Laplace-Fourier linear stability analysis of non-relativistic magnetized rotational jets: mode identification by Hamiltonian analysis and the occurrence of mode transitions

Abstract: In this paper, we conduct a linear stability analysis of magnetized and/or rotating jets propagating in ambient matter that is also magnetized and/or rotating, having in mind the application to the jet penetrating the core/envelope of a massive star. We solve the linearized magneto-hydrodynamic (MHD) equations in the non-relativistic regime by Laplace transform in time and Fourier transform in space. In this formulation all unstable modes with the same translational and azimuthal wave numbers can be obtained simultaneously by searching for pole singularities in the complex plane. In order to determine unambiguously their driving mechanisms, we evaluate the second-order perturbation of the MHD Hamiltonian for individual eigenfunctions derived at these singular points. We identify in our non-rotating models the Kelvin-Helmholtz instability (KHI) as one of the shear-driven modes and the current-driven instability such as the kink instability (KKI). In rotational models we also find the magnetorotational instability (MRI) as another shear-driven mode. In some cases, we find that a mode changes its character continuously from KKI to KHI (and vice versa) or from MRI to KHI as the jet velocity is increased.