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arxiv: 2606.19153 · v1 · pith:FIPIFYHZnew · submitted 2026-06-17 · 🌌 astro-ph.HE

2D magnetohydrodynamic jet simulations: properties of recollimation shocks

Stella Boula , Fabrizio Tavecchio , Gianluigi Bodo , Nektarios Vlahakis , Paolo Coppi This is my paper

Pith reviewed 2026-06-26 19:49 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords recollimation shocksrelativistic jetsmagnetohydrodynamicsAGN jetscentrifugal instabilitysynchrotron emissionRMHD simulations
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The pith

In the magnetically dominated regime, the recollimation distance ratio z_MHD/z_HD scales as (B₀²/P_ext)^{-1/3}.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper runs 2D axisymmetric relativistic magnetohydrodynamic simulations of overpressured jets to measure how magnetization, density contrast, pressure ratio, and magnetic pitch control the location and strength of the first recollimation shock. It reports that magnetic pressure and tension reduce the distance to this shock relative to pure hydrodynamics, and that the reduction settles onto a clean power-law once the jet is magnetically dominated. The same runs show that toroidal fields produce compact, bright emission knots while poloidal fields spread the emission and move the shock farther out. Local conditions for centrifugal instability are diagnosed from the toroidal magnetization and streamline curvature at the recollimation site.

Core claim

In the magnetically dominated regime, the ratio of the magnetized recollimation distance (z_MHD) to its purely hydrodynamic counterpart (z_HD) converges onto a power-law scaling, z_MHD/z_HD ∝ (B₀²/P_ext)^{-1/3}, where B₀ is the initial magnetic field and P_ext the external pressure.

What carries the argument

The recollimation distance ratio z_MHD/z_HD, which quantifies how magnetic forces limit jet expansion compared with the hydrodynamic case.

If this is right

  • Recollimation distance decreases monotonically as magnetization increases.
  • High density contrast or high internal pressure further compresses the magnetic field.
  • A dominant toroidal field produces highly boosted, localized synchrotron knots at the shock.
  • A strong poloidal field yields diffuse emission and shifts the recollimation zone downstream.
  • Centrifugal-instability regions are set by the local toroidal magnetization over Lorentz factor squared and by the streamline curvature during recollimation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the scaling survives in three dimensions it could be inverted to estimate jet magnetization from the locations of stationary radio features.
  • The toroidal versus poloidal difference implies that polarization maps could distinguish which field geometry dominates the observed knots.
  • The same geometric conditions that set CFI susceptibility may also control the onset of other fluid instabilities once the flow becomes three-dimensional.

Load-bearing premise

Two-dimensional axisymmetric geometry together with the chosen initial magnetic-field configurations are sufficient to capture the essential recollimation physics without three-dimensional effects or alternate launch conditions changing the reported scaling.

What would settle it

A sample of AGN jets with independent magnetization estimates whose observed recollimation distances deviate systematically from the (B₀²/P_ext)^{-1/3} relation would falsify the scaling.

Figures

Figures reproduced from arXiv: 2606.19153 by Fabrizio Tavecchio, Gianluigi Bodo, Nektarios Vlahakis, Paolo Coppi, Stella Boula.

