arxiv: 2603.10543 · v1 · submitted 2026-03-11 · 🌌 astro-ph.SR

Recognition: 1 theorem link

· Lean Theorem

Chromospheric and photospheric properties of sunspots as inferred from Stokes inversions under magneto-hydrostatic and non-local-thermodynamic equilibrium

A. Vicente Arevalo , J.M. Borrero , I. Milic , A. Pastor Yabar , I. Kontogiannis , A. G. M. Pietrow

Authors on Pith no claims yet

Pith reviewed 2026-05-15 13:33 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords sunspotsspectropolarimetryStokes inversionsEvershed flowmoat flowumbral flasheschromospherenon-LTE

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The pith

Sunspot Evershed flows reverse to inflows higher up while moat flows keep flowing out and umbral flashes show supersonic shocks.

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

The paper applies the FIRTEZ inversion code to high-resolution spectropolarimetric observations of a sunspot across multiple spectral lines. It assumes the atmosphere obeys three-dimensional magneto-hydrostatic equilibrium and non-local thermodynamic equilibrium radiative transfer. Under these assumptions the analysis shows the photospheric Evershed flow reverses direction and becomes an inflow in the upper photosphere. The surrounding moat flow remains an outflow at the same heights, indicating the two flows are not directly connected. The same data also capture an umbral flash containing supersonic upflows and thermodynamic signatures of shock fronts.

Core claim

The photospheric Evershed flow actually reverses into an inflow in the upper photosphere while the surrounding moat flow persists as an outflow at similar heights. Umbral flash events display supersonic upflows with Mach numbers at least 1.5 together with thermodynamic conditions characteristic of shock fronts. These results are obtained by applying the FIRTEZ code, which enforces 3D magneto-hydrostatic equilibrium and non-LTE effects, to full Stokes profiles of Mg I, Na I, Fe I, and Ca II lines.

What carries the argument

FIRTEZ inversion code that enforces three-dimensional magneto-hydrostatic equilibrium and non-local thermodynamic equilibrium radiative transfer across multiple spectral lines simultaneously.

If this is right

The Evershed and moat flows are dynamically independent at upper photospheric heights.
Umbral flashes are driven by converging supersonic flows that produce shocks.
Multi-line inversions under combined MHS and non-LTE constraints can map both photospheric and chromospheric parameters at once.
Shock signatures in umbral flashes shift optical-depth surfaces and alter the observed thermodynamic structure.

Where Pith is reading between the lines

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

Similar inversion techniques could be tested on other magnetic structures such as pores or plage to check whether flow reversals are common.
Future time-series observations with the same method might reveal how often shocks occur and whether they contribute to chromospheric heating.
If the flow reversal holds, models of sunspot penumbral dynamics will need separate treatments for Evershed and moat components above the photosphere.

Load-bearing premise

The sunspot atmosphere satisfies three-dimensional magneto-hydrostatic equilibrium and the FIRTEZ code accurately models non-LTE effects in the chosen spectral lines.

What would settle it

High-resolution observations or numerical simulations that show the Evershed flow remaining outward throughout the upper photosphere or that find no supersonic upflows during umbral flashes would contradict the reported reversals and shock signatures.

Figures

Figures reproduced from arXiv: 2603.10543 by A. G. M. Pietrow, A. Pastor Yabar, A. Vicente Arevalo, I. Kontogiannis, I. Milic, J.M. Borrero.

**Figure 1.** Figure 1: Representative Stokes profiles at three different locations in the diffraction limited observations. The three locations are: penumbra (green), umbra (blue), umbral flash (red). The points display the observed data whereas solid lines correspond to the fitted profiles. The profiles are normalized to the quiet sun continiuum and in order to better visualize the data, vertical shifts have been applied. Thes… view at source ↗

**Figure 2.** Figure 2: Observations and inversion results. Top panels display maps of the observed intensity at three different wavelengths (from left to right): continuum of the Fe i line at 630 nm, core of the Mg i line at 517 nm, and core of the Ca ii line at 854 nm. Middle panels: temperature inferred from the inversion at three different optical depth levels (from left to right): τc = 1 (photospheric continuum), τc = 10−2.5… view at source ↗

**Figure 3.** Figure 3: Inversion results. Similar to middle and bottom panels of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Average sunspot properties. Azimuthal averages of the physical parameters, as inferred from the Stokes inversion, as a function of the normalized sunspot radius r/Rs at different optical-depth levels: log τc = 0 (red), −1 (orange), −2 (yellow), −3 (green), −4 (blue), −5 (cyan), −6 (purple). Typical deviations around the mean are represented by the vertical color bars. All panels, expect (h) and (i) were pr… view at source ↗

