasma. The analytical solution is accompanied by a numerical simulation of fully non-linear magnetohydrodynamic (MHD) equations for a particular situation of solar type II spicules. Results. Magnetohydrodynamic triangular jets are unstable to the dynamic kink instability depending on the Alfvén Mach number (the ratio of flow to Alfvén speeds) and the ratio of internal and external densities. When the jet has the same density as the surrounding plasma, only super-Alfvénic flows are unstable. However, denser jets are also unstable in a sub-Alfvénic regime. Jets with an angle to the ambient magnetic field have much lower thresholds of instability than field-aligned flows. Growth times of the kink instability are estimated to be 6−15 min for type I spicules and 5−60 s for type II spicules matching with their observed lifetimes. The numerical simulation of full non-linear equations shows that the transverse kink pulse locally destroys the jet in less than a minute in type II spicule conditions. Conclusions. Dynamic kink instability may lead to the full breakdown of MHD flows and consequently to an observed disappearance of spicules.