Figure 1
Figure 1. Figure 1: Anatomy of the fiducial magnetized jet (Case C3: σ = 1, light jet). Far Left: 1D axial profiles along r = 0, showing the conversion of internal energy (Pth dashed blue) to bulk kinetic energy (Γ, solid red), followed by a sharp recollimation shock at z ≈ 3.0. Center Columns: 2D maps of density, thermal pressure, Lorentz factor, and plasma β. The white dashed line is a representative streamline marking the … view at source ↗
Figure 2
Figure 2. Figure 2: Axial profiles of the Lorentz factor normalized to its injection value, Γ/Γ0, as a function of the distance z along the jet axis. Panels (a)– (f) correspond to different model families (see [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Radial profiles of the thermal pressure, the magnetic pressure and its components, and total pressure for the C-Case model family at z0 and zmax. ening of the shocks and the systematic decrease of zr , which is the distance where the recollimation shock reaches the axis. The same effect is present to the following recollimation shocks. We discuss both effects in the following sections. 4.2. Radial structur… view at source ↗
Figure 4
Figure 4. Figure 4: summarizes the global geometry of the first recolli￾mation shock for all models, plotting the axial distance (zmax) against the radial extent (Rmax). The results clearly validate the trends: (a) Magnetization effect (σ): For both light and heavy jets, increasing σ (larger circles) generally results in smaller rmax and slightly smaller zmax. (b) High thermal domination: The points with the highest zmax and … view at source ↗
Figure 5
Figure 5. Figure 5: Ratio of the first recollimation shock distance in the MHD case to the purely hydrodynamic case (zMHD/zHD) as a function of the initial propertis B 2 0 /Pext. Note the log-log scale. After an initial plateau at low magnetization, all simulation families (A–F) exhibit a transition to a magnetically dominated regime, converging on a uniform power-law decline with a slope of approximately −0.33. 5. Role of th… view at source ↗
Figure 6
Figure 6. Figure 6: Impact of magnetic pitch parameter on jet structure. 2D maps in the (x,z) plane showing the steady-state spatial distribution of (from left to right): logarithm of thermal pressure (log P), logarithm of rest-mass density (log ρ), Lorentz factor (Γ), logarithm of the fast magnetosonic Mach number (log MF), the stability proxy (log(Γ 2 /σ)), and the logarithm of the plasma beta (log β). The rows correspond t… view at source ↗
Figure 7
Figure 7. Figure 7: Radial pressure balance analysis for increasing magnetic pitch, from purely toroidal (α = 0, left) to poloidal-dominated (α = 3, right). The location of maximum radial expansion (rmax,zmax) is shown in the top panels. The bottom panel shows the radial pressure balance at z0 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Normalized pressure gradient (|∇Pth|/Pth), white lines are the streamlines. 6. Stability analysis: centrifugal instability The CFI is a local, curvature-driven mode that can develop in jets when the destabilizing effect of motion along bent streamlines overcomes the stabilizing tension of the toroidal magnetic field. 6.1. Mapping the instability [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Radial evolution of the maximum fast magnetosonic Mach num￾ber and its corresponding vertical height. Top panel: The maximum value of MFmax evaluated over the domain z ∈ [1.0, 3.5] as a function of the radial distance r. Bottom panel: The z-coordinate at which this max￾imum is located, effectively tracing the trajectory of the primary shock front or wave structure. The different curves denote magnetic pitc… view at source ↗
Figure 10
Figure 10. Figure 10: 2D synthetic synchrotron emission maps (εobs) for a viewing angle of θ = 5 ◦ , comparing different magnetic pitch parameters profiles (α = 0, 0.1, 1, 3). The maps focus on the structural layout surrounding the primary recollimation shocks [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Radial profiles of the normalized toroidal magnetization σtor/Γ 2 as a function of the radial coordinate r for all simulated cases that correspons to the zmax of the streamline that starts from the position rstreamline = 0.075. unstable, turbulent jets typical of FR0. Quantifying the CFI diag￾nostic in recollimation regions of observed sources such as HST￾1 in M87, where stationary recollimation structure… view at source ↗
Figure 13
Figure 13. Figure 13: Radial profiles and linear analysis results for the Case E3 jet near its recollimation point. Top panel: Radial profiles of key quantities used as input for the linear analysis: normalized toroidal magnetization (σtor), rest mass density (ρ), Lorentz factor (Γ), and specific enthalpy (h). The vertical lines marked a, b, and c indicate the specific radial po￾sitions at xmax where the linear analysis was pe… view at source ↗
read the original abstract