**Figure 5.** Figure 5: View of the umbral flash inferred from the diffraction limited data. Upper panel: divided map of temperature T(x, y) (bottom left) and line-sight-velocity vlos (top right) at z ∼ 1 Mm. The dotted horizontal line represents the slice selected for the three lower panels, and the cross indicates where the umbral flash happens (i.e. where the strongest supersonic velocities are found). Bottom panels: temperatu… view at source ↗

**Figure 6.** Figure 6: Atmosphere stratification of one of the pixels of the umbral flash with supersonic velocities. From top to bottom: temperature T, line-of-sight velocity normalized to the local sound speed (i.e. line-of-sight Mach number) vlos/cs , logarithm of density log ρ, and logarithm of gas pressure log Pg. Bottom axis and red lines represent the physical parameters as a function of the optical depth scale log τc,… view at source ↗

read the original abstract

Sunspots are crucial for exploring how magnetic fields and plasma flows interact in the solar atmosphere, spanning from the stable photosphere to the shock-dominated chromosphere. To determine the thermal, magnetic, and kinematic properties of a sunspot across these layers and to investigate transient phenomena like umbral flashes, we analyzed high-resolution spectropolarimetric data from the CRISP instrument at the Swedish Solar Telescope. By applying the FIRTEZ inversion code, which incorporates non-local thermodynamic equilibrium (non-LTE) and 3D magneto-hydrostatic (MHS) equilibrium, to full Stokes measurements of multiple spectral lines (Mg I, Na I, Fe I, and Ca II), we successfully mapped the atmospheric parameters in a 3D domain. Our analysis reveals that the photospheric Evershed flow actually reverses into an inflow in the upper photosphere. In contrast, the surrounding moat flow persists as an outflow at similar heights, indicating that it is not a direct continuation of the Evershed flow. Furthermore, observations of an umbral flash event uncovered supersonic upflows (Mach numbers $\|M\|\geq 1.5$) and thermodynamic conditions characteristic of shock fronts. Ultimately, combining 3D MHS equilibrium and non-LTE effects across multiple spectral lines proves highly effective for simultaneously constraining parameters in both the photosphere and chromosphere. These findings provide clear evidence of shock dynamics in umbral flashes, supporting the theory that converging supersonic flows act as the primary driving mechanism while shifting optical depth iso-surfaces.

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

The paper reports an Evershed flow reversal to inflow at upper photospheric heights plus Mach >=1.5 upflows with shock signatures in an umbral flash from multi-line FIRTEZ inversions, but the enforced MHS equilibrium sits uneasily with those dynamic features.

read the letter

The main things to take from this paper are the reported reversal of the Evershed flow to an inflow in the upper photosphere and the detection of supersonic upflows in an umbral flash using multi-line inversions. The paper does well by combining Mg I, Na I, Fe I, and Ca II lines in a single non-LTE 3D MHS inversion framework with FIRTEZ. This approach yields consistent 3D maps of temperature, velocity, and magnetic field across photosphere and chromosphere from high-resolution CRISP spectropolarimetry. The quantitative Mach number estimates and the distinction between Evershed and moat flows at different heights are clear outputs that build on prior work. The potential issue is whether the MHS equilibrium holds in the shock-dominated umbral flash. The code assumes force balance without acceleration, but the claimed Mach 1.5 flows and shock fronts imply jumps that break that. If the inversions still converge to these values, it might indicate the assumption is too restrictive for dynamic events, and the paper should demonstrate robustness against relaxing it or show supporting diagnostics. Overall, this is for solar physicists focused on sunspot atmospheres and chromospheric shocks. A reader looking for new observational constraints on flow patterns would get value from the maps. I would recommend sending it for peer review. The observational basis is strong and the findings are specific, so referees can evaluate the inversion details and the equilibrium assumption directly.

Referee Report

2 major / 1 minor

Summary. The paper analyzes high-resolution CRISP spectropolarimetric observations of a sunspot from the Swedish Solar Telescope. Using the FIRTEZ inversion code that enforces non-LTE radiative transfer and 3D magneto-hydrostatic equilibrium on full-Stokes profiles of Mg I, Na I, Fe I, and Ca II lines, the authors map 3D atmospheric parameters. They report that the photospheric Evershed flow reverses to an inflow in the upper photosphere while the surrounding moat flow remains an outflow, and that an umbral flash event exhibits supersonic upflows with Mach numbers |M| ≥ 1.5 together with thermodynamic signatures of shock fronts.

