Linear stability analysis of magnetized relativistic jets: the non-rotating case (original) (raw)
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Stability analysis of magnetized astrophysical relativistic jets without current sheets
Proceedings of High Energy Phenomena in Relativistic Outflows VII — PoS(HEPRO VII), 2020
Astrophysical jets are observed as stable structures, extending in lengths several times their radii. The role of various instabilities and how they affect the observed jet properties has not been fully understood. Using the ideal relativistic MHD equations to describe jet dynamics we aim to study the stability properties through linear analysis. In this work we probe stability properties of jets without current sheets and low magnetizations, moving with mildly relativistic Lorentz factors. In particular we find the dispersion relation for kink (m = ±1) and pinch (m = 0) modes. In the former we find that a wide range of wavelengths ∼ 1-1000 jet radii equally contributes to the instability with growth rates ∼ a few 10 −3 c/r j , while in the latter the large wavelengths are more unstable, giving similar growth rates. Evaluating the eigenfunctions of the instability we see that they attain their highest values near the jet boundary, indicating that the instabilities are most likely of a Kelvin-Helmholtz type rather than current driven.
Astronomy & Astrophysics, 2008
We investigate the linear stability properties of the plane interface separating two relativistic magnetized flows in relative motion. The two flows are governed by the (special) relativistic equations for a magnetized perfect gas in the infinite conductivity approximation. By adopting the vortex-sheet approximation, the relativistic magnetohydrodynamics equations are linearized around the equilibrium state and the corresponding dispersion relation is derived and discussed. The behavior of the configuration and the regimes of instability are investigated following the effects of four physical parameters, namely: the flow velocity, the relativistic and Alfv\'enic Mach numbers and the inclination of the wave vector on the plane of the interface. From the numerical solution of the dispersion relation, we find in general two separate regions of instability, associated respectively with the slow and fast magnetosonic modes. Modes parallel to the flow velocity are destabilized only for sufficiently low magnetization. For the latter case, stabilization is attained, additionally, at sufficiently large relativistic velocities between the two flows in relative motion. The relevance of these results to the study of the stability of astrophysical jets is briefly commented.
Stability of Relativistic Force-free Jets
Astrophysical Journal - ASTROPHYS J, 2009
We consider a two-parameter family of cylindrical force-free equilibria, modeled to match numerical simulations of relativistic force-free jets. We study the linear stability of these equilibria, assuming a rigid impenetrable wall at the outer cylindrical radius R j . We find that equilibria in which the Lorentz factor γ(R) increases monotonically with increasing radius R are stable. On the other hand, equilibria in which γ(R) reaches a maximum value at an intermediate radius and then declines to a smaller value γ j at R j are unstable. The most rapidly growing mode is an m = 1 kink instability which has a growth rate ∼ (0.4/γ j )(c/R j ). The e-folding length of the equivalent convected instability is ∼ 2.5γ j R j . For a typical jet with an opening angle θ j ∼ few/γ j , the mode amplitude grows weakly with increasing distance from the base of the jet, much slower than one might expect from a naive application of the Kruskal-Shafranov stability criterion.
Physical Review E, 2013
We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon such schemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numerical discretization renders them unstable. We include numerical viscosity to restore numerical stability. In relativistic flows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in our KH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbed velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining unperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in the nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvénic Mach number M A. We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, and intermediate turbulence. Sufficiently strong fields (M A < 6) completely suppress vortex formation. Maximum jet deceleration, and viscous dissipation, occur for intermediate vortex-disruptive fields, while electromagnetic energy is maximized for the strongest fields which allow vortex formation. Highly relativistic flows destabilize the system, supporting modes with near-maximum growth at smaller wavelengths than the shear width of the velocity. This helps to explain early numerical breakdown of highly relativistic simulations using numerical viscosity, a long-standing problem. While magnetic fields generally stabilize the system, we have identified many features of the complex and turbulent reorganization that occur for sufficiently weak fields in RMHD flows, and have described the transition from disruptive to stabilizing fields at M A ≈ 6. Our results are qualitatively similar to observations of numerous jets, including M87, whose knots may exhibit vortex-like behavior. Furthermore, in both the linear and nonlinear analyses, we have successfully unified the HD, MHD, RHD, and RMHD regimes.
Magnetic field structure of relativistic jets without current sheets
Monthly Notices of the Royal Astronomical Society, 2012
We present an analytical class of equilibrium solutions for the structure of relativistic sheared and rotating magnetized jets that contain no boundary current sheets. We demonstrate the overall dynamical stability of these solutions and, most importantly, a better numerical resistive stability than the commonly employed force-free structures which inevitably require the presence of dissipative surface currents. The jet is volumetrically confined by the external pressure, with no pressure gradient on the surface. We calculate the expected observed properties of such jets. Given the simplicity of these solution we suggest them as useful initial conditions for relativistic jet simulations.