Recollimation shocks are a frequent outcome in overpressured relativistic jets and are crucial for interpreting stationary features in Active Galactic Nuclei. The precise influence of magnetic fields on jet stability, energy dissipation, and variability remains debated, particularly as different field configurations can significantly alter shock properties and the onset of fluid instabilities. We perform a study of 2D axisymmetric RMHD jets to quantify how the ambient density contrast ($\nu$), pressure ratio ($P$), magnetization ($\sigma$), and magnetic pitch parameter ($\alpha$) govern the formation and strength of the first recollimation shock. We also assess how these parameters create the local geometric conditions favorable for the centrifugal instability (CFI), utilizing linear theory as a diagnostic. We find that the jet's global geometry is affected by the magnetic pressure. The recollimation distance decreases monotonically with increasing magnetization $\sigma$, as increased magnetic forces immediately limit jet expansion. Remarkably, in the magnetically dominated regime, the ratio of the magnetized recollimation distance ($z_{\rm MHD}$) to its purely hydrodynamic counterpart ($z_{\rm HD}$) converges onto a power-law scaling, $z_{MHD}/z_{HD} \propto (B_0^2/P_{ext})^{-1/3}$, where $B_0$ the initial magnetic field and $P_{ext}$ the external pressure. Jets with high density contrast relative to the ambient medium or high internal pressure further enhance field compression. Furthermore, synthetic synchrotron maps show that a dominant toroidal field yields highly boosted, localized emission knots, whereas a strong poloidal field creates a diffuse profile and shifts the recollimation zone downstream. Regions susceptible to CFI are determined primarily by the local $\sigma_{\text{tor}}/\Gamma^2$ profile and streamline curvature created during recollimation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports 2D axisymmetric RMHD simulations of overpressured relativistic jets, systematically varying ambient density contrast (ν), pressure ratio (P), magnetization (σ), and magnetic pitch parameter (α). It finds that recollimation distance decreases with increasing σ due to magnetic forces limiting expansion, and reports that in the magnetically dominated regime the ratio z_MHD/z_HD converges to a power-law scaling ∝ (B₀²/P_ext)^{-1/3}. The work also diagnoses regions prone to centrifugal instability (CFI) via local σ_tor/Γ² and streamline curvature, and presents synthetic synchrotron maps showing differences between toroidal and poloidal field configurations.

Significance. If the scaling is numerically robust, the direct parameter variation (independent inputs ν, P, σ, α) yields a falsifiable, non-circular relation useful for modeling stationary features in AGN jets and separating magnetic from hydrodynamic effects on recollimation. The CFI diagnostic linking simulations to linear theory and the emission maps add interpretive value for jet stability and variability studies.

major comments (2)
  1. [Abstract] Abstract: The central claim that z_MHD/z_HD converges onto the power-law scaling ∝ (B₀²/P_ext)^{-1/3} in the magnetically dominated regime is presented without any information on grid resolution, convergence tests, or quantitative uncertainties on the fitted exponent. This is load-bearing because resolution-dependent artifacts could alter the reported scaling or the CFI diagnostic.
  2. [Abstract] Abstract (parameter study and CFI diagnostic): The reported scaling and CFI assessment are obtained exclusively in 2D axisymmetric geometry with specific initial B-field configurations (toroidal vs. poloidal pitch α). No test is provided of whether 3D kink or current-driven modes would modify the effective expansion, field compression, and thus the z_MHD/z_HD scaling itself; a concrete test would be a limited set of 3D runs at fixed σ to check invariance of the exponent.
minor comments (2)
  1. [Abstract] The symbols B_0 and P_ext are used in the scaling relation but their precise definitions (initial field strength at launch, external pressure) should be stated explicitly when the scaling is first introduced.
  2. The manuscript would benefit from a brief statement of the numerical scheme, Riemann solver, and grid setup (even if details are in a methods section) to allow immediate assessment of the parameter study.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and detailed comments. We address each major comment point by point below, indicating planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that z_MHD/z_HD converges onto the power-law scaling ∝ (B₀²/P_ext)^{-1/3} in the magnetically dominated regime is presented without any information on grid resolution, convergence tests, or quantitative uncertainties on the fitted exponent. This is load-bearing because resolution-dependent artifacts could alter the reported scaling or the CFI diagnostic.

