arxiv: 2601.10675 · v2 · submitted 2026-01-15 · 🌌 astro-ph.SR

MHD modeling of magnetic flux evolution around solar maximum by the coronal model COCONUT

Haopeng Wang , Stefaan Poedts , Andrea Lani , Junyan Liu , Quentin Noraz , Luis Linan , Tinatin Baratashvili , Hyun-Jin Jeong

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Rayan Dhib Wenwen Wei Jia Huang Mahdi Najafi-Ziyazi Hao Wu Rui Zhuo Jos\'e M. L. Murteira Ketevan Arabuli Brigitte Schmieder Jasmina Magdaleni\'c Zhukov

This is my paper

Pith reviewed 2026-05-16 13:47 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords open magnetic fluxMHD coronal modelingsolar maximumCarrington rotationsolar windCOCONUT modelcoronal holes

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The pith

COCONUT MHD simulations produce open magnetic flux near the Sun that matches PSP and WIND in-situ data but exceeds SDO coronal hole estimates by a factor of five.

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

The paper applies the time-evolving COCONUT coronal MHD model to two solar-maximum Carrington rotations to track magnetic flux at different distances from the Sun. The central finding is that the open magnetic flux computed near the solar surface aligns with spacecraft measurements yet stands roughly five times above values inferred from coronal hole areas in SDO images. Most of the flux reduction occurs inside three solar radii, where closed field lines rapidly reconnect or open, and the amount of open flux can be lowered by modest changes to the volumetric heating term. These results indicate that full MHD time evolution, grid resolution, and heating details must be considered together when reconciling surface, coronal, and heliospheric flux measurements.

Core claim

The simulated open magnetic flux near the solar surface is comparable to that derived from in situ observations by PSP and WIND satellites, and is about 5 times larger than that derived from SDO coronal hole observations. The open flux falls by up to 45 percent between 1.01 solar radii and 0.1 AU, with the steepest drop inside 3 solar radii as the closed-flux fraction declines from roughly 60 percent to 4 percent of the total. Moderate adjustment of the heating source term changes the open-flux level, while preprocessing the photospheric magnetogram with a potential-field solver reduces open flux only in the low corona and leaves results beyond 3 solar radii nearly unchanged. The ratio of a

What carries the argument

The COCONUT time-dependent MHD coronal model that evolves the magnetic field from photospheric magnetogram boundary conditions under a prescribed heating source term.

If this is right

Open flux decreases mainly inside 3 solar radii, where closed flux drops from about 60 percent to 4 percent of the total.
Higher-resolution meshes produce larger simulated open-flux values.
The ratio of maximum to minimum open flux within one Carrington rotation can reach 1.4.
Magnetogram preprocessing with a potential-field solver lowers open flux in the low corona but leaves values beyond 3 solar radii essentially unchanged.

Where Pith is reading between the lines

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

Incorporating more physically motivated heating mechanisms could reduce or eliminate the need for manual tuning to match coronal-hole observations.
Static potential-field extrapolations are likely to underestimate open flux compared with full time-dependent MHD runs during solar maximum.
Repeating the same runs at solar-minimum conditions would test whether the factor-of-five discrepancy is phase-dependent.

Load-bearing premise

That moderate adjustments to the volumetric heating term can change the open-flux level without breaking consistency with other observed quantities.

What would settle it

A set of in-situ flux measurements or high-resolution coronal images inside 3 solar radii that either match the model’s five-times-larger open-flux values or align instead with the lower SDO coronal-hole estimates.

Figures

Figures reproduced from arXiv: 2601.10675 by Andrea Lani, Brigitte Schmieder, Haopeng Wang, Hao Wu, Hyun-Jin Jeong, Jasmina Magdaleni\'c Zhukov, Jia Huang, Jos\'e M. L. Murteira, Junyan Liu, Ketevan Arabuli, Luis Linan, Mahdi Najafi-Ziyazi, Quentin Noraz, Rayan Dhib, Rui Zhuo, Stefaan Poedts, Tinatin Baratashvili, Wenwen Wei.

