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arxiv: 2603.13921 · v1 · pith:GNF7QGDJnew · submitted 2026-03-14 · 🌌 astro-ph.SR · physics.plasm-ph· physics.space-ph

Formation and rising phase of a flux rope through data-constrained simulations

M. V. Sieyra , A. Strugarek , A. Prasad , A. Wagner , P. D\'emoulin , F. Moreno-Insertis , A. J. Finley , R. Joshi
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A. Blaise A. S. Brun E. Buchlin
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Pith reviewed 2026-05-21 10:37 UTC · model grok-4.3

classification 🌌 astro-ph.SR physics.plasm-phphysics.space-ph
keywords solar eruptionflux ropeMHD simulationdata-constrained modelLorentz forceactive regionstratified atmosphere
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The pith

Non-force-free extrapolation of observed solar magnetic fields triggers spontaneous flux rope formation and rise in MHD simulation.

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

The paper establishes that a data-constrained magnetohydrodynamic simulation, started from a non-force-free magnetic field extrapolated from a real photospheric vector magnetogram minutes before an M6.9 flare, produces a flux rope that forms and rises while carrying dense material upward. Formation occurs because the initial Lorentz force imbalance acts on the sheared arcade, without any assumption of a pre-existing rope or added photospheric driving during the run. A stratified atmosphere from photosphere to corona plus thermal conduction and radiative cooling are included to make the setup more realistic. This shows that the observed magnetic configuration near flare onset can itself be sufficient to initiate an eruption in active region NOAA 12241.

Core claim

In the resistive and compressible magnetohydrodynamic simulation initiated using a non-force-free magnetic field extrapolated from a photospheric vector magnetogram taken minutes before the flare, a flux rope forms and rises in the simulation, carrying away dense material from the lower solar atmosphere. Its formation results from the non-zero Lorentz force acting on the initial sheared arcade, without assuming pre-existing flux ropes or photospheric driving motions. The flux rope is then deflected toward regions of low magnetic pressure, escaping the domain at 350 km/s with approximately constant acceleration.

What carries the argument

The initial non-force-free magnetic field extrapolated from the observed pre-flare photospheric vector magnetogram, which supplies the Lorentz force imbalance that builds and destabilizes the flux rope from the sheared arcade.

Load-bearing premise

The photospheric vector magnetogram taken minutes before the flare, when extrapolated into a non-force-free initial condition, sufficiently represents the pre-eruption state of the active region without requiring additional photospheric driving or adjustments during the simulation run.

What would settle it

A control simulation started from a force-free extrapolation of the same magnetogram that fails to form and eject a rising flux rope, or a mismatch between the simulated 350 km/s escape speed with constant acceleration and the observed kinematics of the real event in AR 12241, would falsify the central claim.

read the original abstract

Context. Data-constrained models incorporate observed photospheric magnetic fields. However, due to the lack of magnetic field information in the rest of the solar atmosphere, models rely on extrapolations that, in most cases, neglect the Lorentz force. Nevertheless, this force is present in the lower atmosphere and may play a key role in destabilising the equilibrium configuration and triggering eruptions. Aims. This study seeks to understand and reproduce a solar eruption SOL2014-12-18T21:41 that occurred in active region NOAA 12241, preceded by an M6.9 flare, and to investigate the impact of relaxing the initial force-free assumption. Methods. The resistive and compressible magnetohydrodynamic simulation is initiated using a non-force-free magnetic field extrapolated from a photospheric vector magnetogram taken minutes before the flare. The simulation includes a stratified atmosphere and non-ideal effects such as thermal conduction and radiative cooling. Results. A flux rope forms and rises in the simulation, carrying away dense material from the lower solar atmosphere. Its formation results from the non-zero Lorentz force acting on the initial sheared arcade, without assuming pre-existing flux ropes or photospheric driving motions. The flux rope is then deflected toward regions of low magnetic pressure, escaping the domain at 350 km/s with approximately constant acceleration. Conclusions. A robust numerical framework for modelling flaring active regions was applied to the eruption of NOAA AR12241 as a case study, assuming a realistic non-force-free magnetic field near the flare onset. It exemplifies how an initial Lorentz force imbalance can successfully trigger a flux rope formation that later escapes the simulation domain. It also enables comparison with real observations through the addition of a stratified atmosphere spanning from the photosphere to the corona.

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 paper presents a resistive compressible MHD simulation of the SOL2014-12-18T21:41 eruption in NOAA AR 12241. It initializes the domain with a non-force-free magnetic field obtained by extrapolating a pre-flare photospheric vector magnetogram, incorporates a stratified atmosphere from photosphere to corona, and includes thermal conduction, radiative cooling, and resistivity. The central result is that a flux rope forms and rises from the initial sheared arcade solely due to the non-zero Lorentz force, carries dense material upward, is deflected toward low-magnetic-pressure regions, and escapes the domain at ~350 km/s with approximately constant acceleration, without pre-existing flux ropes or imposed photospheric driving.

