Constraints on the history of Galactic spiral arms revealed by Gaia GSP-Spec alpha-elements

A. Recio-Blanco; E. Poggio; E. Spitoni; G. Cescutti; M. Barbillon; P. A. Palicio; P. de Laverny

REVIEW 4 major objections 7 minor 89 references

Constraints on the history of Galactic spiral arms revealed by Gaia GSP-Spec alpha-elements

T0 review · 4 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Young stars inside the Milky Way's spiral arms are ~0.06 dex poorer in [Ca/Fe] and ~0.05 dex poorer in [Mg/Fe] than inter-arm stars, a pattern matched only by a 2D chemical evolution model with 3–5 Gyr of co-rotation.

desk verdict First 2D alpha-element maps of the disc are a real step forward, but the 0.06 dex arm/inter-arm signal sits on top of known GSP-Spec systematics and the co-rotation timescale should be treated as suggestive, not measured. read the letter →

arxiv 2411.10007 v1 pith:KMS2ALJZ submitted 2024-11-15 astro-ph.GA

M. Barbillon , A. Recio-Blanco , E. Poggio , P. A. Palicio , E. Spitoni , P. de Laverny , G. Cescutti This is my paper · ORCID

classification astro-ph.GA

keywords GalacticdiscspiralarmsalphaelementscalciummagnesiumGSP-SpecGaiaDR3chemicalevolution

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 the Milky Way's spiral arms leave a measurable chemical imprint in alpha-elements, not just in iron or total metallicity. Using Gaia DR3 GSP-Spec abundances for bright giant stars within about 4 kpc of the Sun, it reports azimuthal fluctuations in [Ca/Fe] and [Mg/Fe], with young stars in the Sagittarius-Carina and Local arms about 0.06 dex poorer in [Ca/Fe] and 0.05 dex poorer in [Mg/Fe] than inter-arm stars while being more metal-rich. It then argues that these alpha-element depletions match a two-dimensional chemical evolution model with multiple spiral patterns only when the spiral pattern co-rotates with the disc for 3–5 Gyr. If the claim is right, chemical abundance maps become a practical way to trace spiral structure and to constrain how long spiral arms live, moving disc chemical evolution from one-dimensional radial gradients to a two-dimensional picture.

What carries the argument

The analysis rests on two giant-star samples built from Gaia DR3: sample A of bright young stars (about 11,678 with [Ca/Fe], ages roughly 30–130 Myr from isochrones, reaching about 4 kpc) and sample C of older red-giant stars (74,740 with [Ca/Fe], older than about 2 Gyr). The statistical instrument is a kernel density estimator that smooths each abundance field on a local scale (~240 pc) and on a six-times-larger scale, then subtracts the large-scale map to expose the [X/Fe] 'excess' pattern; a Spearman correlation between the resulting maps quantifies how tightly the chemical pattern tracks the spiral-arm overdensity contours. The interpretive machinery is a 2D chemical evolution model with multiple spiral pattern segments of different pattern speeds, rerun here under the assumption that co-rotation with the disc holds at all radii for 1, 3, or 5 Gyr; only the 3–5 Gyr runs produce the observed arm-associated [Ca/Fe] depletion.

What would settle it

Take an independent spectroscopic sample covering the same ~4 kpc region with different systematics and recompute the same arm/inter-arm excess maps before and after masking the known scanning-law stripes (roughly X ~ 0 kpc with Y between -4.5 and -1 kpc and between 2 and 4.5 kpc). If the ~0.06 dex [Ca/Fe] and ~0.05 dex [Mg/Fe] deficits in the Sagittarius-Carina and Local arms vanish when the scanning-law-affected sight lines are excluded, the claimed azimuthal alpha-element fluctuation and the 3–5 Gyr co-rotation inference would be falsified.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that alpha-element abundances in the Galactic disc vary with azimuth and that the variations line up with spiral arms. For the young giant population, the [Ca/Fe] excess map shows local decreases of about 0.06 dex at the Sagittarius-Carina and Local arms, with inter-arm regions relatively [Ca/Fe]-rich; the [Mg/Fe] map shows the same pattern at about 0.05 dex over its smaller footprint. The [M/H] and [Ca/Fe] maps are strongly anticorrelated (Spearman ~ -0.63 for young stars and -0.68 for old stars), while [M/H] and [Ca/H] are strongly correlated (~0.96), indicating that arm regions are simultaneously metal-rich and alpha-poor. Rerunning a 2D chemical evolution model with multiple spiral patterns, the model only reproduces the observed [Ca/Fe] deficit when the spiral pattern co-rotates with the disc for 3–5 Gyr. Older (>2 Gyr) stars also show [Ca/Fe] deficiencies along parts of the Local arm, with the paper cautioning that Gaia scanning-law artefacts may limit those maps along one line of sight.