**Figure 1.** Figure 1: Timing diagrams of the radial velocity Vr (km s−1 ; left) and proton number density (103 cm−3 ; right) measured by a virtual satellite located at 21.5 Rs . The virtual satellite is positioned at the same latitude as Earth but lags by 60◦ in longitude. The solid black, dashed red, and dashed-dot blue lines represent the time-evolving simulation results from Cases 1, 2, and 3, respectively, while the solid… view at source ↗

**Figure 3.** Figure 3: White-light pB images observed by COR2/STEREO-A (first row) and synthesised from the coronal simulation results of Case 1 (second row), Case 2 (third row), and Case 3 (fourth row), respectively, spanning along heliocentric distances from 2.5 to 15 Rs on meridional planes in the STEREO-A view. The orange lines indicate magnetic field lines on the selected meridional planes traced from identical seed points.… view at source ↗

**Figure 4.** Figure 4: Timing diagrams of the radial magnetic field strength measured by the same virtual satellite as in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Distributions of the radial magnetic field at 1.01 Rs evaluated at the 264th, 556th, 832nd, 1060th, and 1316th hours for Case 3. The dashed black, solid orange, and solid blue lines overlaid on the magnetic-field contours denote the boundaries of open-field regions derived from Cases 1, 2, and 3, respectively. colour blueEvolution of the radial magnetic field at the inner boundary, as displayed in the to… view at source ↗

**Figure 6.** Figure 6: Distributions of the radial magnetic field at 3 Rs evaluated at the 0th, 264th, 556th, 832nd, 1060th, and 1316th hours for Case 3. The dashed black, solid orange, and solid blue lines overlaid on the magnetic-field contours denote the boundaries of open-field regions derived from Cases 1, 2, and 3, respectively. alistic representation than commonly used quasi-steady simulations. In this paper, we perform… view at source ↗

read the original abstract

In this paper, we simulate the magnetic flux evolution at different heliocentric distances during two solar-maximum Carrington rotations (CRs) using the time-evolving coronal magnetohydrodynamic (MHD) model COCONUT to investigate the ``open flux problem". The simulated open magnetic flux (OMF) near the solar surface is comparable to that derived from \textit{in situ} observations by PSP and WIND satellites, and is about 5 times larger than that derived from SDO coronal hole (CH) observations, and the variation in the simulated radial solar wind speed is consistent with the evolution of the OMF evaluated around the corresponding solar disk center. We find that the OMF is reduced by up to $45\%$ from 1.01~$R_s$ to 0.1~AU and increases with a higher-resolution mesh. The OMF decreases mainly within 3~$R_s$, where the closed magnetic flux drops more rapidly, from about $60\%$ of the total magnetic flux at 1.01~$R_s$ to about $4\%$ at 3~$R_s$. Moderate adjustment of the heating source term can effectively regulate the simulated OMF. Preprocessing the photospheric magnetograms with a potential field solver that removes many high-order spherical harmonic components reduces the OMF in the low corona, while having little impact beyond 3~$R_s$. Additionally, the ratio of the maximum to the minimum OMF can reach 1.4 during a single solar maximum CR. These findings highlight the necessity of considering higher grid resolution, more realistic heating mechanisms, and the time-evolving regime of coronal MHD modeling when further addressing the ``open flux problem".

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.

Desk Editor's Note private letter to a colleague

COCONUT runs match PSP open flux by tuning heating, but the adjustment lacks independent checks against other observables.

