Modeling brightness temperature of prominences on the solar disk using ALMA single-dish observations

A. Hanslmeier; A. O. Benz; C. L. Selhorst; D. Sudar; F. Matkovi\'c; H.-G. Ludwig; I. Skoki\'c; R. Braj\v{s}a

REVIEW 4 major objections 5 minor 17 references

Modeling brightness temperature of prominences on the solar disk using ALMA single-dish observations

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that a perturbed ATLCW quiet-Sun model with independently varied density and temperature factors, not hydrostatic coupling, explains ALMA and legacy radio measurements of prominence brightness temperatures, implying…

desk verdict Useful new ALMA Band 3 prominence measurement and a transparent modeling exercise, but the statistical preference for non-hydrostatic support is overstated and the hydrostatic baseline is mislabeled. read the letter →

arxiv 2509.08605 v1 pith:YVA5FXSV submitted 2025-09-10 astro-ph.SR

F. Matković , R. Brajša , A. O. Benz , H.-G. Ludwig , C. L. Selhorst , I. Skokić , D. Sudar , A. Hanslmeier This is my paper · ORCID

classification astro-ph.SR

keywords solarprominencesbrightnesstemperatureALMAsingle-dishATLCWmodelthermalbremsstrahlunghydrostaticequilibriummagnetostaticsupportmillimeterradioemission

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to show that a single perturbed quiet-Sun model, the ATLCW atmosphere, can explain millimeter-wave brightness temperatures of solar prominences on the disk, and that the perturbation must treat density and temperature as independent parameters. The best non-hydrostatic fit gives prominence densities 60–68 times the quiet-Sun value and temperatures 155–159 times lower, reproducing the observed absorption at ALMA wavelengths while the hydrostatic fit (densities 159–163 times higher, temperatures the inverse) produces unphysical short-wavelength emission. If the claim holds, prominences are cool, dense plasma supported by magnetic fields rather than gas pressure alone, and their millimeter emission is thermal bremsstrahlung. A reader should care because ALMA single-dish data are sparse but this analysis turns five measurements into quantitative constraints on prominence density, temperature, and stability.

What carries the argument

The load-bearing object is the modified ATLCW quiet-Sun atmosphere: a 1D semi-empirical model of temperature and density versus height that the paper multiplies by constant factors $f_n$ and $f_T$ in a single 10,000-km layer at 40,000–50,000 km. The calculation then integrates the thermal-bremsstrahlung optical-depth formula (Equation 1) through the whole model atmosphere and converts to brightness temperature via the Rayleigh-Jeans radiative-transfer equation (Equation 2). A $\chi^2$-minimization over $f_n$ and $f_T$ against five radio measurements yields the best fits. The key identity is the hydrostatic constraint $f_T = 1/f_n$ compared with the non-hydrostatic case where $f_n$ and $f_T$ are free; the paper's evidence for magnetic support is the statistical and physical preference for the free fit.

What would settle it

Observe a single prominence with interferometric ALMA at arcsecond resolution across multiple bands and measure its electron density independently from spectral lines; if the beam-corrected brightness temperatures no longer prefer free density and temperature factors over the hydrostatic coupling, or the measured density falls outside 15–103 times the quiet Sun, the central claim fails.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that the 1D semi-empirical ATLCW quiet-Sun model, with electron density and temperature multiplied by constant factors over the height range 40,000–50,000 km and integrated over 0–57,797 km, reproduces the measured brightness temperatures of prominences on the solar disk at 1.21, 2.80, 3.10, 8.10, and 8.30 mm. The non-hydrostatic fit, in which the density factor (60–68, with uncertainty 15–103) and the temperature factor (1/159 to 1/155) are independent, is statistically preferred over the hydrostatic fit, in which temperature is forced to be the inverse of density (159–163). The paper interprets this as evidence that prominence stability is maintained by magnetic fields obeying magnetostatic conditions rather than by hydrostatic equilibrium, and that thermal bremsstrahlung is the dominant emission mechanism at these wavelengths. The claim includes derived prominence densities of about $0.35$–$3.9\times10^{10}$ cm$^{-3}$, consistent with earlier optical and EUV estimates, and prominence temperatures of about 6,290–6,957 K, on the cool side of previously reported ranges.