    Authors: We agree that supporting details on numerical resolution and convergence are necessary to substantiate the reported scaling. The revised manuscript will incorporate a dedicated subsection on the numerical setup, including the grid resolution used across the parameter survey, results of convergence tests at selected σ values, and the formal uncertainties on the fitted exponent obtained from the power-law regression. These additions will directly address potential concerns about resolution-dependent effects on both the scaling and the CFI diagnostic. revision: yes

  2. Referee: [Abstract] Abstract (parameter study and CFI diagnostic): The reported scaling and CFI assessment are obtained exclusively in 2D axisymmetric geometry with specific initial B-field configurations (toroidal vs. poloidal pitch α). No test is provided of whether 3D kink or current-driven modes would modify the effective expansion, field compression, and thus the z_MHD/z_HD scaling itself; a concrete test would be a limited set of 3D runs at fixed σ to check invariance of the exponent.

    Authors: The present work is a controlled 2D axisymmetric parameter study intended to isolate the effects of σ and α on recollimation distance and CFI conditions. While 3D kink or current-driven modes could in principle alter the effective expansion and field compression, conducting even a limited set of 3D runs lies outside the scope of this manuscript. We will revise the discussion section to explicitly acknowledge this limitation of the 2D geometry and to identify 3D extensions as a natural direction for follow-up work. revision: partial

Circularity Check

0 steps flagged

No circularity: scaling is empirical output from independent parameter sweeps in simulations

full rationale

The paper reports results from direct 2D axisymmetric RMHD simulations in which ν, P, σ, and α are varied as independent inputs. The claimed power-law scaling z_MHD/z_HD ∝ (B₀²/P_ext)^{-1/3} is presented as an observed convergence in the magnetically dominated regime, not as an analytical derivation, fitted parameter, or quantity obtained by construction from the same data. No self-citations are invoked as load-bearing premises, no ansatz is smuggled via prior work, and no uniqueness theorem or renaming of known results is used to justify the central claim. The derivation chain is therefore self-contained against external benchmarks (the simulations themselves).

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 0 invented entities

The central claims rest on the standard equations of ideal RMHD, the validity of 2D axisymmetric geometry for recollimation, and linear theory as a diagnostic for CFI; four input parameters are varied but not fitted to produce the scaling.

free parameters (4)
  • ambient density contrast (ν)
    Input parameter systematically varied across the simulation suite
  • pressure ratio (P)
    Input parameter systematically varied across the simulation suite
  • magnetization (σ)
    Input parameter systematically varied across the simulation suite
  • magnetic pitch parameter (α)
    Input parameter systematically varied across the simulation suite
axioms (3)
  • standard math Ideal relativistic magnetohydrodynamics equations govern the jet evolution
    Foundation of all RMHD runs described
  • domain assumption Linear stability theory supplies a reliable diagnostic for centrifugal instability onset
    Used to identify susceptible regions from the simulated flow
  • domain assumption 2D axisymmetric geometry captures the dominant recollimation and instability physics
    Explicit choice of simulation dimensionality

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discussion (0)

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Reference graph

Works this paper leans on

66 extracted references · 63 canonical work pages · 22 internal anchors

  1. [1]

    , keywords =

    Simulations of Superluminal Radio Sources. , keywords =. doi:10.1093/mnras/288.4.833 , adsurl =

    work page doi:10.1093/mnras/288.4.833

  2. [2]

    arXiv e-prints , keywords =

    Quasi-Periodic Polarized Emissions from Kink Structure in Magnetized Relativistic Jets. arXiv e-prints , keywords =. doi:10.48550/arXiv.2511.03140 , archivePrefix =. 2511.03140 , primaryClass =

    work page doi:10.48550/arxiv.2511.03140

  3. [3]

    2025 , eprint=

    Spectral curvature and breaks from Fermi acceleration at oblique shocks , author=. 2025 , eprint=

    2025

  4. [4]

    , keywords =

    Instabilities at recollimation shocks in magnetohydrodynamic jets. , keywords =. doi:10.1051/0004-6361/202557516 , archivePrefix =. 2510.01742 , primaryClass =

    work page doi:10.1051/0004-6361/202557516

  5. [5]

    , keywords =

    Consideration of gusts, blasts and prolonged velocity bursts in supersonic overpressured jets. , keywords =. doi:10.1093/mnras/stag742 , adsurl =

    work page doi:10.1093/mnras/stag742

  6. [6]