read the letter

The simulations here get open magnetic flux near the Sun to line up with PSP and WIND in-situ data for two solar-max Carrington rotations, coming out roughly five times higher than SDO coronal hole estimates. Most of the drop happens within 3 Rs, with up to 45 percent reduction out to 0.1 AU and a 1.4 max-to-min ratio in one CR. The closed flux share falls from 60 percent at 1.01 Rs to 4 percent at 3 Rs, which is a clear quantitative result from the time-dependent runs. The work applies the existing COCONUT MHD code to these specific periods and reports how OMF scales with mesh resolution and responds to heating changes. Higher resolution increases the flux, and preprocessing the magnetograms with a potential field solver mainly affects the low corona while leaving results beyond 3 Rs almost unchanged. These sensitivity tests are practical and reproducible. The soft spot is the heating source term. Moderate adjustments are said to bring the near-Sun OMF into agreement with spacecraft values, but the paper gives no numbers on how large those adjustments are, what the baseline value was, or whether the same term reproduces observed density or temperature profiles. Without that grounding, the match reads as parameter fitting rather than a first-principles outcome. This paper is for coronal MHD modelers and groups working on the open flux problem for solar wind forecasting. Readers running similar codes will find the resolution and preprocessing results useful. The concrete trends and data consistency are enough to justify peer review. I would send it to referees rather than desk reject it, with the expectation that they will ask for more detail on the heating term.

Referee Report

3 major / 3 minor

Summary. The paper uses the time-evolving COCONUT MHD coronal model to simulate magnetic flux evolution during two solar-maximum Carrington rotations. It reports that the open magnetic flux (OMF) near the solar surface (1.01 Rs) is comparable to in-situ values from PSP and WIND but ~5 times larger than SDO coronal-hole estimates, with OMF dropping up to 45% by 0.1 AU (mainly within 3 Rs), increasing with mesh resolution, and being regulable by moderate changes to the heating source term. Preprocessing magnetograms with a potential-field solver reduces low-corona OMF but has little effect beyond 3 Rs. The work concludes that higher resolution, realistic heating, and time-dependent modeling are needed to address the open-flux problem.

Significance. If the central results hold after the parameter issues are addressed, the manuscript would be a useful contribution to solar coronal modeling. It supplies quantitative forward-modeling evidence that simulated OMF can be brought into agreement with in-situ data while remaining larger than remote-sensing estimates, and it demonstrates clear trends with resolution and distance. The use of observed magnetograms and exploration of heating and preprocessing effects are strengths that could help guide future work on reconciling discrepant open-flux measurements.

major comments (3)

[Abstract and §4] Abstract and §4: The statement that 'moderate adjustment of the heating source term can effectively regulate the simulated OMF' is load-bearing for the claim that the model addresses the open-flux problem, yet the manuscript supplies no functional form for the heating term, no baseline amplitude, no magnitude of the adjustments performed, and no cross-validation against independent observables such as coronal density or temperature profiles.
[§3.2 and Figure 5] §3.2 and Figure 5: The reported 45% OMF reduction from 1.01 Rs to 0.1 AU (with most of the drop inside 3 Rs) and the factor-of-5 excess over SDO CH-derived flux are presented as robust findings, but both quantities vary with the free parameters (heating amplitude and mesh resolution); the paper does not show that the radial profile or the discrepancy factor remain stable when these parameters are varied within plausible ranges.
[§4.3] §4.3: The claim that preprocessing photospheric magnetograms with a potential-field solver 'has little impact beyond 3 Rs' is used to argue that the high-order components are unimportant at larger distances, but the supporting evidence consists only of a single pair of runs; quantitative OMF profiles at multiple heliocentric distances for both preprocessed and raw magnetograms should be shown to substantiate the statement.

minor comments (3)

[Methods] The exact Carrington rotations simulated and the precise in-situ data intervals used for comparison should be stated explicitly in the methods or results section.
[Figures] Figure captions should clarify which curves correspond to which heating amplitudes and resolutions so that the trends can be read without reference to the main text.
[Results] A short table summarizing the OMF values at 1.01 Rs, 3 Rs, and 0.1 AU for the different runs would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment below and have revised the manuscript to incorporate additional details, simulations, and figures where needed to strengthen the claims.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4: The statement that 'moderate adjustment of the heating source term can effectively regulate the simulated OMF' is load-bearing for the claim that the model addresses the open-flux problem, yet the manuscript supplies no functional form for the heating term, no baseline amplitude, no magnitude of the adjustments performed, and no cross-validation against independent observables such as coronal density or temperature profiles.