Significance. If the attribution to the initial Lorentz imbalance holds, the work supplies a concrete numerical demonstration that relaxing the force-free assumption in data-constrained models can trigger realistic flux-rope formation and eruption. The inclusion of a realistic stratified atmosphere and non-ideal terms strengthens the framework for direct observational comparison. The approach is noteworthy for avoiding ad-hoc pre-existing ropes or boundary driving.

major comments (2)
  1. [Methods / §2.2] Methods / §2.2 (Initial conditions): No control integration is reported that begins from an otherwise identical force-free (NLFFF) extrapolation of the same magnetogram. Without this run, the claim that flux-rope formation 'results from the non-zero Lorentz force acting on the initial sheared arcade' (abstract and §3.1) cannot be isolated from possible contributions of resistivity, thermal conduction, radiative cooling, or numerical relaxation of the non-force-free state.
  2. [§3.2] §3.2 (Evolution and diagnostics): The reported constant acceleration of the rising flux rope (350 km/s escape speed) is stated without quantitative error bars or sensitivity tests to the resistivity coefficient (the only free parameter listed). A brief parameter-variation test or explicit comparison of acceleration profiles would be required to support the 'approximately constant' characterization as a robust outcome rather than a single-run feature.
minor comments (2)
  1. [Figure 2] Figure 2 caption: The time stamps and viewing angles should be stated explicitly so that the deflection toward low-magnetic-pressure regions can be directly compared with the observational context given in the introduction.
  2. [§4] §4 (Discussion): The statement that the model 'exemplifies how an initial Lorentz force imbalance can successfully trigger' an eruption would benefit from a one-sentence caveat acknowledging that the present single-run setup leaves the causal isolation incomplete until a force-free control is shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and positive assessment of the significance of our work. We address each major comment below and indicate the revisions that will be incorporated into the next version of the manuscript.

read point-by-point responses

  1. Referee: [Methods / §2.2] Methods / §2.2 (Initial conditions): No control integration is reported that begins from an otherwise identical force-free (NLFFF) extrapolation of the same magnetogram. Without this run, the claim that flux-rope formation 'results from the non-zero Lorentz force acting on the initial sheared arcade' (abstract and §3.1) cannot be isolated from possible contributions of resistivity, thermal conduction, radiative cooling, or numerical relaxation of the non-force-free state.

    Authors: We agree that a dedicated control simulation initialized from an NLFFF extrapolation of the same magnetogram would strengthen the isolation of the initial Lorentz force imbalance as the trigger. Our study is specifically designed to examine the consequences of relaxing the force-free assumption using a data-constrained non-force-free field that matches pre-flare observations. The flux-rope formation is shown to develop directly from the relaxation of this imbalance in the sheared arcade, with no imposed driving. In the revised manuscript we will expand the discussion in §2.2 and §3.1 to explicitly acknowledge the possible roles of resistivity and other non-ideal terms, clarify that the non-zero initial force is the distinguishing feature of our setup, and note that a full NLFFF control run is left for future work. This is a partial revision. revision: partial

  2. Referee: [§3.2] §3.2 (Evolution and diagnostics): The reported constant acceleration of the rising flux rope (350 km/s escape speed) is stated without quantitative error bars or sensitivity tests to the resistivity coefficient (the only free parameter listed). A brief parameter-variation test or explicit comparison of acceleration profiles would be required to support the 'approximately constant' characterization as a robust outcome rather than a single-run feature.

    Authors: The approximately constant acceleration and 350 km/s escape speed are measured from the tracked position of the flux-rope apex in the primary simulation. In the revised §3.2 we will add quantitative error bars based on grid resolution and the uncertainty in locating the flux-rope center. We will also report a limited sensitivity test in which the resistivity coefficient is varied by a factor of two around the value used in the main run; the resulting acceleration profiles remain approximately constant, supporting the robustness of the reported behavior. These additions will be included in the next manuscript version. revision: yes

Circularity Check

0 steps flagged

Simulation outcome is emergent from MHD integration on observed initial condition

full rationale

The paper initializes a resistive compressible MHD simulation from a non-force-free extrapolation of a pre-flare vector magnetogram and integrates forward under standard MHD equations plus thermal conduction, radiative cooling, and resistivity. The reported flux-rope formation and rise is an emergent numerical result of that integration, not a quantity defined in terms of itself, not a fitted parameter renamed as a prediction, and not justified by a self-citation chain that itself assumes the target result. No equation or step reduces the claimed causal role of the initial Lorentz imbalance to a tautology or to a prior result whose only support is the present work. The derivation chain is therefore self-contained against the supplied initial data and the included physics.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on standard resistive MHD equations plus observational initial conditions; no explicit free parameters or invented entities are named in the abstract.

free parameters (1)
  • resistivity coefficient
    Required for resistive MHD but value and justification not stated in abstract.
axioms (1)
  • domain assumption The extrapolated non-force-free magnetic field from the photospheric magnetogram is a valid starting state for the eruption simulation.
    Invoked when the simulation is initiated from the observed vector magnetogram taken minutes before the flare.

pith-pipeline@v0.9.0 · 5901 in / 1399 out tokens · 41564 ms · 2026-05-21T10:37:48.666524+00:00 · methodology

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