Decay of the toroidal field in magnetically driven jets

A 3D simulation of a non-relativistic, magnetically driven jet propagating in a stratified atmosphere is presented, covering about three decades in distance and two decades in sideways expansion. The simulation captures the jet acceleration through the critical surfaces and the development of (kink-)instabilities driven by the free energy in the toroidal magnetic field component. The instabilities destroy the ordered helical structure of the magnetic field, dissipating the toroidal field energy on a length scale of about 2-15 times the Alfven distance. We compare the results with a 2.5D (axisymmetric) simulation, which does not become unstable. The acceleration of the flow is found to be quite similar in both cases, but the mechanisms of acceleration differ. In the 2.5D case approximately 20% of the Poynting flux remains in the flow, in the 3D case this fraction is largely dissipated internally. Half of the dissipated energy is available for light emission; the resulting radiation would produce structures resembling those seen in protostellar jets.

💡 Research Summary

This paper presents a comprehensive three‑dimensional (3D) ideal magnetohydrodynamic (MHD) simulation of a non‑relativistic, magnetically driven jet propagating through a stratified atmosphere, extending over three orders of magnitude in distance (up to ~1000 R₀) and two orders of magnitude in lateral expansion. The authors compare the 3D run with an axisymmetric 2.5‑dimensional (2.5D) simulation that uses the same initial magnetic field configuration, boundary conditions, and driving rotation profile, allowing a direct assessment of the role of non‑axisymmetric instabilities.

Simulation setup – The jet is launched from a rotating “disk” at the lower boundary (radius R_b) within a static gravitational potential Φ ∝ r⁻¹. The initial magnetic field is a linear combination of a monopole (ψ_mono ∝ 1 − cos ϑ) and a parabolic field (ψ_para) weighted by ζ = 30, which yields a strongly collimating configuration. The plasma β on the axis is set to 1/9, the opening angle at the launch point is 5°, and the Alfvénic Mach number of the rotating footpoints is M_A = 0.1. A spherical grid with logarithmic spacing in radius and uniform angular spacing is employed (768 × 128 × 128 cells for the 3D case, 768 × 96 for the 2.5D case).

Acceleration and critical surfaces – Most of the jet acceleration occurs below r ≈ 100 R_b, where the flow passes the sonic, Alfvén, and fast‑magnetosonic surfaces. The Alfvén surface is located primarily near the jet boundary because the rigid rotation profile concentrates toroidal field generation there. By r ≈ 100 R_b the jet reaches about 80 % of its asymptotic speed.

Development of non‑axisymmetric kink instabilities – In the 3D simulation, m = 1 and higher‑order kink modes grow rapidly once the toroidal magnetic pressure becomes dominant. The toroidal component B_φ decays over a length scale of roughly 2–15 r_A (Alfvén radii). This decay is accompanied by a substantial reduction of the Poynting flux: roughly 80 % of the initial electromagnetic energy is dissipated internally, whereas in the 2.5D run the toroidal field remains largely intact and about 20 % of the Poynting flux survives to large distances.

Impact on collimation and mass loading – The 2.5D jet maintains a narrow, nearly conical shape after an initial modest decrease in opening angle. The 3D jet, however, exhibits a fluctuating boundary due to the instabilities, resulting in a slightly larger, more irregular opening angle. Mass flux through spherical shells is modestly higher in the 3D case and shows temporal fluctuations beyond r ≈ 200 R_b, suggesting enhanced entrainment of ambient material caused by the turbulent motions.

Energy conversion and radiative implications – The dissipation of toroidal magnetic energy converts magnetic enthalpy into thermal energy. The authors estimate that about half of the dissipated energy could be radiated away. A simple emissivity model based on temperature and magnetic field strength produces synthetic volume‑rendered images that display bright knots and wiggles, reminiscent of observed structures in protostellar jets (e.g., HH 30) and the inner regions of AGN jets such as M87. The knots travel at a substantial fraction of the bulk flow speed, sometimes merging or fading, providing a plausible explanation for observed knotty jet morphologies without invoking internal shocks.

Conclusions and broader relevance – The study demonstrates that in strongly collimated, magnetically driven jets, kink‑type instabilities can efficiently dissipate the toroidal magnetic field on relatively short distances from the source. This process alters the acceleration mechanism: instead of relying solely on magnetic pressure gradients that persist when B_φ is conserved, the jet gains additional acceleration from the steepened magnetic pressure gradient caused by B_φ decay. The results support the idea that many astrophysical jets become kinetically dominated already within a few Alfvén radii, consistent with VLBI observations of AGN jets that show low magnetization on parsec scales. Moreover, the work suggests that magnetic dissipation, rather than only internal shocks, may play a significant role in powering the observed radiation from both protostellar and extragalactic jets.

Overall, the paper provides a valuable quantitative bridge between idealized axisymmetric jet models and realistic three‑dimensional dynamics, highlighting the importance of non‑axisymmetric magnetic instabilities in shaping jet structure, energetics, and observable signatures.