arxiv: 2605.15048 · v1 · submitted 2026-05-14 · 🌌 astro-ph.GA

Recognition: no theorem link

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

Authors on Pith no claims yet

Pith reviewed 2026-05-15 14:13 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords electron temperatureH II regionsstar-forming galaxiestemperature diagnostics[N II] linesphotoionization modelsionic abundances

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The pith

Relations using Te([N II]) show lower dispersions than other low-ionization diagnostics across 699 spectra of H II regions and star-forming galaxies.

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

The study assembles 699 spectra that each contain at least two direct electron-temperature measurements from Galactic and extragalactic H II regions plus local star-forming galaxies. After recomputing densities and temperatures uniformly with updated atomic data, the authors compare the resulting Te-Te relations using orthogonal distance regression. Relations that include Te([N II]) display noticeably smaller intrinsic scatter than those involving Te([O II]) or Te([S II]), which are more sensitive to density variations and recombination effects. Slopes of the better-constrained relations match predictions from photoionization models. The work supplies an empirical reference for estimating the low-ionization-zone temperature when only higher-ionization diagnostics are observable.

Core claim

From the homogeneous reanalysis of 699 multi-diagnostic spectra, the authors derive Te-Te relations for the ionic species [N II], [O II], [O III], [S II], [S III] and [Ar III]. Relations involving Te([N II]) exhibit lower total and intrinsic dispersions, indicating that this diagnostic supplies a more reliable estimate of the low-ionization zone temperature even when only higher-ionization Te values are available. Overall slopes agree with photoionization model predictions, especially for the low-dispersion pairs, while relations involving Te([O II]) and Te([S II]) show larger scatter attributed to sensitivity to ne inhomogeneities and recombination contributions.

What carries the argument

The set of Te-Te relations obtained by orthogonal distance regression on the 699 spectra after consistent recomputation of ne and Te with updated atomic data.

If this is right

Slopes of the Te relations agree with photoionization model predictions, particularly for pairs with low intrinsic dispersion such as those involving Te([N II]) and Te([S III]).
Te([N II]) provides a more reliable proxy for the low-ionization zone temperature when only higher-ionization diagnostics are available.
Relations involving Te([O II]) and Te([S II]) display larger dispersions due to sensitivity to density inhomogeneities and recombination effects.
The derived relations supply an empirical basis for estimating Te in spectra where only a limited set of diagnostics is detected.

Where Pith is reading between the lines

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

If the lower dispersion of Te([N II]) relations persists, temperature-based metallicity calibrations that rely on it could reduce scatter in abundance determinations for galaxies observed at moderate redshift.
The same relations might be tested on integrated spectra of entire galaxies to check whether the local-H II-region patterns survive averaging over multiple regions.
Extending the comparison to samples at higher redshift could reveal whether the relative reliability of Te([N II]) changes with cosmic epoch or metallicity range.

Load-bearing premise

The 699 spectra that possess multiple Te diagnostics form a representative sample of star-forming regions and the recomputed temperatures accurately reflect true values without introducing new systematic offsets.

What would settle it

Measure a fresh sample of spectra containing both Te([N II]) and Te([O III]) and test whether the dispersion around the Te([N II])–Te([O III]) relation remains smaller than the dispersion around the Te([O II])–Te([O III]) relation.

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: Diagrams showing log([O iii]𝜆5007/H𝛽) versus log([N ii]𝜆6584/H𝛼) (BPT, top) and log([O iii]𝜆5007/H𝛽) versus 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: 𝑇e([O ii])–𝑇e([N ii]) (top) and 𝑇e([S ii])–𝑇e([N ii]) (bottom) relations 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: Same as the upper panel of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**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: 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

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.

Desk Editor's Note private letter to a colleague

The paper delivers updated Te-Te fits from a large homogeneous sample but the claim that Te([N II]) is more reliable outside that sample rests on untested extrapolation.

read the letter

The core result is a new set of empirical Te-Te relations fitted to 699 spectra that all have at least two direct temperature diagnostics. They re-derived ne and Te uniformly with updated atomic data, then used orthogonal distance regression to report both total and intrinsic dispersions. That separation is useful, and the finding that relations involving Te([N II]) show noticeably lower intrinsic scatter than those with Te([O II]) or Te([S II]) is the main practical takeaway. Slopes line up with photoionisation models in the better-constrained cases, which is reassuring for abundance work that needs to guess a low-ionisation temperature from high-ionisation lines alone. The sample size and consistent reprocessing are clear improvements over earlier compilations. The selection effect is the soft spot. Every spectrum in the 699 was kept only because the auroral lines were detectable, so the low-dispersion result for Te([N II]) is measured precisely where the low-ionisation lines are strong enough to see. The headline claim—that this diagnostic stays reliable when only higher-ionisation lines are available—requires the scatter to behave the same way in the complementary population (low-metallicity or low-S/N objects where [N II] 5755 drops below detection). The abstract gives no subset test or extrapolation check on that point, and the stress-test concern holds up. Error propagation details in the recomputed values are also thin. For people who routinely derive abundances in H II regions or local star-forming galaxies, the numerical relations and the quantified intrinsic dispersions are worth having on hand. The work is straightforward empirical analysis with no circularity, so it deserves a serious referee even if the generalization step needs tightening in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a homogeneous analysis of electron temperature (Te) relations among ionic species (Te([N II]), Te([O II]), Te([O III]), Te([S II]), Te([S III]), Te([Ar III])) using 699 spectra from the DESIRED-E database of H II regions and star-forming galaxies that possess at least two direct Te diagnostics. It recomputes ne and Te with updated atomic data under a consistent methodology, fits the relations via orthogonal distance regression, separates total and intrinsic dispersions, and compares slopes to prior empirical relations and photoionisation models, concluding that Te([N II]) relations exhibit lower intrinsic dispersions and therefore supply a more reliable low-ionisation zone temperature estimate when only higher-ionisation diagnostics are available.

