How Plasma Properties of the Fanaroff-Riley Jet can Shape its Morphology

Abstract: Extragalactic jets are broadly classified into two categories based on radio observations: core-brightened jets, known as Fanaroff-Riley Type I (FR I), and edge-brightened jets, classified as Type II (FR II). This FR dichotomy may arise due to variation in the ambient medium and/or the properties of the jet itself, such as injection speed, temperature, composition, magnetization, etc. To investigate this, we perform large-scale three-dimensional magnetohydrodynamic (3D-MHD) simulations of low-power, supersonic jets extending to kiloparsec scales. We inject a jet beam carrying an initially toroidal magnetic field into a denser, unmagnetized, and stratified ambient medium through a cylindrical nozzle. Our simulations explore jets with varying injection parameters to investigate their impact on morphology and emission properties. Furthermore, we examine jets with significantly different plasma compositions, such as hadronic and mixed electron-positron-proton configurations, to study the conditions that may drive transitions between FR I and FR II morphologies. We find that, under the same injection parameters, mixed plasma composition jets tend to evolve into FR I structures. In contrast, electron-proton jets exhibit a transition between FR I and FR II morphologies at different stages of their evolution.

• The paper establishes that plasma properties—such as composition, temperature, and magnetization—are key determinants of the observed FR I/FR II jet morphologies.
• High-resolution 3D MHD simulations reveal that variations in Mach number, lepton fraction, and magnetic field strength trigger transitions via mechanisms like kink instabilities and shock disruptions.
• The study highlights practical implications for AGN observations, suggesting synchrotron mapping and spectral analysis to infer jet composition and evolving morphology.

Morphological Determination of Fanaroff-Riley Jets via Plasma Properties: An Expert Analysis

Introduction

The Fanaroff-Riley dichotomy distinguishes radio jets emanating from AGNs into two principal classes: FR I, exhibiting core-brightened, diffuse morphologies, and FR II, characterized by edge-brightened structures and terminal hotspots. The source of this dichotomy—central engine characteristics, ambient interaction, or intrinsic jet properties—has remained an unresolved domain. The paper "How Plasma Properties of the Fanaroff-Riley Jet can Shape its Morphology" (2601.09349) undertakes a systematic numerical investigation using high-resolution 3D magnetohydrodynamic (MHD) simulations to probe the role of jet injection speed, temperature, magnetization, and plasma composition on large-scale jet evolution, emission, and the resultant FR classification.

Methodology

The study utilizes a non-relativistic, ideal MHD formulation augmented with the CR EoS, which employs a variable adiabatic index $\Gamma$ to encode multispecies thermodynamics. Six simulation setups are explored, controlling jet velocity, Mach number, ambient/jet temperature, magnetic field strength, and the proton-to-lepton ratio ($\xi$) in the plasma. The computational framework employs a second-order Godunov finite volume method, HLLD Riemann solver, TVD-RK2 temporal integration, and hyperbolic divergence cleaning. Initial conditions comprise a low-power, supersonic jet injected into a King-profile stratified ambient medium, carrying only toroidal magnetic fields.

Jet Evolution and Morphological Outcomes

Reference Jet Morphology and Temporal Transitions

In the baseline (Model-REF), the jet starts as a collimated, supersonic structure, forming distinct forward shocks and corresponding Mach cones. As the simulation progresses, interaction with the ambient medium leads to weakening of the terminal shock and increasing diffusion of the jet head. Notably, morphological transitions from FR I to FR II and vice versa are observed depending on the evolutionary epoch and head propagation characteristics.

Figure 1: Jet morphology in X-Z plane for Model-REF at several epochs, highlighting transitions between collimated and diffusive states.

The accompanying synthetic synchrotron maps reveal periods where emission is distributed along the jet beam with faint outer lobes (FR I-like), contrasted by epochs where a dominant terminal hotspot forms (FR II-like).

Figure 2: Synthetic synchrotron $I(x,z)$ maps for Model-REF at two late stages; both FR I and FR II features are observed.

Mach Number, Magnetization, and Ambient Temperature Effects

Increasing jet Mach number (Model-HYP) leads to persistent FR II morphology, with minimal diffusion and efficient energy delivery to the jet head producing stable terminal shocks and hotspots. Conversely, higher ambient and jet temperature (Model-HOT) results in decreased Mach number and enhanced thermal pressure support, promoting lateral expansion and susceptibility to kink instabilities. The jet in this regime is rapidly destabilized at its head, with the collimated beam giving way to a broad diffused region—characteristic of FR I morphology.