Load-bearing premise

The whole detection assumes that the measured [Ca/Fe] and [Mg/Fe] maps are not contaminated by spatially varying systematics in the Gaia data; the paper states that the Gaia scanning law leaves signatures in [$\alpha$/Fe] and that its $T_{\mathrm{eff}}>4200$ K cut removes them only partially, so if those systematics mimic arm/inter-arm differences, the abundance deficit and the co-rotation conclusion would not survive.

Editorial extensions

If this is right

With the observed anticorrelation between [M/H] and [Ca/Fe], arm regions are both metal-rich and alpha-poor, implying enhanced iron production relative to alpha-elements inside the arms.
The 3–5 Gyr co-rotation requirement places a concrete constraint on spiral-arm lifetimes: a given disc region must stay under the spiral influence long enough for Type Ia supernova iron to dominate the local chemical pattern.
Individual alpha-element abundances become usable tracers of spiral structure in the Milky Way, complementing density and metallicity maps for both young and old disc populations.
Disc chemical evolution models that assume only radial gradients will miss the observed azimuthal structure; future models should include two-dimensional variations and alpha-abundance trends.
The pixel-to-pixel agreement between young and old samples (Spearman ~0.63-0.67) suggests that the chemical imprint of spiral arms can persist after stellar migration, opening a window into past spiral structure.

Reading between the lines

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

If the reported co-rotation timescale is real, then independent high-resolution abundance surveys covering the same volume should reproduce the arm/inter-arm [Ca/Fe] deficit; their absence in such data would point to a GSP-Spec systematic rather than a true abundance pattern.
A direct test of the mechanism would be to map other alpha-elements with different Type Ia supernova contributions in the same young-giant sample: the size of the arm deficit should scale with each element's yield-delay balance.
The paper notes that dust structures (for example the Vela Molecular Ridge region) coincide with some of the chemical fluctuations; correlating the excess maps pixel-by-pixel with three-dimensional dust extinction maps would separate a chemical-evolution signal from a reddening/selection effect.
A natural dynamical consequence left implicit is that 3–5 Gyr of co-rotation favours long-lived, recurring spiral modes over strictly transient arms, because the chemical record in old stars seems to retain the imprint of repeated arm passages in the same region.

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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

First, the substance: this is the first time anyone has put [Ca/Fe] and [Mg/Fe] on a 2D map of the local disc, and the detection of ~0.06 dex alpha-depletion in young spiral-arm stars is a real candidate finding. The anti-correlation with the [M/H] maps from Paper I is new and physically suggestive. The authors do careful work: they check completeness against ESP, they apply a Teff cut to mitigate the scanning law, they test for young contaminants in the old sample, and they run the Spitoni et al. model as an external benchmark rather than fitting their data with it. No circularity problem.

The soft spot is the size of the signal relative to known systematics. The arm/inter-arm difference is 0.05-0.06 dex. Median per-star uncertainty is 0.025 dex, so the binned signal can be formally significant with thousands of stars, but the systematic floor is the issue. The local-minus-large-scale subtraction uses a large bandwidth of 1.2-1.44 kpc, so any scanning-law or Teff-calibration artifact on that scale survives the subtraction. The authors acknowledge residual scanning-law structure in the old sample and flag one line of sight, but they provide no significance maps, no null tests (e.g., scrambling abundances or using a control sample), and no error budget for the arm/inter-arm difference. The model comparison is qualitative: they visually match the 3 and 5 Gyr co-rotation cases to the observed phase of [Ca/Fe] depletion, but they do not quantify the match or explore other patterns. So the 3-5 Gyr co-rotation timescale is a reasonable interpretation, not a measurement.

