On the linear stability of magnetized jets without current sheets – relativistic case

In our prior papers, we considered the non-relativistic linear stability analysis of magnetized jets that do not have current sheet at the boundary. In this paper, we extend our analysis to relativistic jets. In order to find the unstable modes of current sheet-free, magnetized relativistic jets, we linearize full relativistic magnetohydrodynamics equations and solve them numerically. We find the dispersion relation of the pinch and kink mode instabilities. By comparing the dispersion relations of a mildly relativistic jet (Lorentz factor 2) with a moderately relativistic jet (Lorentz factor 10), we find that the jet with a higher Lorentz factor is significantly more stable in both pinch and kink modes. We show that inclusion of the current sheet-free magnetic field in the jet further enhances the stability. Both pinch and kink mode instabilities become progressively more stable with increasing magnetization. We also show a scaling relation between the maximum temporal growth rate of the unstable mode and the Lorentz factor of the jet. The maximum temporal growth rates of the unstable modes are inversely proportion to the Lorentz factors for most of the modes that we study. However, for the fundamental pinch mode, it is inversely proportional to the square of the Lorentz factor. This very beneficial scaling relation holds regardless of the presence of a magnetic field.