Figure 3: Volume rendering of Model-HOT jet showing strong kink instability and transition to a diffused jet head.

Figure 4: Model-HOT jet evolution depicts beam destabilization and FR I morphology in synthetic emission.

Enhanced magnetization (Model-MAG) initially facilitates beam collimation, but also increases vulnerability to current-driven non-axisymmetric instabilities, with observable morphological switching throughout the simulation.

Figure 5: Model-MAG shows transient FR I/II morphologies due to interplay of collimation and disruption by kink instability.

Plasma Composition and Lepton Fraction Impacts

Models with reduced proton fractions (CMp5, CMp2: $\xi<1$) display prominent changes in jet dynamics. Higher lepton content augments the thermal energy for a given $T$, lowering the Mach number and suppressing the stability of the Mach disk. These jets consistently evolve into FR I morphologies. The diffused regions dominate the jet head, the length scale of propagation is reduced, and the synthetic emission is strongly beam-dominated with faint lobes.

Figure 6: Volume rendering for Model-CMp5 reveals progressive beam disruption resulting in persistent FR I characteristics.

Figure 7: Model-CMp5 tracer and emission maps confirm FR I morphology dominated by gradual energy dissipation along the beam.

Figure 8: Model-CMp2 demonstrates stagnation and early disruption of the jet, with the emission map lacking a terminal shock region.

Instability Growth and Jet Head Propagation

Quantitative analysis of jet head positions and corresponding kink ($m=1$) mode power reveals direct correlation between plasma parameters, instability growth, and FR morphology. Diffusive head length and instability amplitude are maximal for high-lepton, hot, or highly magnetized jets. Models with sufficiently high jet velocities, even at lower Mach numbers, can evade significant kink disruption, maintaining FR II morphology.

Figure 9: Left: Axial propagation of jet beam and diffused region for all models; Right: Kink ($m=1$) mode power temporal evolution for select models.

Comparisons of advection time with kink growth timescale provide a predictive metric: jets for which $$\mathcal{T}_{\mathrm{adv}}/\mathcal{T}_{\mathrm{kink}} \geq 1$$ are disrupted, favoring FR I outcomes. Fast jets with strong axial $B_z$ components suppress kink growth, sustaining FR II morphologies.

Figure 10: Ratio of advection time to kink growth timescale along the jet axis for five models; only models with $$\mathcal{T}_{\mathrm{adv}}/\mathcal{T}_{\mathrm{kink}} < 1$$ retain collimation and avoid FR I transitions.

Theoretical and Practical Implications

This study establishes a set of plasma-physical controls governing Fanaroff-Riley classification. Contradicting the notion that macroscopic jet power or velocity alone dictate morphology, the findings highlight the central impact of composition, temperature, and instability-driven dynamics. The consistent evolution to FR I morphologies for lepton-rich (low-$\xi$0) jets, even with identical injection parameters, is a strong claim that can inform future observational discrimination of jet content in AGNs. The dynamical connection between Mach disk weakening, kink instability, and FR I morphology is robust across parameter space. The results provide simulation-derived predictions for morphological transitions at varying epochs and in response to environmental changes.

Theoretically, the variable-$\xi$1 EoS with composition dependence offers a physically complete prescription for jet thermodynamics and radiative output. Practically, these results motivate direct observational campaigns utilizing synchrotron maps and radio spectral analysis to infer jet baryon loading, employing morphology as a secondary diagnostic. Simulations integrating improved radiation transport and 3D polarization signatures (see [uvs24]) could refine links between instability growth and observable properties.

Conclusion

The morphological fate of extragalactic radio jets emerges as a non-trivial output of multi-parametric plasma properties: jet Mach number, magnetization, thermodynamic state, and baryon/lepton ratio. FR I and FR II structures are not solely determined by injection velocity or AGN power, but by a confluence of intrinsic jet instabilities modulated by composition and environment. Transitioning or hybrid morphologies can arise naturally within the same system over time.

Strong numerical outcomes—including persistent FR I morphology for lepton-rich, thermally-augmented, or kink-unstable jets—underline the necessity of high-fidelity three-dimensional simulations with composition-sensitive EoS for interpreting AGN jet dynamics. These findings have direct implications for the interpretation of radio galaxy survey data and the design of future MHD simulation campaigns aimed at resolving plasma-physical origins of AGN jet diversity.