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arxiv: 2605.15048 · v2 · pith:AWIRS5U5new · submitted 2026-05-14 · 🌌 astro-ph.GA

The DESIRED electron temperature relations in star-forming regions of the local Universe

M. Orte-Garc\'ia , C. Esteban , J. Garc\'ia-Rojas , J. E. M\'endez-Delgado , K. Z. Arellano-C\'ordova , A. Z. Lugo-Aranda , L. Toribio San Cipriano , F. F. Rosales-Ortega
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I. R. Mart\'inez-Hern\'andez E. Reyes-Rodr\'iguez
This is my paper

Pith reviewed 2026-05-19 16:38 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords electron temperatureH II regionsstar-forming galaxiestemperature diagnosticslow-ionisation zonedirect Te measurementsphotoionisation models
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The pith

Relations using Te([N II]) show lower dispersions and provide a more reliable low-ionisation zone temperature estimate when higher-ionisation diagnostics are the only ones available.

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

The paper examines electron temperature relations among various ionic species using 699 spectra of H II regions and star-forming galaxies. It recomputes temperatures and densities with updated atomic data and a consistent method, then quantifies slopes and intrinsic dispersions via orthogonal distance regression. Relations involving Te([N II]) exhibit lower dispersions than those with Te([O II]) or Te([S II]), which suffer from sensitivity to density inhomogeneities and recombination effects. Slopes generally match photoionisation model predictions, especially for the lower-dispersion pairs. These results supply an empirical basis for estimating temperatures when only limited direct diagnostics are present.

Core claim

The study of 699 spectra reveals that Te-Te relations involving the [N II] diagnostic exhibit lower intrinsic dispersions than those with [O II] or [S II], indicating that Te([N II]) offers a more reliable proxy for the low-ionisation zone temperature when only higher-ionisation Te diagnostics are accessible, despite observational difficulties at low metallicity.

What carries the argument

The Te-Te relations between ionic temperature diagnostics such as Te([N II]), Te([O II]), Te([O III]), Te([S II]), Te([S III]) and Te([Ar III]), with their slopes and intrinsic dispersions derived from orthogonal distance regression on recomputed direct measurements.

If this is right

  • Slopes of the relations agree with photoionisation model predictions, especially for pairs with low intrinsic dispersion such as Te([N II]) and Te([S III]).
  • Te([N II]) can be used as a more stable estimate of low-ionisation zone temperature when direct measurement of that zone is unavailable.
  • The empirical relations supply a practical basis for temperature estimation in spectra that contain only higher-ionisation diagnostics.
  • Relations involving Te([O II]) and Te([S II]) display larger dispersions, consistent with greater sensitivity to electron density inhomogeneities and recombination contributions.

Where Pith is reading between the lines

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

  • These relations could improve temperature and abundance work on distant galaxies where only a subset of the usual temperature-sensitive lines are detected.
  • At low metallicities the practical advantage of Te([N II]) may be limited by observational difficulties, suggesting targeted high-S/N observations to test the dispersion claim further.
  • The homogeneous recomputation approach reduces method-to-method scatter and could be extended to other emission-line databases for cross-checks.

Load-bearing premise

The 699 spectra with at least two direct Te diagnostics remain free of systematic biases that would change the measured intrinsic dispersions or slopes after recomputation with updated atomic data.

What would settle it

A new sample of low-metallicity H II regions showing substantially higher dispersion in Te([N II]) relations than in higher-ionisation pairs would falsify the claim of superior reliability for the [N II] diagnostic.

Figures

Figures reproduced from arXiv: 2605.15048 by A. Z. Lugo-Aranda, C. Esteban, E. Reyes-Rodr\'iguez, F. F. Rosales-Ortega, I. R. Mart\'inez-Hern\'andez, J. E. M\'endez-Delgado, J. Garc\'ia-Rojas, K. Z. Arellano-C\'ordova, L. Toribio San Cipriano, M. Orte-Garc\'ia.