Internal instabilities in magnetized jets
Monthly Notices of the Royal Astronomical Society, 2018
We carry out an extensive linear stability analysis of magnetized cylindrical jets in a global framework. Foregoing the commonly invoked force-free limit, we focus on the small-scale, internal instabilities triggered in regions of the jet dominated by a toroidal magnetic field, with a weak vertical field and finite thermal pressure gradient. Such regions are likely to occur far from the jet source and boundaries, and are potential sites of magnetic energy dissipation that is essential to explain the particle acceleration and radiation observed from astrophysical jets. We validate the local stability analysis of Begelman by verifying that the eigenfunctions of the most unstable modes are radially localized. This finding allows us to propose a generic stability criterion in the presence of a weak vertical field. A stronger vertical field with a radial gradient complicates the stability criterion, due to the competition between the destabilizing thermal pressure gradient and stabilizing magnetic pressure gradients. Nevertheless, we argue that the jet interiors generically should be subject to rapidly growing small-scale instabilities, capable of producing current sheets that lead to dissipation. We identify some new instabilities, not predicted by the local analysis, which are sensitive to the background radial profiles but have smaller growth rates than the local instabilities, and discuss the relevance of our work to the findings of recent numerical jet simulations.
Magnetic Dissipation in Relativistic Jets
Galaxies, 2016
The most promising mechanisms for producing and accelerating relativistic jets, and maintaining collimated structure of relativistic jets involve magnetohydrodynamical (MHD) processes. We have investigated the magnetic dissipation mechanism in relativistic jets via relativistic MHD simulations. We found that the relativistic jets involving a helical magnetic field are unstable for the current-driven kink instability, which leads to helically distorted structure in relativistic jets. We identified the regions of high current density in filamentary current sheets, indicative of magnetic reconnection, which are associated to the kink unstable regions and correlated to the converted regions of magnetic to kinetic energies of the jets. We also found that an over-pressured relativistic jet leads to the generation of a series of stationary recollimation shocks and rarefaction structures by the nonlinear interaction of shocks and rarefaction waves. The differences in the recollimation shock structure due to the difference of the magnetic field topologies and strengths may be observable through mm-VLBI observations and space-VLBI mission.
Magnetic acceleration of relativistic jets
2007
This is a brief review of the recent developments in the theory of magnetic acceleration of relativistic jets. We attempt to explain the key results of this complex theory using basic physical arguments and simple calculations. The main focus is on the standard model, which describes steady-state axisymmetric ideal MHD flows. We argue that this model is over-restrictive and discuss various alternatives.
Structure and Stability of Keplerian Magnetohydrodynamic Jets
Astrophysical Journal, 2000
MHD jet equilibria that depend on source properties are obtained using a simplified model for stationary, axisymmetric and rotating magnetized outflows (Lery et al.). The present rotation laws are more complex than previously considered and include a Keplerian disc. The ensuing jets have a dense, current-carrying central core surrounded by an outer collar with a return current. The intermediate part of the jet is almost current-free and is magnetically dominated. Most of the momentum is located around the axis in the dense core, and this region is likely to dominate the dynamics of the jet. We address the linear stability and the nonlinear development of instabilities for our models using both analytical and 2.5 dimensional numerical simulations. The instabilities seen in the simulations develop with a wavelength and growth time that are well matched by the stability analysis. The modes explored in this work may provide a natural explanation for knots observed in astrophysical jets.
Magnetic collimation of relativistic outflows in jets with a high mass flux
Monthly Notices of the Royal Astronomical Society, 2002
Self-collimation of relativistic magnetohydrodynamic (MHD) plasma outflows is inefficient in a single-component model consisting of a wind from a stellar object or an accretion disc, in the sense that the collimated portion of the mass and magnetic fluxes is uncomfortably low. The theory of magnetic collimation is applied here to a two-component model consisting of a relativistic wind-type outflow from a central source and a non-relativistic wind from the surrounding disc. Through a direct numerical simulation of the MHD flow in the nearest zone by the relaxation method and a solution of the steady-state problem in the far zone, it is shown that in this two-component model it is possible to collimate into cylindrical jets, in principle, up to all the mass and magnetic fluxes that are available from the central source. In such a case the non-relativistic disc-wind plays the role of the jet collimator. It is also shown that this collimation is accompanied by the formation of a sequence of shock waves at the interaction interface of the relativistic and non-relativistic outflows.