Load-bearing premise

The five radio measurements come from different prominences observed by different instruments at different epochs and spatial resolutions (beams from 17 to 144 arcsec), yet the fitting treats them as one dataset and applies one pair of multiplicative factors over a fixed height range; the paper itself notes that different structures were observed and that beam convolution is not corrected.

Editorial extensions

If this is right

Prominences on the solar disk should appear darker than the quiet Sun at all ALMA wavelengths, with contrast growing toward longer wavelengths; the non-hydrostatic model keeps this true even below 2 mm, where the hydrostatic model predicts excess emission.
Electron densities in quiescent prominences at chromospheric heights are about 60–68 times the quiet Sun (up to 103 with uncertainties), and temperatures about 155–159 times lower, giving values around $10^{10}$ cm$^{-3}$ and roughly 6,300–7,000 K.
The statistical preference for the non-hydrostatic fit implies that the global minimum of the brightness-temperature fit is reached with the plasma not in hydrostatic equilibrium, favoring magnetostatic support as the stability mechanism.
Thermal bremsstrahlung, with the same Gaunt-factor treatment, is sufficient to explain millimeter and sub-millimeter prominence emission; no additional emission mechanism is required.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the magnetic-support interpretation is right, the same modeling framework could be inverted: given measured brightness-temperature contrasts, one could map the excess magnetic field required for pressure balance, potentially yielding prominence field estimates from routine ALMA single-dish data without polarimetry.
The weak density dependence of the fitted brightness temperature noted in the paper suggests that millimeter observations primarily constrain prominence temperature, not density; combining ALMA with a density-sensitive diagnostic (e.g., EUV line ratios or H-alpha emission measure) for the same structure could break this degeneracy.
The method's reliance on perturbing a quiet-Sun model in a single layer could be extended to other magnetically supported cool structures, such as filaments in transition or coronal rain, where the same height range and free density and temperature factors may apply.
Future ALMA Band 5 and Band 7 observations, by filling the 3–10 mm gap now bridged by Metsähovi and Nobeyama, would test whether the fitted wavelength trend holds within a single instrument and without cross-calibration differences.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper has two genuine contributions: a new 2.8 mm ALMA single-dish prominence brightness temperature measurement, and a systematic two-parameter fit of the ATLCW quiet-Sun model to a composite radio dataset. The reported density and temperature factors are in line with earlier prominence work, and the authors are honest about the heterogeneity of the data, including the different instruments, beams, and structures, and the likely beam-convolution effect. The radiative transfer calculation is standard, and Table 1 gives enough information for someone to reproduce the fit. That is real value.

The soft spots are mostly in the interpretation. The paper claims the non-hydrostatic fit is 'highly statistically significant' over the hydrostatic fit, but the numbers in Table 2 do not support that. With Δχ² = 2.7 (procedure a) and 2.3 (procedure b) for one extra free parameter, the p-values are about 0.10 and 0.13. That is not significant at the 5% level. The authors even note that the non-hydrostatic model has an extra free parameter, so they should know better; this is not a minor wording issue, it is the main support for the magnetic-support conclusion. Relatedly, the 'hydrostatic equilibrium' baseline is not actually a hydrostatic atmosphere. Fixing f_T = 1/f_n enforces constant gas pressure between the PR and the quiet Sun, not dP/dh = -ρg. That is a different physical assumption, and calling it hydrostatic muddies the comparison. A true hydrostatic stratified model would be the right baseline, and the paper should either implement one or clearly state that it is testing constant-pressure versus independent density/temperature.

The other concern is the dataset. Five measurements from three instruments at different epochs, with beams from 17" to 144", are fit as if they sample one homogeneous prominence. The authors acknowledge the issue but do not correct or model the beam convolution, so the fitted factors may be biased toward lower contrast at long wavelengths. This does not destroy the modeling exercise, but it means the quoted density and temperature factors should carry larger effective uncertainties than the nominal parameter ranges in Table 2.

I would not defend the 'confirms thermal bremsstrahlung' statement either: the model assumes bremsstrahlung and fits to the data, so a good fit is not independent confirmation.