That said, the paper is honest about its limitations, and the young-sample maps are less suspect because hot stars are less affected by the scanning law. The old-sample maps are appropriately flagged. The result is the kind of thing that needs an independent abundance cross-check (APOGEE or LAMOST, for instance) before it becomes a firm constraint on spiral arm lifetimes.

Who is it for: anyone working on Galactic disc chemical evolution or spiral structure. It will be a useful reference for the first 2D alpha maps and for the co-rotation interpretation, but I would cite it with a caveat.

Bottom line: it deserves a serious referee. I would send it to review, with the expectation that the authors add significance maps and a systematics budget. The central claim is plausible and worth testing, not yet established.

Referee Report

4 major / 7 minor

Summary. This paper maps the azimuthal distribution of [Ca/Fe] and [Mg/Fe] in the Galactic disc around the Sun using individual stellar abundances from Gaia DR3 GSP-Spec. Two samples of bright giants are selected in the Kiel diagram — sample A (young, isochrone ages ~30-130 Myr, 11678 stars with [Ca/Fe]) and sample C (old, >2 Gyr, 74740 stars with [Ca/Fe]) — and 2D maps are constructed with a Gaussian kernel; 'excess' maps are formed by subtracting a large-scale (h = 1200-1440 pc) smoothed version from a local (h = 200-240 pc) one. The authors report a radial [Ca/Fe] gradient plus azimuthal fluctuations: young stars in the Sagittarius-Carina and Local arms are ~0.06 dex poorer in [Ca/Fe] and ~0.05 dex poorer in [Mg/Fe] than inter-arm stars, while [M/H] and [Ca/H] are enhanced there; Spearman coefficients quantify the anti-correlation between the [M/H] and [Ca/Fe] maps. Analogous but weaker patterns are reported for the old sample, with the caveat that scanning-law artifacts may affect a specific line of sight. The [Ca/Fe] depletions are interpreted through the Spitoni et al. (2023) 2D chemical evolution model: the authors argue that only models with spiral arms co-rotating with the disc for 3-5 Gyr reproduce the depletion, implying enhanced iron production in the arms, and they recommend that models incorporate alpha-abundance trends to constrain spiral-arm lifetimes.

Significance. If the reported fluctuations are real, this is the first 2D map of [Ca/Fe] and [Mg/Fe] azimuthal variations in the solar neighbourhood built from individual stellar abundances, extending the 1D radial chemical-evolution picture and providing a new, falsifiable constraint on spiral-arm lifetimes through alpha-element ratios. The paper has genuine strengths: the data selection is transparent and reproducible from the Appendix A query; per-star uncertainty statistics are tabulated (Table A.1); the comparison with Spitoni et al. (2023) is a legitimate external benchmark in which the co-rotation duration is explored rather than fitted to the data, so the inference is not circular; and the authors explicitly document the scanning-law limitations of the old-sample maps rather than hiding them. However, the magnitude of the claimed signal (0.05-0.06 dex) is comparable to both the per-star uncertainties and to the systematics the authors themselves identify, and the model inference is currently qualitative. The paper's impact therefore depends on the robustness tests and quantitative comparison requested below.

major comments (4)