    , keywords =

    How do recollimation-induced instabilities shape the propagation of hydrodynamic relativistic jets?. , keywords =. doi:10.1051/0004-6361/202554698 , archivePrefix =. 2503.18602 , primaryClass =

    work page doi:10.1051/0004-6361/202554698

  7. [7]

    , keywords =

    Numerical simulations of jets. , keywords =. doi:10.1016/j.newar.2021.101610 , adsurl =

    work page doi:10.1016/j.newar.2021.101610 2021

  8. [8]

    , keywords =

    Simulating radio emission from flickering AGN jets: travelling shocks and hotspot brightening. , keywords =. doi:10.1093/mnras/stag131 , archivePrefix =. 2601.13138 , primaryClass =

    work page doi:10.1093/mnras/stag131

  9. [9]

    Physica D Nonlinear Phenomena , keywords =

    Rayleigh-Taylor and Richtmyer-Meshkov instabilities: A journey through scales. Physica D Nonlinear Phenomena , keywords =. doi:10.1016/j.physd.2020.132838 , adsurl =

    work page doi:10.1016/j.physd.2020.132838 2020

  10. [10]

    Annual Review of Fluid Mechanics , year = 2002, month = jan, volume =

    The richtmyer-meshkov instability. Annual Review of Fluid Mechanics , year = 2002, month = jan, volume =. doi:10.1146/annurev.fluid.34.090101.162238 , adsurl =

    work page doi:10.1146/annurev.fluid.34.090101.162238 2002

  11. [11]

    , keywords =

    Particle acceleration in shearing flows: the self-generation of turbulent spine-sheath structures in relativistic magnetohydrodynamic jet simulations. , keywords =. doi:10.1093/mnras/stac3616 , archivePrefix =. 2212.03226 , primaryClass =

    work page doi:10.1093/mnras/stac3616

  12. [12]

    Causality and stability of cosmic jets

    Causality and stability of cosmic jets. , keywords =. doi:10.1093/mnras/stv1295 , archivePrefix =. 1408.3318 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stv1295

  13. [13]

    , keywords =

    On the Stability of Magnetized Rotating Jets: The Axisymmetric Case. , keywords =. doi:10.1086/167522 , adsurl =

    work page doi:10.1086/167522

  14. [14]

    Linear stability analysis of magnetized relativistic rotating jets

    Linear stability analysis of magnetized relativistic rotating jets. , keywords =. doi:10.1093/mnras/stz591 , archivePrefix =. 1902.10781 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stz591 1902

  15. [15]

    Rotation and toroidal magnetic field effects on the stability of two-component jets

    Rotation and toroidal magnetic field effects on the stability of two-component jets. , keywords =. doi:10.1093/mnras/stx1288 , archivePrefix =. 1706.06912 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stx1288

  16. [16]

    Studies of the Jet in Bl Lacertae. II. Superluminal Alfv \'e n Waves. , keywords =. doi:10.1088/0004-637X/803/1/3 , archivePrefix =. 1409.3599 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/803/1/3

  17. [17]

    The Structure and Dynamics of the Sub-parsec Scale Jet in M87 Based on 50 VLBA Observations Over 17 Years at 43 GHz

    The Structure and Dynamics of the Subparsec Jet in M87 Based on 50 VLBA Observations over 17 Years at 43 GHz. , keywords =. doi:10.3847/1538-4357/aaafcc , archivePrefix =. 1802.06166 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aaafcc

  18. [18]

    , keywords =

    Multi-epoch Modeling of TXS 0506+056 and Implications for Long-term High-energy Neutrino Emission. , keywords =. doi:10.3847/1538-4357/ab76d0 , archivePrefix =. 1911.04010 , primaryClass =

    work page doi:10.3847/1538-4357/ab76d0 1911

  19. [19]

    and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and

    Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and. Nature Methods , year =

  20. [20]

    Nature585(7825), 357–362 (Sep 2020)

    Charles R. Harris and K. Jarrod Millman and St. Array programming with. 2020 , month = sep, journal =. doi:10.1038/s41586-020-2649-2 , publisher =

    work page doi:10.1038/s41586-020-2649-2 2020

  21. [21]

    Hunter, J. D. , Title =. Computing in Science & Engineering , Volume =

  22. [22]