Figure 1
Figure 1. Figure 1: Diagrams showing log([O iii]𝜆5007/H𝛽) versus log([N ii]𝜆6584/H𝛼) (BPT, top) and log([O iii]𝜆5007/H𝛽) ver￾sus log([S ii]𝜆𝜆6716 + 31/H𝛼) (bottom) of the sample of spectra of Galactic and extragalactic H ii regions (blue dots) and star-forming galaxies (SFGs) (black squares) compiled in DESIRED-E used in this study. The dashed lines in both diagrams represent the empirical relations that have been used to dis… view at source ↗
Figure 2
Figure 2. Figure 2: 𝑇e([O ii])–𝑇e([N ii]) (top) and 𝑇e([S ii])–𝑇e([N ii]) (bottom) re￾lations obtained for our DESIRED-E sample. In both panels, blue dots correspond to H ii regions and black squares to SFGs, while the red continuous lines represent the ODR linear fits to the data. The grey dashed line shows the 1:1 relation that coincides with the approximate predictions of photoionisation models by Garnett (1992), and the m… view at source ↗
Figure 3
Figure 3. Figure 3: Same as the upper panel of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: illustrates the remarkably tight correlation of the 𝑇e([N ii])–𝑇e([S iii]) relation – especially for 𝑇e([S iii]) < 9000 K – with a small dispersion. In fact the values of 𝜎𝑡𝑜𝑡 and 𝜎𝑖𝑛𝑡 of this relation for 𝑇e([N ii]) are 1240 K and 650 K, respectively – 1540 K and 800 K for 𝑇e([S iii]) –, one of the lowest 𝜎𝑖𝑛𝑡 values found in this study. The Pearson coefficient of the fit is 0.75, one of the highest value… view at source ↗
Figure 6
Figure 6. Figure 6: 𝑇e([S iii])–𝑇e([O iii]) (top) and 𝑇e([Ar iii])–𝑇e([O iii]) (bottom) relations obtained for our DESIRED-E sample. The red continuous lines represent the ODR linear fits to the data. The grey dashed lines show the 1:1 relation. The black continuous lines represent the linear fits obtained from photoionisation models by Garnett (1992). In the upper panel, the orange dashed line represent the linear fits to th… view at source ↗
read the original abstract

(Abridged) Aims. We present a homogeneous observational study of electron temperature ($T_{\rm e}$) relations between ionic species: $T_{\rm e}$([N II]), $T_{\rm e}$([O II]), $T_{\rm e}$([O III]), $T_{\rm e}$([S II]), $T_{\rm e}$([S III]) and $T_{\rm e}$([Ar III]), using 699 spectra of Galactic and extragalactic H II regions and local star-forming galaxies (SFGs). Methods. We use the DEep Spectra of Ionised REgions Database Extended (DESIRED-E), comprising more than 3000 spectra with direct $T_{\rm e}$ determinations, selecting those with at least two $T_{\rm e}$ diagnostics. We recompute electron density ($n_{\rm e}$) and $T_{\rm e}$ using updated atomic data and a consistent methodology. The resulting $T_{\rm e}$--$T_{\rm e}$ relations are analysed using orthogonal distance regression, quantifying total and intrinsic dispersions and comparing slopes with previous works and photoionisation models. Results. Relations involving low-ionisation $T_{\rm e}$ diagnostics show large intrinsic dispersions, especially for $T_{\rm e}$([O II]) and $T_{\rm e}$([S II]), likely due to sensitivity to $n_{\rm e}$ inhomogeneities, recombination contributions, and uncertainties. In contrast, relations using $T_{\rm e}$([N II]) show lower dispersions, indicating that this diagnostic provides a more reliable estimate of the low-ionisation zone temperature when only higher-ionisation $T_{\rm e}$ diagnostics are available, despite observational difficulties at low metallicity. Overall, slopes agree with model predictions, particularly for relations with low intrinsic dispersion, such as those involving $T_{\rm e}$([N II]) and $T_{\rm e}$([S III]). These results provide a robust empirical basis for estimating $T_{\rm e}$ when limited diagnostics are available.

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 homogeneous observational study of electron temperature (Te) relations between ionic species (Te([N II]), Te([O II]), Te([O III]), Te([S II]), Te([S III]), Te([Ar III])) using 699 spectra of Galactic and extragalactic H II regions and local star-forming galaxies from the DESIRED-E database. Spectra are selected for having at least two direct Te diagnostics, recomputed with updated atomic data and consistent methodology for ne and Te, then analyzed via orthogonal distance regression to quantify total and intrinsic dispersions, with slopes compared to prior works and photoionisation models. The central result is that relations involving Te([N II]) exhibit lower intrinsic dispersions, indicating greater reliability for estimating the low-ionisation zone temperature when only higher-ionisation diagnostics are available, despite challenges at low metallicity; overall slopes agree with models, especially for low-dispersion relations.

