Linear stability analysis of relativistic magnetized jets
Authors: Sinnis Charalampos , Vlahakis Nektarios 
Published: October 2023

Aims. We study the stability properties of relativistic magnetized astrophysical jets in the linear regime. We consider cylindrical cold jet configurations with constant Lorentz factor and constant density profiles across the jet. We are interested in probing the properties of the instabilities and identifying the physical quantities that affect the stability profile of the outflows.
Methods. We conducted a linear stability analysis on the unperturbed outflow configurations we are interested in. We focus on the unstable branches, which can disrupt the initial outflow. We proceeded with a parametric study regarding the Lorentz factor, the ratio of the rest mass density of the jet to that of the environment, the magnetization, and the ratio of the poloidal component of the magnetic field to its toroidal counterpart measured on the boundary of the jet. We also consider two choices for the pressure of the environment, either thermal or magnetic, and check if this choice affects the results. Additionally, we applied a WKBJ method at the radius of the jet in order to study the local stability properties. Finally, we adapted the jet configuration in Cartesian geometry and compared the planar flow results with the results of the cylindrical counterpart.
Results. While investigating the stability properties of the configurations, we observed the existence of a specific solution branch, which showcases the growth timescale of the instability comparable to the light crossing time of the jet radius. Our analysis focuses on this solution. All of the quantities considered for the parametric study affect the behavior of the mode while the magnetized environments seem to hinder its development compared to the hydrodynamic equivalent. Also, our analysis of the eigenfunctions of the system alongside the WKBJ results show that the mode develops in a very narrow layer near the boundary of the jet, establishing the notion of locality for the specific solution. The results indicate that the mode is a relativistic generalization of the Kelvin-Helmholtz instability. We compare this mode with the corresponding solution in Cartesian geometry and define the prerequisites for the Cartesian Kelvin-Helmholtz to successfully approximate the cylindrical counterpart.
Conclusions. We identify the Kelvin-Helmholtz instability for a cold nonrotating relativistic jet carrying a helical magnetic field. Our parametric study reveals the important physical quantities that affect the stability profile of the outflow and their respective value ranges for which the instability is active. The Kelvin-Helmholtz mode and its stability properties are characterized by the locality of the solutions, the value of the angle between the magnetic field and the wavevector, the linear dependence between the mode’s growth rate and the wavevector, and finally the stabilization of the mode for flows that are ultrafast magnetosonic. The cylindrical mode can be approximated successfully by the Cartesian Kelvin-Helmholtz instability whenever certain length scales are much larger than the jet radius.