    The Kelvin-Helmholtz mode

    Linear stability analysis of relativistic magnetized jets. The Kelvin-Helmholtz mode. , keywords =. doi:10.1051/0004-6361/202347647 , adsurl =

    work page doi:10.1051/0004-6361/202347647

  23. [23]

    Spectral evolution of flaring blazars from numerical simulations

    Spectral evolution of flaring blazars from numerical simulations. , keywords =. doi:10.1051/0004-6361/201527139 , archivePrefix =. 1601.03181 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201527139

  24. [24]

    , keywords =

    Stochastic particle acceleration in the lobes of giant radio galaxies. , keywords =. doi:10.1111/j.1365-2966.2009.15442.x , archivePrefix =. 0903.1259 , primaryClass =

    work page doi:10.1111/j.1365-2966.2009.15442.x 2009

  25. [25]

    , keywords =

    The polarization of the synchrotron radiation from a recollimated jet: Application to high-energy BL Lacs. , keywords =. doi:10.1051/0004-6361/202554490 , archivePrefix =. 2503.09180 , primaryClass =

    work page doi:10.1051/0004-6361/202554490

  26. [26]

    arXiv e-prints , keywords =

    How do recollimation-induced instabilities shape the propagation of hydrodynamic relativistic jets?. arXiv e-prints , keywords =. doi:10.48550/arXiv.2503.18602 , archivePrefix =. 2503.18602 , primaryClass =

    work page doi:10.48550/arxiv.2503.18602

  27. [27]

    , keywords =

    Current-driven kink instabilities in relativistic jets: dissipation properties. , keywords =. doi:10.1093/mnras/stab3492 , archivePrefix =. 2111.14575 , primaryClass =

    work page doi:10.1093/mnras/stab3492

  28. [28]

    Journal of Computational Physics , year = 1999, month = mar, volume =

    A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations. Journal of Computational Physics , year = 1999, month = mar, volume =. doi:10.1006/jcph.1998.6153 , adsurl =

    work page doi:10.1006/jcph.1998.6153 1999

  29. [29]

    On the Divergence-Free Condition in Godunov-Type Schemes for Ideal Magnetohydrodynamics: the Upwind Constrained Transport Method

    On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method. Journal of Computational Physics , keywords =. doi:10.1016/j.jcp.2003.09.016 , archivePrefix =. astro-ph/0310183 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.jcp.2003.09.016 2003

  30. [30]

    The Journal of Open Source Software , keywords =

    PyPLUTO: a data analysis Python package for the PLUTO code. The Journal of Open Source Software , keywords =. doi:10.21105/joss.08448 , archivePrefix =. 2501.09748 , primaryClass =

    work page doi:10.21105/joss.08448

  31. [31]

    , keywords =

    Tavecchio, F. and Ghisellini, G. and Bonnoli, G. and Ghirlanda, G. , title = ". Monthly Notices of the Royal Astronomical Society: Letters , volume =. 2010 , month =. doi:10.1111/j.1745-3933.2010.00867.x , url =

    work page doi:10.1111/j.1745-3933.2010.00867.x 2010

  32. [32]

    , keywords =

    A shocking outcome: Jet dynamics and polarimetric signatures of the multi-band flare in blazar OJ 248. , keywords =. doi:10.1051/0004-6361/202553689 , archivePrefix =. 2502.12232 , primaryClass =

    work page doi:10.1051/0004-6361/202553689

  33. [33]

    , keywords =

    Expanding one-zone model for blazar emission. , keywords =. doi:10.1051/0004-6361/202142126 , archivePrefix =. 2110.05325 , primaryClass =

    work page doi:10.1051/0004-6361/202142126

  34. [34]

    title Relativistic Jets from Active Galactic Nuclei

    Relativistic Jets from Active Galactic Nuclei. , keywords =. doi:10.1146/annurev-astro-081817-051948 , archivePrefix =. 1812.06025 , primaryClass =

    work page doi:10.1146/annurev-astro-081817-051948

  35. [35]

    Studies of the Jet in Bl Lacertae. I. Recollimation Shock and Moving Emission Features. , keywords =. doi:10.1088/0004-637X/787/2/151 , archivePrefix =. 1404.0976 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/787/2/151

