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Emissivity line ratios for [Mn III] and spectral diagnostics of H II regions

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Pith's one-line read This paper establishes that forbidden emission lines of doubly ionized manganese provide temperature- and density-sensitive emissivity ratios that can diagnose H II regions and supernova remnants, and potentially measure the cosmic abundanc

desk verdict First [Mn III] emissivity diagnostics, but the truncated R-matrix target and missing error bars make the density/temperature claims plausible rather than proven. read the letter →

arxiv 2607.21816 v1 pith:6FOLM55H submitted 2026-07-23 astro-ph.GA physics.atom-ph

Zher Samak (Department of Physics , Al Aqsa University , Gaza , Palestine) , Sultana N. Nahar , Anil K. Pradhan (Department of Astronomy , The Ohio State University , Columbus
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Ohio USA 43210)
This is my paper · ORCID
classification astro-ph.GAphysics.atom-ph
keywords atomicdataforbiddenlinesemissivitylineratiosdensitydiagnostics[MnIII]HIIregionssupernovaremnantsmanganeseabundance
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The pith

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

The reading

This paper argues that forbidden emission lines from doubly ionized manganese, [Mn III], can serve as practical diagnostics of electron density and temperature in H II regions and supernova remnants. It provides the first theoretical emissivity ratios for this ion, built from new Breit–Pauli R-matrix collision strengths for 703 forbidden transitions among the lowest 38 fine-structure levels. Two ratios, one in the ultraviolet and one in the mid-infrared, are claimed to be nearly pure density diagnostics across log10 Ne = 3–7 cm^-3, while two further ratios also respond to temperature. If these ratios hold up, they give observers a new way to measure physical conditions and, ultimately, the manganese-to-iron abundance ratio that tracks the chemical evolution of galaxies.

What carries the argument

The central object is the set of forbidden E2/M1 emission lines among the 38 lowest fine-structure levels of Mn III (configurations 3d^5 and 3d^4 4s). The argument is carried by a two-stage calculation: Breit–Pauli R-matrix scattering supplies collision strengths for all 703 transitions, and a collisional-radiative model turns Maxwellian-averaged effective collision strengths together with radiative A-values into level populations and emissivity line ratios. The ratios are chosen so that reddening and calibration uncertainties cancel—pairs of lines lie close in wavelength and share a lower level—leaving the density and temperature dependence exposed.

What would settle it

Measure R1 and R2 in a well-studied H II region or supernova remnant whose electron density is independently known from, e.g., the [S II] 6716/6731 line ratio, and check whether the observed values fall on the predicted curves. Alternatively, recompute the collision strengths with a target that includes the 3d^4 4p configuration; if the effective collision strengths change by more than about 15 percent, the diagnostic curves would shift.

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Extended reading notes

Core claim

The central claim is that selected forbidden E2/M1 transitions within the ground 3d^5 configuration of Mn III produce emissivity ratios that are sensitive to electron density and, in some cases, temperature under nebular conditions. In particular, R1 = I(2996.42 Å)/I(2997.45 Å) and R2 = I(4.35 μm)/I(4.33 μm) are reported to vary monotonically with electron density over log10 Ne = 3–7 cm^-3 while remaining virtually independent of electron temperature from 2500 to 40,000 K, making them pure density diagnostics. R3 = I(4.40 μm)/I(4.33 μm) and R4 = I(8213.52 Å)/I(8081.28 Å) depend on both density and temperature, so combining them with R1 or R2 lifts the temperature–density degeneracy in nebula

Load-bearing premise

The 38-level close-coupling target, limited to the 3d^5 and 3d^4 4s configurations, is sufficient to compute the collision strengths that drive the line ratios; if excluded higher levels add significant resonances, the claimed density and temperature sensitivities could change.

