Kelvin-Helmholtz instability in coronal mass ejecta in the lower corona

¹ Faculty of Physics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
e-mail: izh@phys.uni-sofia.bg
² Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
³ Abastumani Astrophysical Observatory at Ilia State University, 3/5 Cholokashvili Avenue, 0162 Tbilisi, Georgia
⁴ Department of Physics, DSB Campus, Kumaun University, 263 002 Nainital, India

Received: 12 August 2014
Accepted: 17 December 2014

Abstract

Aims. We modelled an imaged Kelvin-Helmholtz (KH) instability in coronal mass ejections (CME) in the lower corona by investigating conditions under which kink (m = 1) and m = −3 magnetohydrodynamic (MHD) modes in a uniformly twisted flux tube moving along its axis become unstable.

Methods. We employed the dispersion relations of MHD modes derived from the linearised MHD 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 (taken from observational data) and various mass flow velocities.

Results. It is shown that the stability of the modes 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 Alfvén Mach number (the ratio of the tube velocity to Alfvén speed inside the flux tube). For a twisted magnetic flux tube at a density contrast of 0.88, a background magnetic field ratio of 1.58, and a normalised magnetic field twist of 0.2, the critical speed for the kink (m = −3) mode (where m is the azimuthal mode number) is 678 km s^-1 , just as observed. The growth rate for this harmonic at KH wavelength of 18.5 Mm and ejecta width of 4.1 Mm is equal to 0.037 s^-1, in agreement with observations. KH instability of the m = −3 mode may also explain why the KH vortices are seen only at one side of arising CME.

Conclusions. The good agreement between observational and computational data shows that the imaged KH instability on CME can be explained in terms of an emerging KH instability of the m = −3 MHD mode in twisted magnetic flux tubes moving along its axis.