Who is this for? Solar radio astronomers working on prominence millimeter emission and semi-empirical modeling. The paper deserves a serious referee because it contains new data and a reproducible analysis, but it needs major revision on the statistics, the hydrostatic baseline, and the strength of the conclusions. I would send it to peer review, not desk reject, and would ask the authors to report a proper significance test (p-value or AIC) and resubmit.

Referee Report

4 major / 5 minor

Summary. This paper adapts the 1D semi-empirical ATLCW quiet-Sun model to compute the brightness temperature of solar prominences on the disk at millimeter wavelengths. The authors use ALMA single-dish Band 3 and Band 6 measurements, supplemented by Metsähovi 8.1 mm and Nobeyama 3.1/8.3 mm observations, and apply multiplicative factors to the electron density and temperature of the ATLCW model within a 40,000–50,000 km layer. They fit the factors by χ² minimization under two assumptions: a 'hydrostatic' case with f_T = 1/f_n and a 'non-hydrostatic' case with f_n and f_T free. The best fits give PR densities 60–68 times (hydrostatic: 159–163 times) the quiet-Sun value and temperatures roughly 155–163 times lower, with the non-hydrostatic model yielding, the authors claim, a statistically significant better fit. From this they conclude that prominences appear in absorption at mm wavelengths, that their stability is likely magnetic rather than hydrostatic, and that thermal bremsstrahlung is the dominant mm emission mechanism.

Significance. The radiative-transfer calculation is standard and the data are presented transparently in Table 1, with a useful sensitivity check excluding Metsähovi discussed in Section 5. If the model comparison were statistically sound, the paper would provide a simple semi-empirical description of prominence mm emission and a testable prediction of absorption contrast. However, the central statistical claim is not supported by the paper's own numbers, the 'hydrostatic' baseline is not a true hydrostatic stratification, and the five measurements are heterogeneous in structure and beam size. As presented, the work is a promising framework rather than an established result.

major comments (4)

[§4.2, Table 2] The statement that the difference in χ²_min between the hydrostatic and non-hydrostatic fits is 'highly statistically significant' is not supported. The models are nested with one extra free parameter; from Table 2, Δχ² = 14.39 − 11.69 = 2.70 (procedure a) and Δχ² = 8.11 − 5.84 = 2.27 (procedure b), corresponding to p ≈ 0.10 and p ≈ 0.13 on one degree of freedom. These are not significant at the 5% level, and the absolute χ² values for procedure a indicate poor fits even for the preferred model (χ²_min = 11.69 with 3 degrees of freedom). The conclusion that the data 'strongly favor' the non-hydrostatic/magnetic-support model must be revised or supported by a proper likelihood-ratio test with reported p-values.
[§4.1, Table 2] The 'hydrostatic equilibrium' case is not modeled as hydrostatic equilibrium. Setting f_T = 1/f_n imposes constant gas pressure (n_e T_e = const.), not the hydrostatic relation dP/dh = −ρg with a stratified atmosphere. A true hydrostatic model would have scale-height pressure and density profiles varying with height, which is incompatible with applying a single uniform f_T across the 40,000–50,000 km layer. Because the comparison between the two cases is the basis for the paper's main conclusion, the baseline model must be either correctly implemented or explicitly relabeled as 'constant pressure' and the conclusions adjusted accordingly.
[§3, §4.1] The joint fit treats five measurements of different prominences from different instruments and epochs as a single homogeneous dataset, despite the paper's own statement in Section 4.1 that 'ALMA, Metsähovi, and Nobeyama all observed a different PR structure.' Beam sizes range from 17″ to 144″ and beam-convolution effects are acknowledged but not corrected. Under these conditions, the fitted f_n and f_T values and the model comparison could be biased by unknown structure-to-structure variations and by resolution-dependent contrast loss. A quantitative treatment—for example, convolving the modeled profiles with the respective beams or fitting per-structure normalization parameters—is needed before the reported factors can be taken at face value.
[§5] The statement that the good agreement 'confirms that thermal bremsstrahlung is indeed the dominant radiation mechanism' is partly circular. Thermal bremsstrahlung is assumed in the optical-depth expression (Eq. 1), and the density/temperature factors are fitted to the same measured brightness temperatures used for the comparison. The agreement therefore validates internal consistency but does not independently confirm the emission mechanism; a direct test would require comparing against an alternative emission model or using independent constraints on n_e and T_e.