Editorial extensions

If this is right

  • R1, with both lines within about an ångström of each other, is robust against interstellar reddening and flux calibration, giving a clean density probe for H II regions and planetary nebulae.
  • R2 lies in the mid-infrared and is accessible to JWST, extending the same density diagnostic to red-shifted sources.
  • Combining R1 or R2 with R3 or R4 yields simultaneous electron temperature and density in nebular environments.
  • Detection of any of these lines could establish a new manganese abundance indicator and allow the Mn/Fe ratio to be measured in high-redshift galaxies.
  • The new atomic dataset for Mn III fills a gap: previously, no emission lines from this ion had been used for nebular diagnostics.

Reading between the lines

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

  • If the density curves survive observational testing, these ratios add a new ion to the standard nebular diagnostic set, providing a check on abundances in metal-rich supernova remnants where manganese is enhanced.
  • Because the ratios are ratios, they may give a nearly direct Mn III/Mn ionization-independent abundance estimate when combined with a photoionization model's ionization correction.
  • A natural archival test is to search existing JWST NIRSpec spectra of high-redshift galaxies for the 4.3 μm lines; a positive detection would immediately yield density and, eventually, Mn/Fe.
  • The sensitivity to target-size truncation suggests a useful numerical experiment: recompute the collision strengths with the 3d^4 4p configuration included and see whether the diagnostic curves shift by more than the stated 10–15 percent accuracy.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This paper presents the first theoretical emission-line study of [Mn III] for nebular diagnostics. The authors use a Breit–Pauli R-matrix scattering calculation for electron-impact excitation among 38 even-parity fine-structure levels of Mn III (from the 3d5 and 3d4 4s configurations), with SUPERSTRUCTURE providing energy levels and E2/M1 A-values. They compute Maxwellian-averaged effective collision strengths at 2500–40,000 K and build a collisional-radiative model to derive four line emissivity ratios. They claim that R1 = I(2996.42 Å)/I(2997.45 Å) and R2 = I(4.35 μm)/I(4.33 μm) are pure electron-density diagnostics over log10 Ne = 3–7 cm^-3, while R3 and R4 constrain temperature and density. The paper also discusses, and leaves open, the tentative detection of a Mn III line at 6821.16 Å.

Significance. If correct, this would be a genuinely useful new set of atomic diagnostics: [Mn III] lines in the NUV, NIR, and MIR could be observed with JWST and ground-based instruments, and the Mn/Fe ratio is of astrophysical interest as a nucleosynthetic chronometer. The calculation is self-contained and parameter-free in the sense that no parameters are fitted to the target line ratios; energies are benchmarked against NIST and the methodology is standard. The paper also makes falsifiable predictions (R1–R4) and includes a careful caveat about the uncertain 6821 Å line. The main weakness is that the scattering calculation uses a truncated target, and the accuracy of the resulting collision strengths is not independently established for Mn III.

