Instabilities at recollimation shocks in MHD jets

TL;DR

This study tackles how jet magnetization and physical conditions shape downstream instabilities beyond the first recollimation shock in relativistic AGN jets. Using a two-step approach, it combines high-resolution 2D axisymmetric RMHD simulations with 3D runs and a linear centrifugal instability analysis to map where and when instability can grow. Key findings show that centrifugal instability can develop even in moderately magnetized jets ($sigma$ ~ 0.1) under suitable local curvature, with magnetic tension delaying but not guaranteeing stability; 3D dynamics reveal non-axisymmetric modes and turbulence that 2D models cannot capture. The results highlight the intricate interplay between magnetic confinement, jet geometry, and external pressure, with direct implications for interpreting variability and polarization signatures in AGN jets.

Abstract

AGN jet structure and stability remain uncertain; recollimation shocks are linked to morphology and variability, but the role of downstream instabilities is still unclear. We aim to investigate how jet magnetization and other physical parameters influence the development of instabilities beyond the first recollimation shock. In particular, we focus on identifying the conditions under which the centrifugal instability (CFI) is effective. We perform high-resolution 2D and 3D simulations using the relativistic magnetohydrodynamics code PLUTO. The jets are initialized with a conical geometry and propagate into an ambient medium, and we follow by axisymmetric simulations how they evolve towards a steady-state. In 2D we explore a range of magnetizations (from 0 to 1), pressure contrasts, and inertia ratios to characterize the formation and evolution of recollimation shocks. The results are further evaluated using linear stability analysis to assess the growth and suppression of CFI. Finally, we perform 3D simulations of unstable and stable jets. We discuss how the different parameters of the axisymmetric steady solutions influence the location and strength of recollimation. We find that, even in moderately magnetized jets, $σ$=0.1, the CFI can still develop under suitable local conditions and disrupt the jet structure. This instability is governed by the jet radius, curvature, Lorentz factor, and magnetization, and is not always predictable from injection conditions. While magnetization can delay or locally suppress instability growth, it does not guarantee long-term jet stability. Our 3D results highlight the limitations of 2D models in capturing non-axisymmetric and nonlinear effects, and underline the complex interplay between magnetic confinement and destabilizing mechanisms. These findings have implications for interpreting variability, and polarization structure in AGN jets.

Figures (19)

• Figure 1: Profiles along the $z$-axis at position $x=0$ of the normalized Lorentz factor for the 2D simulations presented in Tab.\ref{['tab:parameters']}. The normalization is taken at the position $(0,0)$ for simulations A, B, C, and D with magnetization $\sigma = 0$, $0.1$, and $1$.
• Figure 2: For the 2D simulation A_0.1 with magnetization $\sigma = 0.1$, the logarithmic maps of total pressure, thermal pressure, magnetic pressure, and total magnetization are shown. The initial parameters are: density ratio $\nu = 10^{-5}$, Lorentz factor $\Gamma = 10$, jet opening angle $\theta_\text{jet} = 0.1$, and pressure ratio $P_\text{ratio} = 10^{-3}$. The maps correspond to the final time step $t = 3000 \, t_\text{cr}$ in units of $z_0/c$.
• Figure 3: Streamlines (initialized from the same starting point) overlaid on the spatial distribution of $\sigma_{\mathrm{tor}}/\Gamma^2$ for all simulation runs. This ratio serves as a local diagnostic for the onset of centrifugal instability, with low values marking regions where the jet is most susceptible to curvature-driven perturbations. In the widest jets (e.g. Case D_0.1), outer streamlines would likely reach regions satisfying the CFI criterion; here we show a representative streamline to illustrate the overall trend.
• Figure 4: Left: Streamlines for cases A_0.1--D_0.1 (as in Fig. \ref{['fig:2Dsigma01']}), starting at $x_0 = 0.082, 0.098, 0.091,$ and $0.124$ respectively, with curvature and the ratio $R_{\mathrm{j,max}}/R_{\mathrm{c}}$. Right: Profiles of $\sigma_{\mathrm{tor}}/\Gamma^{2}$ versus $x$ at $z = z_{x_{\max}}$, with vertical lines marking $x_{\max} = R_{\mathrm{j,max}}$.
• Figure 5: Comparison of radial profiles of toroidal magnetization $\sigma_{\mathrm{tor}}$ (blue), Lorentz factor $\Gamma$ (orange), rest-mass density $\rho$ (green), and enthalpy $h/\rho$ (red) at $z = z_{\max}$ for Case A_0.1 (top) and Case D_0.1 (bottom). Case A_0.1 shows smooth, monotonic profiles, whereas Case D_0.1 exhibits sharp gradients and non-monotonic behavior, underscoring the complexity of its internal structure. The vertical dashed line marks the position of $x_{\max}$ determined from the streamline analysis. Profiles are plotted on a logarithmic scale.