Significance. If the central claims hold after addressing selection effects, the work supplies a valuable empirical calibration for Te relations in star-forming regions, strengthening abundance analyses where direct diagnostics are limited. Strengths include the large sample size, homogeneous reanalysis with updated atomic data, consistent methodology across all spectra, and explicit quantification of intrinsic dispersions alongside model comparisons; these elements provide a more controlled basis than heterogeneous prior compilations.

major comments (2)
  1. [Methods (sample selection)] Methods section on sample selection: The criterion of selecting only the 699 spectra with at least two direct Te diagnostics risks biasing the low-metallicity subsample, since [N II] auroral lines weaken at low Z; objects entering via detectable [N II] may preferentially have higher S/N or atypical conditions, potentially truncating the high-dispersion tail and artificially lowering the reported intrinsic dispersion for Te([N II]) relations. This is load-bearing for the claim of greater reliability.
  2. [Results (dispersion analysis)] Results section on dispersion quantification and model comparison: The analysis of intrinsic dispersions and slope agreement with photoionisation models does not test whether the Te([N II]) dispersion advantage persists in a metallicity-matched control sample without the multiple-diagnostic requirement; without this, the reported lower dispersions cannot be confirmed as intrinsic rather than selection-induced.
minor comments (2)
  1. [Abstract and Methods] The abstract and methods should explicitly list the specific atomic data updates applied (e.g., which collision strengths or transition probabilities were revised) to ensure full reproducibility.
  2. [Figures] Figures displaying the Te-Te relations would be clearer if individual data points included error bars and if the intrinsic dispersion values were annotated directly on the panels.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and have revised the manuscript to incorporate additional discussion and checks where feasible.

read point-by-point responses

  1. Referee: Methods section on sample selection: The criterion of selecting only the 699 spectra with at least two direct Te diagnostics risks biasing the low-metallicity subsample, since [N II] auroral lines weaken at low Z; objects entering via detectable [N II] may preferentially have higher S/N or atypical conditions, potentially truncating the high-dispersion tail and artificially lowering the reported intrinsic dispersion for Te([N II]) relations. This is load-bearing for the claim of greater reliability.

    Authors: We acknowledge the potential for selection bias at low metallicity arising from the weakening of [N II] auroral lines. Our selection of spectra with at least two direct Te diagnostics is required to derive the empirical relations that form the core of the study. In the revised manuscript we have expanded the Methods section with a new analysis of the sample metallicity distribution and added a test splitting the sample into metallicity bins. The lower intrinsic dispersion for Te([N II]) relations persists across these bins. We have also inserted an explicit caveat in the Discussion section regarding possible selection effects. revision: yes

  2. Referee: Results section on dispersion quantification and model comparison: The analysis of intrinsic dispersions and slope agreement with photoionisation models does not test whether the Te([N II]) dispersion advantage persists in a metallicity-matched control sample without the multiple-diagnostic requirement; without this, the reported lower dispersions cannot be confirmed as intrinsic rather than selection-induced.

    Authors: We agree that a direct test against a metallicity-matched control sample lacking the multiple-diagnostic requirement would be desirable. Such a control sample cannot be used to compute the Te-Te relations themselves, since paired measurements are required. As an alternative, we have added to the revised Results section a comparison of our dispersions with those reported in earlier heterogeneous compilations that include single-diagnostic objects. These external comparisons show consistent trends supporting the relative reliability of Te([N II]). revision: partial

Circularity Check

0 steps flagged

No circularity: empirical Te relations derived directly from selected observational spectra

full rationale

The paper selects 699 spectra requiring at least two direct Te diagnostics from the DESIRED-E database, recomputes ne and Te values with updated atomic data under a uniform methodology, then applies orthogonal distance regression to derive Te-Te relations and measure their total and intrinsic dispersions. These dispersions and slopes are computed outputs from the data rather than inputs redefined as predictions. Slopes are compared to external photoionisation models and prior literature, providing independent benchmarks. No self-definitional equations, fitted parameters renamed as predictions, load-bearing self-citations, or ansatz smuggling appear in the chain; the lower dispersion reported for Te([N II]) relations is an empirical finding from the analysis, not a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central results rest on the assumption that updated atomic data and a uniform re-computation procedure introduce no net systematic offset in the Te values used for the regressions. No free parameters are explicitly fitted beyond the regression itself; no new physical entities are introduced.

axioms (1)
  • domain assumption Updated atomic data and consistent methodology yield unbiased Te and ne values across the selected spectra
    Invoked when recomputing all diagnostics prior to regression analysis

pith-pipeline@v0.9.0 · 5998 in / 1212 out tokens · 50804 ms · 2026-05-19T16:38:56.778531+00:00 · methodology

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