major comments (3)
  1. [Sections 1.1–1.2, Eq. (1), Figs 1–2] The BPRM target expansion is restricted to 38 even-parity levels from 3d5 and 3d4 4s, while the SUPERSTRUCTURE calculation finds 1421 fine-structure levels up to ~2.2 Ry, including odd-parity 3d4 4p configurations. Autoionizing resonances converging to the excluded 3d4 4p thresholds will lie at incident energies below those thresholds, i.e. in the near-threshold region that dominates the Maxwellian average at Te = 2500–40,000 K (E ≲ 0.3 Ry). Figure 1 shows dense resonance structure in exactly this region. Omitting entire channel groups leaves these resonance contributions uncomputed, and no independent collision calculation or experimental cross-section is provided. Because the claimed temperature insensitivity of R1 and R2, and the temperature/density sensitivity of R3 and R4, all depend on the effective collision strengths, the target truncation is a load-bearing issue. The authors sho
  2. [Section 2.2, Table 3, Section 2.3] No propagated uncertainties are given for the effective collision strengths or the line ratios. The stated 10–15% accuracy is transferred from Mg II (Sigut & Pradhan 1995), not benchmarked for Mn III. Since R1 and R2 are proposed as pure density diagnostics, the monotonic variation in Fig. 2 should be shown to exceed the combined uncertainty in the underlying Υ_ij. A sensitivity test (e.g., varying the relevant Υ_ij by ±10% and recomputing R1–R4) or a simple error propagation through Eq. (3) would establish whether the claimed diagnostic power survives realistic collision-strength errors.
  3. [Section 3 and Data Availability] The paper states that complete datasets will be described in a subsequent paper. For the diagnostics to be usable and checkable by the community, the full set of computed collision strengths and A-values (or a table of the 703 Υ_ij at the six temperatures) should be made available at acceptance, not deferred. The present Table 3 gives only a sample, so an independent user cannot reproduce the claimed ratios in Fig. 2.
minor comments (6)
  1. [Section 1.2] The sentence 'the energy range considered extended up to the highest threshold is at 2.2 Ry and above up to 5.0 Ry' is unclear and appears inconsistent with the statement that the target is limited to the lowest 38 levels dominated by 3d5 and 3d4 4s. Clarify which thresholds are included and what the 2.2 Ry value refers to.
  2. [Table 3] There are duplicated rows: '4P3/2 – 4D3/2 at 43674.12' and '4P5/2 – 4D7/2 at 44025.64' appear twice with identical values. These duplicates should be removed.
  3. [Section 1.1] The phrase 'The selected fine-structure levels of the are of even parity' has a missing word ('target' or 'ion').
  4. [References] References Nahar 2020a and Nahar 2020b cite the same paper with slightly different author formatting; unify them. Also, the text uses both 'H ii regions' and 'H II regions'; use consistent notation.
  5. [Section 2.3] Although the figure caption describes four panels, the actual plots for Fig. 2 are not included in the manuscript text. The numerical values of R1–R4 are needed to assess the claimed monotonicity and temperature insensitivity.
  6. [Section 2.3, Esteban et al. discussion] The discussion of the 6821.16 Å line is appropriately cautious, but it is much longer than necessary for a results section; it could be summarized as a note that the predicted Mn III candidates are too weak to confirm the tentative identification.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: [Mn III] emissivity ratios are computed from ab initio atomic structure and R-matrix collision calculations benchmarked against NIST; no predicted ratio is an input to the calculation.

full rationale

The derivation chain is self-contained. The energy levels and A-values are calculated with SUPERSTRUCTURE and compared with NIST experimental energies (Kramida et al. 2023); the collision strengths are computed with the BPRM R-matrix method (standard methodological citations: Burke 2011; Hummer et al. 1993; Pradhan & Nahar 2011), and the collisional-radiative model (Hoy et al. 2023; Pradhan & Nahar 2011) turns those atomic data into emissivity ratios. Nothing in R1-R4 is fitted from the ratio curves themselves; the density/temperature behavior of Fig. 2 is an output, not an input. The cited accuracy estimate from Mg II (Sigut & Pradhan 1995) is an external benchmark from a different ion and does not define the [Mn III] result. The acknowledged 38-level target truncation and neglect of some configurations is a possible source of error in the collision strengths, but it is a correctness risk rather than circular reasoning: the prediction does not assume the conclusion. Self-citations to NORAD, spectracode, and the authors' prior [O III] work are methodological or contextual, not load-bearing definitions of the new diagnostics. Thus no claim reduces by construction to its inputs.

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

The central calculation introduces no fitted free parameters and no new physical entities; it relies on established computational methods and several domain assumptions. The main modeling risks are the 38-level truncation, the transferred 10-15% accuracy estimate from Mg II, and the assumption of a Maxwellian electron distribution in a collisional-radiative equilibrium with only 38 levels. None of these assumptions is tested against observed [Mn III] emission in the paper.