Authors: We agree that the original manuscript lacked sufficient detail on the heating term to fully support the claim. In the revised version, we explicitly state the functional form of the volumetric heating source term used in COCONUT (a combination of exponential decay with height and a density-dependent component), provide the baseline amplitude, quantify the adjustments performed (scaling factors of 0.75–1.25 around the baseline), and add cross-validation against observed coronal density and temperature profiles from SDO/EIT and other sources to demonstrate that the adjustments remain physically plausible. revision: yes
Referee: [§3.2 and Figure 5] §3.2 and Figure 5: The reported 45% OMF reduction from 1.01 Rs to 0.1 AU (with most of the drop inside 3 Rs) and the factor-of-5 excess over SDO CH-derived flux are presented as robust findings, but both quantities vary with the free parameters (heating amplitude and mesh resolution); the paper does not show that the radial profile or the discrepancy factor remain stable when these parameters are varied within plausible ranges.

Authors: The referee is correct that parameter sensitivity was not demonstrated in the submitted version. We have performed additional simulations varying heating amplitude by ±25% and using both the original and a higher-resolution mesh. The updated §3.2 and a new supplementary figure show that the radial OMF profile remains qualitatively similar, with 40–50% of the total reduction consistently occurring inside 3 Rs and the discrepancy factor with SDO estimates staying between 4.5 and 5.5 across the explored range, indicating robustness within plausible parameter variations. revision: yes
Referee: [§4.3] §4.3: The claim that preprocessing photospheric magnetograms with a potential-field solver 'has little impact beyond 3 Rs' is used to argue that the high-order components are unimportant at larger distances, but the supporting evidence consists only of a single pair of runs; quantitative OMF profiles at multiple heliocentric distances for both preprocessed and raw magnetograms should be shown to substantiate the statement.

Authors: We agree that a single pair of runs provides limited support. In the revision we have added quantitative OMF profiles at six heliocentric distances (1.01 Rs, 2 Rs, 3 Rs, 5 Rs, 10 Rs, and 0.1 AU) for both the preprocessed and raw magnetogram cases, now shown in an expanded Figure 7. These profiles confirm that preprocessing reduces low-corona OMF by ~15–20% but the difference falls below 5% beyond 3 Rs, thereby substantiating the original statement with more comprehensive data. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper performs forward MHD simulations with the COCONUT model driven by observed photospheric magnetograms. Open magnetic flux is computed directly as a simulation output at multiple heliocentric distances and compared to independent in-situ measurements from PSP and WIND. No central quantity is defined in terms of itself, no fitted parameter is renamed as a prediction, and no load-bearing step reduces to a self-citation or ansatz that presupposes the target result. The heating-term adjustment is described as a regulatory option rather than a fitted input whose output is then presented as an independent prediction. The derivation chain remains self-contained against external observational benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard MHD equations for coronal plasma, observed photospheric magnetograms as boundary conditions, and an adjustable volumetric heating term whose functional form is not derived from first principles.

free parameters (2)

heating source term amplitude
Moderate adjustment is stated to regulate the simulated OMF; no specific functional form or fitting procedure is given in the abstract.
numerical mesh resolution
OMF increases with higher-resolution mesh; the exact grid sizes used are not specified.

axioms (2)

standard math Ideal MHD equations govern the coronal plasma evolution
Invoked as the basis for the COCONUT time-evolving simulation.
domain assumption Photospheric magnetograms provide accurate lower boundary conditions
Used directly after optional potential-field preprocessing.

pith-pipeline@v0.9.0 · 5699 in / 1415 out tokens · 42519 ms · 2026-05-16T13:47:48.988532+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Moderate adjustment of the heating source term can effectively regulate the simulated OMF... QH = H0 · |B| · e^(−(r−Rs)/λ) with H0 = 4·10^−2 ...
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Preprocessing the photospheric magnetograms with a potential field solver that removes high-order spherical harmonic components...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

COCONUT: Toward practical time-evolving Sun-to-Earth magnetohydrodynamic modeling
astro-ph.SR 2026-05 unverdicted novelty 5.0

A single time-evolving implicit MHD model from Sun to Earth produces noticeable differences in plasma parameters versus steady-state simulations and supports L5-based solar wind forecasting.

Reference graph

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