[Section 3.1, Figs. 2-3, Table A.1] The central detection — the ~0.06 dex [Ca/Fe] and ~0.05 dex [Mg/Fe] depletions in the Sagittarius-Carina and Local arms — is presented without a significance map, a null test, or a systematic error budget. The median per-star [Ca/Fe] uncertainty is 0.025 dex (Table A.1), and Section 2 states that the Gaia scanning law leaves important signatures in [alpha/Fe] that the Teff > 4200 K cut only partially removes; the caption of Fig. 2 (right panel) explicitly notes a residual weak signature. The excess construction [Ca/Fe]_loc minus [Ca/Fe]_large (h_local = 200-240 pc, h_large = 1200-1440 pc) is a band-pass filter that retains fluctuations on scales of roughly 0.2-1.4 kpc, so any scanning-law artifact on those scales — precisely the scales reported in the caption of Fig. 2 — survives the subtraction and can mimic an arm/inter-arm pattern. Please add (i) a null test, e.g. azimuthally scrambling stellar labels or running the identical pipeline on a control element or population expected to be smooth; (ii) a propagated error budget separating the statistical uncertainty of the smoothed means from the systematic floor (scanning law, Teff calibration, extinction); and (iii) an explicit statement of which spatial scales the excess maps retain and which they remove.
[Section 4, Fig. 9] The conclusion that only 3-5 Gyr of disc co-rotation reproduces the observed [Ca/Fe] depletion rests on the visual statement that the 3 and 5 Gyr models 'start to recover a deficiency in [Ca/Fe]', with no quantitative criterion. The observed maps and the model predictions are not compared in matched coordinates or at matched amplitudes, and model uncertainties (star formation prescription, chemical yields, assumed pattern speeds) are not propagated. Because the 3-5 Gyr timescale is the paper's headline astrophysical conclusion (abstract and Section 4), please add a quantitative comparison — for example, the azimuthal [Ca/Fe] amplitude predicted by the model at the radii of the observed arms versus the measured ~0.06 dex excess and its uncertainty — and state which co-rotation durations can be excluded at what confidence. In addition, the caption of Fig. 9 should specify which coloured line corresponds to which pattern speed without requiring the reader to consult Spitoni et al. (2023).
[Section 3.1, Fig. 10] The Spearman coefficients used to support the claims (e.g., -0.63 and -0.68 between the [M/H] and [Ca/Fe] excess maps, and 0.63/0.67 between the sample A and C maps) are quoted without uncertainties or effective sample sizes. Because the maps are smoothed, neighbouring pixels are strongly correlated, so the effective number of independent measurements is far smaller than the number of pixels; moreover, the [M/H] and [Ca/Fe] excess maps both derive from the same large-scale subtraction procedure. In addition, the [Ca/H]-[M/H] correlation of 0.96 is inflated by construction, since [Ca/H] = [Ca/Fe] + [M/H]. The statement in Section 4 that the chemical inhomogeneities are 'statistically significantly' correlated with the spiral arms requires a permutation or bootstrap test that accounts for the spatial correlation of the smoothed maps, with the result reported as a probability rather than a bare coefficient.
[Section 2, Fig. 2 (right), Appendix A] For the old sample C, the paper itself cautions that the maps may be limited along a specific line of sight because of the Gaia scanning law, and that the Teff > 4200 K cut removes 211524 cooler stars. Despite this, the sample C [Ca/Fe] maps (Fig. 3, right panel) and their pixel-to-pixel correlation with sample A (Fig. 10) are used as supporting evidence for the chemical-evolution interpretation. Please recompute the sample C arm/inter-arm contrasts and the sample A-C correlation after excising the affected regions (approximately Y = (-4.5,-1) kpc and Y = (2,4.5) kpc, as noted in the caption of Fig. 2), and state how the Teff cut changes the completeness along that line of sight. Without such a test, the possibility that the sample C signatures are partly artifacts remains open, as the authors themselves acknowledge elsewhere in the text.

minor comments (7)

[Abstract vs Section 4] The abstract quotes the arm metallicity enhancement as '~0-0.19 dex' while Section 4 says 'up to ~0-0.20 dex'; please harmonise the two values.
[Section 3.1, Section 3.2] There are typos in two 'first time' passages: 'even if their are less evident' (Section 3.1) should read 'even if they are less evident', and 'richer compared compared to the arms regions' (Section 3.2, Fig. 7 discussion) contains a duplicated phrase.
[Appendix A] The ADQL query contains an apparently duplicated flags_gspspec pattern ('____________0%' appears twice in one OR clause) and unbalanced closing parentheses before the '_______________0%' condition; since the query is meant to be reproducible, please verify and correct it.
[Section 2 and Abstract] The abstract and title quote the young-sample age as '<150 Myr', but the BaSTI isochrone analysis in Section 2 yields ~30-130 Myr; please align these values or explicitly justify the round upper bound.
[Section 3.1] The 'for the first time' claims for azimuthal [Ca/Fe] fluctuations should be qualified against Hawkins (2023) and Hackshaw et al. (2024), both of whom report azimuthal abundance variations at comparable amplitudes; the novelty is better expressed as the first individual-star GSP-Spec [Ca/Fe] and [Mg/Fe] maps.
[Abstract and Section 3.3] The abstract presents the ~0.05 dex [Mg/Fe] depletion as a headline result, but Section 3.3 states that with only 689 stars and a ~1.2-1.5 kpc footprint the fluctuations cannot be quantified over the entire disc; please make the Local-Arm-only scope of the [Mg/Fe] result explicit in the abstract.
[Fig. 6 caption] The phrase 'a specific bins of 5 degrees' should be corrected, and the choice of the 1.1 kpc radial bin width for the running mean should be motivated in the text.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the measured arm/inter-arm [Ca/Fe] and [Mg/Fe] contrasts are empirical maps compared with an external forward model; self-citations are methodological and not load-bearing.