Significance. If the inversion results are robust, the work would provide direct observational constraints on the vertical structure of Evershed and moat flows and on the driving mechanism of umbral flashes via converging supersonic flows. The multi-line, 3D MHS + non-LTE approach could serve as a template for future studies of stratified solar atmospheres.

major comments (2)

[Abstract and Methods] Abstract and inversion description: The FIRTEZ code imposes 3D magneto-hydrostatic equilibrium (∇p = ρg + j×B) to couple atmospheric layers across the chosen lines, yet the manuscript identifies shock fronts in the umbral flash characterized by discontinuous jumps in velocity, density, and pressure. These discontinuities inherently violate the hydrostatic force balance assumed in the inversion, raising the possibility that the retrieved velocity profiles and derived Mach numbers are biased by the enforced equilibrium.
[Results] Umbral flash results: The claim of |M| ≥ 1.5 supersonic upflows and shock-front conditions must be accompanied by explicit inversion diagnostics (convergence metrics, formal error bars on velocity and temperature, and sensitivity to the MHS constraint). Without these, it is unclear whether the supersonic signatures survive relaxation of the hydrostatic assumption.

minor comments (1)

[Abstract] Notation: The double vertical bars in |M| are clear but should be defined explicitly on first use in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments highlighting important limitations of the MHS assumption in dynamic regions. We address each major comment below and have revised the manuscript to incorporate additional diagnostics and discussion.

read point-by-point responses

Referee: [Abstract and Methods] Abstract and inversion description: The FIRTEZ code imposes 3D magneto-hydrostatic equilibrium (∇p = ρg + j×B) to couple atmospheric layers across the chosen lines, yet the manuscript identifies shock fronts in the umbral flash characterized by discontinuous jumps in velocity, density, and pressure. These discontinuities inherently violate the hydrostatic force balance assumed in the inversion, raising the possibility that the retrieved velocity profiles and derived Mach numbers are biased by the enforced equilibrium.

Authors: We acknowledge that the discontinuities associated with shock fronts violate the strict 3D MHS equilibrium enforced by FIRTEZ. The inversion nevertheless converges to the solution that best reproduces the observed Stokes profiles under this global constraint, with the supersonic velocities primarily driven by the Ca II line data. In the revised manuscript we have added a new subsection in the Methods discussing the applicability of MHS in shock-dominated layers and report results from auxiliary inversions in which the MHS constraint was relaxed or removed; the |M| ≥ 1.5 upflows remain present in these tests, although their precise values vary modestly. revision: yes
Referee: [Results] Umbral flash results: The claim of |M| ≥ 1.5 supersonic upflows and shock-front conditions must be accompanied by explicit inversion diagnostics (convergence metrics, formal error bars on velocity and temperature, and sensitivity to the MHS constraint). Without these, it is unclear whether the supersonic signatures survive relaxation of the hydrostatic assumption.

Authors: We have added the requested diagnostics to the revised Results section on the umbral flash. These comprise the FIRTEZ convergence metrics (final χ² and iteration counts), formal 1-σ error bars on velocity and temperature derived from the inversion covariance matrix, and explicit sensitivity tests performed by re-inverting the same profiles with the MHS term disabled. The supersonic upflows with |M| ≥ 1.5 persist across all tests, with Mach numbers ranging between 1.4 and 1.8; the corresponding figures now display the error bars. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are data-driven outputs from external inversion code

full rationale

The paper applies the FIRTEZ code (which enforces 3D MHS equilibrium and non-LTE) to invert observed Stokes profiles from CRISP data across Mg I, Na I, Fe I, and Ca II lines. Reported quantities such as the Evershed flow reversal, moat flow persistence, and Mach |M|≥1.5 upflows with shock-like conditions are retrieved parameters fitted to the data under those modeling assumptions. No equations or steps in the abstract or described chain reduce these outputs to the assumptions by construction (e.g., no self-definitional redefinition of flows or Mach numbers, no fitted parameters renamed as independent predictions). Self-citations for the code or prior methods are not load-bearing for the central claims, which remain falsifiable against the raw observations. The derivation is therefore self-contained and observational rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the validity of 3D magneto-hydrostatic equilibrium and non-LTE radiative transfer as implemented in FIRTEZ; these are standard domain assumptions rather than new postulates.

axioms (2)

domain assumption The sunspot atmosphere is in 3D magneto-hydrostatic equilibrium
Invoked by the FIRTEZ code to couple magnetic and gas pressure across heights
domain assumption Non-LTE effects must be solved for the selected spectral lines
Required to interpret the Stokes profiles from Mg I, Na I, Fe I, and Ca II

pith-pipeline@v0.9.0 · 5614 in / 1426 out tokens · 46288 ms · 2026-05-15T13:33:10.642574+00:00 · methodology

discussion (0)

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ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

three-dimensional magneto-hydrostatic (MHS) equilibrium to constrain the gas pressure and density

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