minor comments (5)

[Abstract and §4.2] The ranges '60–68' and '159–163' for density factors should be labeled by stability assumption at first mention to avoid apparent inconsistency with the abstract's combined '60–163' range.
[Table 1] The Nobeyama 3.10 mm entry displays '= 𝑻𝐛(PR)' in an unusual way; the column should be cleaned up, and the date range '1984-07-16 (start) ... 1984-07-22 (end)' should be presented more clearly.
[Figure 2 caption] The symbols for the three instruments are listed without a legend definition in the caption; add the symbol definitions as is done for Figure 3.
[§2] The statement that only two height points fall in the 40,000–50,000 km range, followed by cubic-spline interpolation by a factor of 100, should be accompanied by a quantitative convergence test showing that the interpolated profiles are stable over the wavelength range of interest; the text asserts this verbally but gives no numerical check.
[Eq. (5)] Equation (5) could benefit from a short derivation, and the approximation B_QS² ≈ 0 should be stated as an explicit assumption before the ΔB calculation, not only in the following paragraph.

Circularity Check

2 steps flagged · score 6.0 of 10

The 'confirmation' of thermal bremsstrahlung is a fitted-input validation and procedure 'b' builds its data from the model being fitted; the core fitted density/temperature values are externally compared, so the circularity is partial.

fitted input called prediction [Section 5, paragraph beginning 'We should note that the good fit...'; assumption set in Section 2, Eq. (1).]
"We should note that the good fit between the calculated and measured brightness temperatures also confirms that the previously assumed thermal bremsstrahlung is indeed the dominant radiation mechanism of PRs in the mm and sub-mm wavelength range, as was the case for QS, AR, and CH structures studied in Paper I."

The brightness temperature is computed with Eq. (1), which assumes thermal bremsstrahlung, and the model's free parameters f_n and f_T are adjusted by chi-square minimization against the very five measurements that are then said to be in 'good fit' with the resulting profile. A fit with free parameters to the data cannot confirm the radiation mechanism assumed to generate the fit; the 'confirmation' is logically the assumed mechanism plus optimized parameters, not an independent test.
self definitional [Section 4, paragraph defining measurement procedures 'a' and 'b'.]
"The second set, referred to as differential measurements, is obtained using a similar procedure by now adding ΔTb from Table 1 to the QS brightness temperature predicted by the brightness temperature profile obtained for the original and unperturbed ATLCW QS model based on the procedure described in Section 2 for each wavelength."

For procedure 'b', the 'measured' blue points are constructed by adding the observed contrast ΔTb to the brightness-temperature prediction of the very ATLCW model that is being perturbed and fitted. The subsequent agreement of the best-fit b-profiles with these blue points is therefore partly built into the dataset definition, although the ΔTb term itself is observational. This makes the b-procedure a self-referential sensitivity check rather than an independent validation.

full rationale

The paper's substantive fitted quantities (f_n, f_T, derived PR density and temperature) are not circular per se: they are optimization outputs and are compared with external constraints such as Parenti (2014), Engvold et al. (1990), and Jensen & Wiik (1990). The hydrostatic/non-hydrostatic comparison is a fit comparison, not a circular reduction by the paper's own equations; its alleged 'highly statistically significant' preference is a statistical-correctness issue (Table 2 gives Δχ² ≈ 2.3-2.7 for one extra degree of freedom, p≈0.10-0.13), not a circularity. However, two load-bearing validation claims do reduce by construction: (1) the statement that the good fit confirms thermal bremsstrahlung uses the same assumed mechanism and the same fitted data points as the fit itself, so the confirmation is not independent; (2) procedure 'b' defines its 'measurements' partly from the ATLCW QS model being fitted, making the blue-profile agreement partially definitional. These are partial circularities in the validation logic, not a complete equivalence of the derivation to its inputs; hence score 6 rather than 8-10. No load-bearing self-citation chain was found: Paper I is used for method and prior validation, while the central thermal-bremsstrahlung assumption is also backed by standard external references.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central model has two physical free parameters (f_n and f_T, with f_T dependent on f_n in the hydrostatic case). The background ATLCW model, the bremsstrahlung emissivity, the chosen perturbation height range, the uniform 5% errors, and the pressure-balance relation for the magnetic field estimate are all assumed inputs. No new physical entities are introduced.