  36. [36]

    Universe , keywords =

    Linear Stability Analysis of Relativistic Magnetized Jets: Methodology. Universe , keywords =. doi:10.3390/universe9090386 , archivePrefix =. 2306.16835 , primaryClass =

    work page doi:10.3390/universe9090386

  37. [37]

    Universe , keywords =

    Linear Stability Analysis of Relativistic Magnetized Jets: The Minimalist Approach. Universe , keywords =. doi:10.3390/universe10040183 , archivePrefix =. 2404.10613 , primaryClass =

    work page doi:10.3390/universe10040183

  38. [38]

    , keywords =

    On the linear stability of sheared and magnetized jets without current sheets - relativistic case. , keywords =. doi:10.1093/mnras/stx3065 , adsurl =

    work page doi:10.1093/mnras/stx3065

  39. [39]

    , keywords =

    Instabilities in Astrophysical Jets. , keywords =. doi:10.1007/BF00645111 , adsurl =

    work page doi:10.1007/bf00645111

  40. [40]

    Linear stability analysis of magnetized relativistic jets: the nonrotating case

    Linear stability analysis of magnetized relativistic jets: the non-rotating case. , keywords =. doi:10.1093/mnras/stt1225 , archivePrefix =. 1307.6388 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stt1225

  41. [41]

    Two-dimensional Numerical Study for Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in Relativistic Jets

    Two-dimensional Numerical Study for Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in Relativistic Jets. , keywords =. doi:10.1088/2041-8205/772/1/L1 , archivePrefix =. 1306.1046 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/772/1/l1 2041

  42. [42]

    , keywords =

    A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics. , keywords =. doi:10.1111/j.1365-2966.2008.14221.x , archivePrefix =. 0811.1483 , primaryClass =

    work page doi:10.1111/j.1365-2966.2008.14221.x 2008

  43. [43]

    , keywords =

    Magnetic inhibition of the recollimation instability in relativistic jets. , keywords =. doi:10.1093/mnras/stab828 , archivePrefix =. 2010.11012 , primaryClass =

    work page doi:10.1093/mnras/stab828 2010

  44. [44]

    Recollimation Shocks in Magnetized Relativistic Jets

    Recollimation Shocks in Magnetized Relativistic Jets. , keywords =. doi:10.1088/0004-637X/809/1/38 , archivePrefix =. 1505.00933 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/809/1/38

  45. [45]

    Three-Dimensional Relativistic Magnetohydrodynamic Simulations of Current-Driven Instability. I. Instability of a Static Column. , keywords =. doi:10.1088/0004-637X/700/1/684 , archivePrefix =. 0903.5358 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/700/1/684

  46. [46]

    Three-dimensional Simulations of AGN Jets: Magnetic Kink Instability versus Conical Shocks

    Simulations of AGN jets: magnetic kink instability versus conical shocks. , keywords =. doi:10.1093/mnras/stx1165 , archivePrefix =. 1612.06929 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stx1165

  47. [47]

    The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics

    The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics. , keywords =. doi:10.1086/430905 , archivePrefix =. astro-ph/0505200 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/430905

  48. [48]

    , keywords =

    FR0 jets and recollimation-induced instabilities. , keywords =. doi:10.1051/0004-6361/202348954 , adsurl =

    work page doi:10.1051/0004-6361/202348954

  49. [49]

    Recollimation shocks and radiative losses in extragalactic relativistic jets

    Recollimation shocks and radiative losses in extragalactic relativistic jets. , keywords =. doi:10.1051/0004-6361/201732000 , archivePrefix =. 1710.06713 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201732000

  50. [50]

    PLUTO: a Numerical Code for Computational Astrophysics

    PLUTO: A Numerical Code for Computational Astrophysics. , keywords =. doi:10.1086/513316 , archivePrefix =. astro-ph/0701854 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/513316

  51. [51]

    Reconfinement and Loss of Stability in Jets from Active Galactic Nuclei

    Reconfinement and loss of stability in jets from active galactic nuclei. Nature Astronomy , keywords =. doi:10.1038/s41550-017-0338-3 , archivePrefix =. 1806.05683 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s41550-017-0338-3