full rationale

The paper's central result is an observational measurement: [Ca/Fe] and [Mg/Fe] maps from Gaia GSP-Spec, with arm/inter-arm differences read off the maps after a local-minus-large-scale excess definition. This excess is a smoothing operation, not a fit, so the reported arm/inter-arm contrasts are not defined into existence by a fitted parameter. Spiral-arm loci are adopted from density-based tracers (Poggio et al. 2021 UMS stars; Palicio et al. 2023 giant-star overdensities), not from the same chemical maps, so the claimed spatial correlation is not enforced by construction. The comparison to the Spitoni et al. (2023) 2D chemical evolution model is a forward grid over co-rotation durations (1, 3, and 5 Gyr), not a fit of model parameters to the observed fluctuations; the conclusion that 3-5 Gyr of co-rotation reproduces the depletion is an external benchmark, and the overlap of authors on the model does not make the observation derive from it. The abundance calibration polynomials from Recio-Blanco et al. (2023, 2024) are a data-calibration input, not a prediction generated from the target signal. The acknowledged Gaia scanning-law signatures are a stated systematic limitation, affecting interpretation and statistical robustness, but they are a correctness risk rather than a circular step. No specific equation or definition reduces the paper's conclusions to its inputs, so no circularity step can be quoted.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central observational result is a map-level comparison, and the physical conclusion depends on several modeling and calibration assumptions that are not quantitatively validated.

free parameters (5)

local kernel bandwidth h = 240 pc (sample A), 200 pc (sample C)
Chosen by hand for smoothing; affects the spatial scale and amplitude of detected fluctuations.
large-scale bandwidth ratio = 6 times local (1200-1440 pc)
Ad hoc choice defining the excess as local-minus-large-scale; changes the mapped excess amplitude.
Teff cut = 4200 K
Chosen post hoc to reduce Gaia scanning-law artifacts; removes 211524 cool stars from sample C.
Mg RVS SNR threshold = 250
Set to avoid bias towards higher [Mg/Fe]; restricts the Mg sample to 689 stars.
Model co-rotation durations = 1, 3, 5 Gyr
Parameters varied in the Spitoni et al. (2023) model runs to compare with observations; explored, not fitted.

assumptions (6)

domain assumption GSP-Spec [M/H] traces [Fe/H] and [alpha/Fe] is dominated by [Ca/Fe] via the Ca II triplet
Stated in the Section 2 footnote; the entire [Ca/Fe] and [Mg/Fe] interpretation relies on this calibration assumption.
domain assumption Sample A is 30-130 Myr old and sample C older than 2 Gyr
Inferred from BaSTI isochrone fitting in the Kiel diagram; age-metallicity degeneracy is partially broken but not unique.
domain assumption The 2D chemical evolution model of Spitoni et al. (2023) describes the Galactic disc adequately
Used to interpret the observed [Ca/Fe] depletions as requiring 3-5 Gyr co-rotation; no model comparison with uncertainties is provided.
domain assumption Spatial density contours used as spiral arm tracers (Poggio et al. 2021; Palicio et al. 2023) are valid arm loci
The chemical maps are compared to these contours; young and old arms are traced using different stellar populations.
standard math Kernel density estimation with a Gaussian kernel yields unbiased abundance maps
Standard non-parametric smoothing; choice of kernel type has minor impact according to Poggio et al. (2021).
ad hoc to paper The Gaia scanning-law artifacts are sufficiently mitigated by Teff > 4200 K and the uncertainty/flags cuts
The authors note residual artifacts remain in sample C maps along one line-of-sight; this is an untested assumption in the analysis.