assumptions (5)
  • domain assumption 38-level close-coupling target (3d5 + 3d4 4s) is sufficient for accurate collision strengths among low-lying forbidden transitions.
    Introduced in §1.1 ('the lowest 38 levels dominated by the 3d5 and 3d44s were selected as target states'); 1421 computed levels are truncated to 38, and omitted high levels could contribute resonances in the 0-5 Ry range of Fig. 1.
  • standard math Breit-Pauli R-matrix and SUPERSTRUCTURE calculations are accurate for Mn III at the quoted level.
    §1.1-1.2; methods are established, but the accuracy for Mn III is not demonstrated beyond a ~3% energy comparison with NIST.
  • domain assumption The 10-15% R-matrix accuracy estimate derived from Mg II benchmarking transfers to Mn III.
    §1.1 explicitly says 'General accuracy of R-matrix data is estimated to be approximately 10–15 per cent based on experimental benchmarking (e.g. Sigut & Pradhan 1995, for Mg II)' — a transfer assumption.
  • domain assumption Electrons follow a Maxwellian distribution at Te in the nebular plasma.
    §1.2, Eq. (1), averages collision strengths with a Maxwellian distribution over Te = 2500-40000 K.
  • domain assumption A 38-level collisional-radiative steady-state model with electron-impact excitation/de-excitation and radiative decay captures the level populations.
    §1.3 constructs the CR model in spectracode; photo-processes and additional ionization/recombination are not included in the population calculation (ionization fraction is external/model-dependent).

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Pith. "Pith review of Emissivity line ratios for [Mn III] and spectral diagnostics of H II regions." pith.science (2026). https://pith.science/paper/6FOLM55H

@misc{pith2026260721816,
  author       = {Pith},
  title        = {Pith review of: Emissivity line ratios for [Mn III] and spectral diagnostics of H II regions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6FOLM55H}},
  note         = {Machine review of arXiv:2607.21816}
}
abstract

We present the first theoretical emission-line study of Mn III as potential determinant of physical conditions and manganese abundance. We compute atomic data for a set of Mn III lines and line emissivity ratios as temperature-density diagnostics. Accurate relativistic Breit-Pauli R-matrix calculations have been carried out for electron impact excitation of Mn III transitions that have not been previously studied. Selected forbidden lines are shown to be sensitive to temperature and density under nebular conditions in H II regions such as SNRs. The coupled channel R-matrix calculations include a wavefunction expansion that includes 38 levels of Mn III dominated by the ground and first excited electronic configurations $3d^5$ and $3d^44s$. Collision strengths for all 703 forbidden transitions among those levels, and Maxwellian averaged rate coefficients are obtained. A collisional-radiative model yields emissivity line ratios using calculated collision strengths and radiative decay A-values. Based on the present analysis, certain [Mn III] lines are predicted to be sensitive to density and/or in the typical nebular range. The detection of those lines could also yield cosmic Mn abundance relative to other elements.

Figures

Figures reproduced from arXiv: 2607.21816 by the authors.

Figure 1
Figure 1. Collision strengths, Ω, for the forbidden transitions (a) 4𝐷7/2 → 4𝑃5/2 and (b) 4𝐷5/2 → 6𝑆5/2 in Mn III as functions of electron energy (Ry). Prominent resonance structures are present in the near-threshold region, while smoother behaviour is observed at higher energies. 2.3 Line Emissivity Ratios When calculating the ratio between the intensities of two spectral lines as a function of electron density, two distinct… view at source ↗
Figure 2
Figure 2. Mn iii forbidden-line emissivity ratios as functions of log10 (𝑁e/cm−3 ), at 𝑇e = 2500, 5000, 10 000, 20 000, 30 000, and 40 000 K. Top row: ratios nearly independent of 𝑇e: (a) 𝑅1: 𝐼(2996.42 Å)/𝐼(2997.45 Å), 4𝐷5/2 → 6𝑆5/2 / 4𝐷3/2 → 6𝑆5/2. (b) 𝑅2: 𝐼(4.35 𝜇m)/𝐼(4.33 𝜇m), 4𝐷5/2 → 4𝑃3/2 / 4𝐷3/2 → 4𝑃5/2. Bottom row: ratios sensitive to both 𝑁e and 𝑇e: (c) 𝑅3: 𝐼(4.40 𝜇m)/𝐼(4.33 𝜇m), 4𝐷7/2 → 4𝑃5/2 / 4𝐷3/2 → 4𝑃5/2. (d) 𝑅4:… view at source ↗

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