  52. [52]

    , keywords =

    The structure of weakly magnetized -ray burst jets. , keywords =. doi:10.1093/mnras/staa2567 , archivePrefix =. 2007.11590 , primaryClass =

    work page doi:10.1093/mnras/staa2567 2007

  53. [53]

    , keywords =

    Magnetic inhibition of centrifugal instability. , keywords =. doi:10.1093/mnras/stz1973 , adsurl =

    work page doi:10.1093/mnras/stz1973

  54. [54]

    , keywords =

    Numerical investigation of instabilities in over-pressured magnetized relativistic jets. , keywords =. doi:10.1051/0004-6361/202451573 , archivePrefix =. 2411.17389 , primaryClass =

    work page doi:10.1051/0004-6361/202451573

  55. [55]

    , year = 1974, month = aug, volume =

    3C236, DA240; the largest radio sources known. , year = 1974, month = aug, volume =. doi:10.1038/250625a0 , adsurl =

    work page doi:10.1038/250625a0 1974

  56. [56]

    , keywords =

    Kelvin-Helmholtz instability for relativistic fluids. , keywords =. doi:10.1103/PhysRevE.70.036304 , adsurl =

    work page doi:10.1103/physreve.70.036304

  57. [57]

    Relativistic Centrifugal Instability

    Relativistic centrifugal instability. , keywords =. doi:10.1093/mnrasl/sly016 , archivePrefix =. 1710.01345 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnrasl/sly016

  58. [58]

    Internal instabilities in magnetized jets

    Internal instabilities in magnetized jets. , keywords =. doi:10.1093/mnras/sty2675 , archivePrefix =. 1807.11480 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty2675

  59. [59]

    , keywords =

    Evolution of current- and pressure-driven instabilities in relativistic jets. , keywords =. doi:10.1093/mnras/stae1788 , archivePrefix =. 2407.15477 , primaryClass =

    work page doi:10.1093/mnras/stae1788

  60. [60]

    Probing an X-ray flare pattern in Mrk 421 induced by multiple stationary shocks: a solution to the bulk Lorentz factor crisis

    Probing an X-Ray Flare Pattern in Mrk 421 Induced by Multiple Stationary Shocks: A Solution to the Bulk Lorentz Factor Crisis. , keywords =. doi:10.3847/1538-4357/ab1906 , archivePrefix =. 1904.06802 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab1906 1904

  61. [61]

    , keywords =

    Magnetic acceleration of relativistic active galactic nucleus jets. , keywords =. doi:10.1111/j.1365-2966.2007.12050.x , archivePrefix =. astro-ph/0703146 , primaryClass =

    work page doi:10.1111/j.1365-2966.2007.12050.x 2007

  62. [62]

    Asymptotic structure of Poynting dominated jets

    Asymptotic Structure of Poynting-Dominated Jets. , keywords =. doi:10.1088/0004-637X/698/2/1570 , archivePrefix =. 0902.3357 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/698/2/1570

  63. [63]

    , keywords =

    Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole. , keywords =. doi:10.1111/j.1745-3933.2011.01147.x , archivePrefix =. 1108.0412 , primaryClass =

    work page doi:10.1111/j.1745-3933.2011.01147.x 2011

  64. [64]

    MOJAVE: Monitoring of Jets in Active galactic nuclei with VLBA Experiments. IX. Nuclear opacity. , keywords =. doi:10.1051/0004-6361/201219173 , archivePrefix =. 1207.5457 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201219173

  65. [65]

    Magnetized relativistic jets and helical magnetic fields. I. Dynamics. , keywords =. doi:10.1051/0004-6361/202037898 , adsurl =

    work page doi:10.1051/0004-6361/202037898

  66. [66]

    Probing the Innermost Regions of AGN Jets and Their Magnetic Fields with RadioAstron. III. Blazar S5 0716+71 at Microarcsecond Resolution. , keywords =. doi:10.3847/1538-4357/ab7dae , archivePrefix =. 2003.08776 , primaryClass =

    work page doi:10.3847/1538-4357/ab7dae 2003