free parameters (2)

density multiplicative factor f_n = hydrostatic: 159-163; non-hydrostatic: 60-68 (uncertainty ranges extend 15-103)
Multiplicative factor applied to the ATLCW QS electron density in the 40,000-50,000 km layer; determined by chi-square minimization against the radio measurements.
temperature multiplicative factor f_T = hydrostatic: 1/f_n (1/159 to 1/163); non-hydrostatic: 1/155 to 1/159
Multiplicative factor applied to the ATLCW QS temperature in the same layer; independent in the non-hydrostatic fit, tied to f_n in the hydrostatic fit.

assumptions (5)

domain assumption Thermal bremsstrahlung is the dominant emission mechanism at mm and sub-mm wavelengths for prominences, and the magnetic field can be neglected in the emissivity.
Invoked in Section 2 and used to derive Equation 1. It is consistent with prior literature but is not independently tested here; the paper later treats the good fit as confirmation, which is circular.
domain assumption The ATLCW quiet-Sun model is a valid background atmosphere for the chromosphere and corona at heights 0 to 57,797 km, and the prominence can be represented by scaling its density and temperature only within 40,000-50,000 km.
The modeling relies entirely on this input model (Avrett et al. 2015) and on the chosen scaling layer, which is justified only by citations (Bastian et al. 1993; Brajša et al. 2009).
ad hoc to paper Under 'hydrostatic equilibrium' the temperature factor is the inverse of the density factor (constant gas pressure).
Called hydrostatic equilibrium in Sections 4.1 and 5, but the relation f_T = 1/f_n is isobaric (equal gas pressure), not a stratified hydrostatic equilibrium. This modeling choice drives the comparison between the two cases.
ad hoc to paper All radio measurements can be assigned a uniform 5% measurement uncertainty.
Used for the chi-square minimization and for the factor uncertainty ranges; no instrument-specific error analysis is provided.
domain assumption For the magnetic field estimate, the quiet-corona magnetic field at 40,000-50,000 km is negligible compared to the prominence field, and the pressure-balance equation (Equation 5) applies.
Used in Section 5 to derive Delta B = 1 G from the fitted factors, citing Yang et al. 2024 for weak quiet-corona fields.

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Cite this review

Pith. "Pith review of Modeling brightness temperature of prominences on the solar disk using ALMA single-dish observations." pith.science (2026). https://pith.science/paper/YVA5FXSV

@misc{pith2026250908605,
  author       = {Pith},
  title        = {Pith review of: Modeling brightness temperature of prominences on the solar disk using ALMA single-dish observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YVA5FXSV}},
  note         = {Machine review of arXiv:2509.08605}
}

read the original abstract

Prominences (PRs) are among the most common solar phenomena, yet their full physical picture, particularly their chromospheric mm emission, remains incomplete. The new Atacama Large Millimeter/submillimeter Array (ALMA) presents an opportunity to study PRs at mm and sub-mm wavelengths through a combination of measurements and theoretical modeling. We utilize ALMA single-dish measurements alongside data from other radio instruments to model the PR brightness temperature through adaptation and modification the 1D semi-empirical Avrett-Tian-Landi-Curdt-W\"ulser (ATLCW) quiet-Sun (QS) model. The calculated and measured PR brightness temperatures were found to be lower than the measured QS value and predictions from the unperturbed ATLCW QS model across the ALMA wavelength range, consistent with PRs appearing in absorption. The PR density was found to be 60 - 163 times higher and temperature 155 - 163 times lower than the QS level, aligning with previous measurements. A key finding emerged with the non-hydrostatic equilibrium assumption, yielding a more physically consistent PR brightness temperature. This suggests that PR stability is most likely maintained by its magnetic field obeying magnetostatic conditions rather than by pure hydrostatic equilibrium, supporting recent studies. Additionally, our results confirm that thermal bremsstrahlung is the dominant radiation mechanism for PRs at mm and sub-mm wavelengths.

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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