Kelvin--Helmholtz instability of magnetohydrodynamic waves propagating on solar surges

Abstract

In the present paper, we study the evolutionary conditions for Kelvin--Helmholtz (KH) instability in a high-temperature solar surge observed in NOAA AR11271 using the Solar Dynamics Observatory data on 2011 August 25. We study the propagation of normal MHD modes in a flux tube considering the two cases, notably of untwisted magnetic flux tube and the twisted one. The numerical solution to the dispersion relation shows that the kink ($m = 1$) wave traveling in an untwisted flux tube becomes unstable if the jet speed exceeds $1060$ km\,s$^{-1}$ -- a speed which is inaccessible for solar surges. A weak twist (the ratio of azimuthal to longitudinal magnetic field component) of the internal magnetic field in the range of $0.025$--$0.2$ does not change substantially the critical flow velocity. Thus, one implies that, in general, the kink mode is stable against the KH instability. It turns out, however, that the $m = -2$ and $m = -3$ MHD modes can become unstable when the twist parameter has values between $0.2$ and $0.4$. Therefore, the corresponding critical jet speed for instability onset lies in the range of $93.5$--$99.3$ km\,s$^{-1}$. The instability wave growth rate, depending on the value of the wavelength, is of the order of several dozen inverse milliseconds. It remains to be seen whether these predictions will be observationally validated in future in the coronal jet-like structures in abundant measure.