Significance. If the central relations hold, the work supplies a useful empirical foundation for Te estimation in nebular spectra with incomplete diagnostics. Notable strengths are the large, homogeneous sample, consistent re-derivation with updated atomic data, explicit separation of intrinsic versus total dispersion, and direct slope comparisons to models. These elements support practical application in the field provided the sample-selection limitations are addressed.

major comments (2)

[Methods] Methods (sample selection paragraph): The 699 spectra are defined by the presence of at least two detectable Te diagnostics, which necessarily includes strong low-ionisation auroral lines ([N II] 5755, [O II] 7325, [S II] 4069). The reported lower intrinsic dispersion for all Te([N II]) relations is therefore measured exclusively inside this selection. The headline claim that Te([N II]) is more reliable when only higher-ionisation diagnostics are available requires the same low dispersion to hold in the complementary population (low-metallicity or low-S/N objects where [N II] 5755 is undetectable); no subset test or extrapolation is described.
[Results] Results (dispersion analysis): The separation of intrinsic from total dispersion is central to the reliability ranking of the diagnostics, yet the text provides no explicit description of the error-propagation procedure used in the orthogonal distance regression or of the statistical method employed to isolate the intrinsic component. This omission prevents independent verification of the quantitative claim that Te([N II]) relations are demonstrably tighter.

minor comments (2)

[Abstract] Abstract: Add one sentence summarising the error-propagation approach and the effect of the multi-diagnostic selection criterion on the reported dispersions.
[Figures/Tables] Figure captions and tables: Ensure all panels and rows are labelled with the exact ionic species and the number of spectra used, and that the intrinsic-dispersion values are quoted with their uncertainties.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thoughtful and constructive report. Their comments have identified key areas where the manuscript can be clarified and strengthened. We address each major comment in detail below and outline the revisions we will make.

read point-by-point responses

Referee: [Methods] Methods (sample selection paragraph): The 699 spectra are defined by the presence of at least two detectable Te diagnostics, which necessarily includes strong low-ionisation auroral lines ([N II] 5755, [O II] 7325, [S II] 4069). The reported lower intrinsic dispersion for all Te([N II]) relations is therefore measured exclusively inside this selection. The headline claim that Te([N II]) is more reliable when only higher-ionisation diagnostics are available requires the same low dispersion to hold in the complementary population (low-metallicity or low-S/N objects where [N II] 5755 is undetectable); no subset test or extrapolation is described.

Authors: We acknowledge that our sample selection requires detectable auroral lines for at least two diagnostics, which inherently favors objects with measurable low-ionization lines. The Te([N II]) relations are derived from this homogeneous set and are intended for application in spectra possessing only higher-ionization diagnostics (e.g., Te([O III])), where the fitted relations can be used to infer the low-ionization temperature. The lower intrinsic dispersions we report support greater reliability for this purpose. In the revised manuscript we will expand the discussion of sample selection to explicitly address potential biases, note the assumptions required for extrapolation to the complementary population, and highlight the supporting agreement with photoionization models across the observed metallicity range. A direct subset test on objects lacking [N II] λ5755 is not feasible, as those objects lack Te([N II]) measurements by construction. revision: partial
Referee: [Results] Results (dispersion analysis): The separation of intrinsic from total dispersion is central to the reliability ranking of the diagnostics, yet the text provides no explicit description of the error-propagation procedure used in the orthogonal distance regression or of the statistical method employed to isolate the intrinsic component. This omission prevents independent verification of the quantitative claim that Te([N II]) relations are demonstrably tighter.

Authors: We agree that a clear description of the statistical procedures is necessary for reproducibility and verification. In the revised version we will add a dedicated paragraph (in the Methods section) detailing the orthogonal distance regression implementation, including how measurement uncertainties in both Te variables are incorporated via the ODR algorithm, and the exact procedure used to isolate the intrinsic dispersion component. The intrinsic dispersion is obtained by subtracting the average measurement variance in quadrature from the total observed scatter around the best-fit line, following standard astronomical practice for such relations. This addition will enable readers to reproduce and verify the lower intrinsic dispersions found for the Te([N II]) relations. revision: yes

standing simulated objections not resolved

Direct empirical measurement of dispersions for Te([N II]) relations in the population of objects where [N II] λ5755 is undetectable, since such objects lack Te([N II]) measurements by definition.

Circularity Check

0 steps flagged

No circularity: purely empirical relations measured from direct observations

full rationale

The paper selects 699 spectra that yield at least two direct Te diagnostics, recomputes ne and Te values with updated atomic data using a uniform method, then applies orthogonal distance regression to quantify observed Te-Te relations and their total/intrinsic dispersions. All reported slopes, dispersions, and the comparative claim for Te([N II]) are direct statistical summaries of these measured data points; no parameter is fitted to a subset and then re-used as a prediction, no self-referential definition equates inputs to outputs, and no load-bearing step reduces to a prior self-citation or ansatz. The derivation chain is therefore self-contained observational analysis without any reduction by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the representativeness of the selected spectra and the accuracy of recomputed Te values using updated atomic data; no free parameters are introduced beyond the regression itself, and no new physical entities are postulated.

axioms (2)

domain assumption Updated atomic data produce more accurate Te and ne than previous compilations
Invoked when the authors recompute all quantities with a consistent methodology
standard math Orthogonal distance regression correctly separates intrinsic and total dispersion
Used to quantify scatter in the Te-Te relations

pith-pipeline@v0.9.0 · 5764 in / 1302 out tokens · 47562 ms · 2026-05-15T14:13:52.440988+00:00 · methodology

discussion (0)

Reference graph

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