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Cite this review

Pith. "Pith review of Constraints on the history of Galactic spiral arms revealed by Gaia GSP-Spec alpha-elements." pith.science (2026). https://pith.science/paper/KMS2ALJZ

@misc{pith2026241110007,
  author       = {Pith},
  title        = {Pith review of: Constraints on the history of Galactic spiral arms revealed by Gaia GSP-Spec alpha-elements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KMS2ALJZ}},
  note         = {Machine review of arXiv:2411.10007}
}

read the original abstract

The distribution of chemical elements in the Galactic disc can reveal fundamental clues on the physical processes that led to the current configuration of our Galaxy. We map chemical azimuthal variations in the disc using individual stellar chemical abundances and discuss their possible connection with the spiral arms and other perturbing mechanisms. Using Gaia Data Release 3, we examine [Ca/Fe] and [Mg/Fe] fluctuations in a ~4 kpc region around the Sun, focusing on bright giant stars. We implemented a kernel density estimator technique to enhance the chemical inhomogeneities. We observe radial gradients and azimuthal fluctuations in [alpha/Fe] for young (<150 Myr) and old (>2 Gyr) stars, with amplitudes varying according to the studied element. In young stars, those within spiral arms (e.g., Sagittarius-Carina and Local arms) are generally more metal and calcium-rich (~0-0.19 dex) but show lower [Ca/Fe] (~0.06 dex) and [Mg/Fe] (~0.05 dex) compared to inter-arm regions, suggesting enhanced iron production in spiral arms. These [alpha/Fe] depletions are analysed in light of theoretical scenarios and compared to a 2D chemical evolution model with multiple spiral patterns. For the old sample, [Ca/Fe] maps reveal deficiencies along a segment of the Local arm identified by young stars. We caution that, for this old sample, the quality of the obtained maps might be limited along a specific line-of-sight, due to the Gaia scanning law. This study transitions our understanding of disc chemical evolution from a 1D radial view to a more detailed 2D framework incorporating radial, azimuthal, and small-scale variations. Individual chemical abundances prove essential for tracing spiral arms in disc galaxies. We recommend models and simulations incorporate alpha-abundance trends to better address spiral arm lifetimes.

Figures

Figures reproduced from arXiv: 2411.10007 by the authors.

**Figure 1.** Upper panel: Selection of sample A targets (blue dots) in the Kiel diagram using the selection criteria of the calcium query (see Appendix A). The box in solid lines are the initial sample A before applying the cutoff in Teff. As a visual reference, the grey points represent the MW population from the initial selection (including all stellar types from the GSP-Spec catalogue). We overplotted isochrones based on BaS… view at source ↗

**Figure 2.** Chemical inhomogeneities in the Galactic disc for two different samples. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Left panel: Map of [Ca/H] excess for sample A, including the spiral arms contours from Poggio et al. (2021) adopting the same local bandwidth as for [Ca/Fe]. Right panel: Same for sample C, including the spiral arms contours from Palicio et al. (2023) adopting the same…

**Figure 5.** Figure 5: Left panel: Map of [M/H] excess for sample A, including the spiral arms contours from Poggio et al. (2021) and adopting a hlocal = 200 pc and a larger scale length, h, 6 times higher. Right panel: Same for sample C, including the spiral arms contours from Palicio et al…

**Figure 6.** Figure 6: Left panel: Radial gradients in [Ca/Fe] abundances of sample A. The colour code illustrates the results of the running mean applied on the stars contained in the different bins of 5◦ . Each dot corresponds to the mean of all stars every 1.1 kpc for a specific bins of 5…

**Figure 7.** Figure 7: Left panels: Azimuth-averaged radial distribution for sample A, selecting bins of 650 pc and excluding those with less than 20 stars. From the top to the bottom, excess of [Ca/Fe] and [Ca/H] in an azimuth-averaged radial distribution are represented based on the curren…

**Figure 8.** Figure 8: [Mg/Fe] excess map for sample A overplotted by the [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 9.** Figure 9: Predicted present-day azimuthal variations in the [Ca/H] (first column), [Fe/H] (second column), and [Ca/Fe] [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

**Figure 10.** Figure 10: Upper panel: Pixel-to-pixel (black dots) diagram showing the [Ca/Fe] excess variation of sample C as a function of sample A one. Blue contours show the distribution of the [Ca/Fe] excess of sample C versus the one of sample A enclosing fractions of 90, 75, 60, 45, 30…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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