Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

On the origin of the Hercules group: I. chemical signatures indicating the outer bar origin

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Super metal-rich Hercules stars trace to the Milky Way's outer bar

desk verdict A credible multi-element chemical fingerprint for the low-Lz Hercules subgroups, but the APOGEE half of the evidence depends on a post-hoc [Mg/Fe] cut and needs robustness testing before the outer-bar claim can carry weight. read the letter →

arxiv 2411.19085 v2 pith:YM42UYS6 submitted 2024-11-28 astro-ph.GA

Yusen Li , Kenneth Freeman , Helmut Jerjen , Sven Buder , Michael Hayden , Ankita Mondal This is my paper · ORCID
classification astro-ph.GA
keywords HerculeskinematicgroupMilkyWaybarstellarabundancesthindiskthickcontaminationGALAHAPOGEEsolarneighbourhood
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

Stars in the lowest-angular-momentum part of the Hercules kinematic group, the subgroups called Hercules III and IV, are chemically distinct from their neighbours in the solar neighbourhood. After removing thick-disk stars with a cut at $[\mathrm{Mg}/\mathrm{Fe}] < 0.1$, these stars show strong enhancements in iron-peak elements (Fe, Ni, Mn) and odd-Z elements (Na, Al), a slight deficiency in $\alpha$ elements (O, Ca, Ti), and older ages than other thin-disk stars. The paper argues that this abundance pattern matches what is expected near the outer thin bar of the Milky Way, where the radial metallicity profile peaks, and therefore that these Hercules stars were born in the inner Galaxy and later transported to the solar neighbourhood. If correct, this constrains the dynamical mechanism behind the Hercules group: it must be able to carry inner-Galaxy stars outward, which the companion paper argues is achieved by Trojan orbits at the bar's corotation resonance.

What carries the argument

The load-bearing device is a chemical selection: the paper partitions the solar-neighbourhood sample in the $L_Z$–$V_R$ plane, then discards all stars with $[\mathrm{Mg}/\mathrm{Fe}] \ge 0.1$ to remove the high-$\alpha$ thick-disk population. This cut, chosen from the flat kinematic distribution of thick-disk stars, resolves the inconsistencies among iron-peak elements and between the GALAH and APOGEE surveys, and exposes a sharp 'low-$L_Z$ patch' at Hercules III and IV that is chemically uniform in its iron-peak, odd-Z, and $\alpha$ abundances. The comparison of these abundances with the Galaxy's radial metallicity gradient and with Na/Al age tracers is what carries the argument from a kinematic group to an inner-Galactic birthplace.

What would settle it

A direct test would be an infrared spectroscopic survey of stars in the outer bar region (around $R \sim 4$–$6$ kpc): if those stars are not unusually rich in Ni, Na, and Al and poor in O, Ca, and Ti relative to the solar neighbourhood, the claimed outer-bar origin for the Hercules III and IV stars fails. Alternatively, if the low-$L_Z$ patch disappears when the $\alpha$ cut is varied or when the dwarf/giant calibration offsets noted for Al and Si are corrected, the signature would be a selection artefact rather than a real population.

Watch

Extended reading notes

Core claim

On its own terms, the paper discovers a chemically distinct stellar population inside the Hercules kinematic group. In the angular momentum–radial velocity ($L_Z$–$V_R$) plane, the Hercules subgroups III and IV at low angular momentum contain a low-alpha (thin-disk) population that is significantly enhanced in iron-peak elements and odd-Z elements and slightly deficient in alpha elements compared with kinematically local stars. The Na and Al enhancements identify these stars as the youngest members of the old sequence that originates in the inner disc. Interpreting the super metal-rich, alpha-poor, odd-Z-rich composition as the fingerprint of the peak of the Galaxy's radial metallicity profile, the paper concludes that Hercules III and IV formed in the outer thin bar region of the inner Galaxy and were subsequently delivered to the solar neighbourhood, implying that the Hercules formation mechanism must transport stars outward from the inner Galaxy.

Load-bearing premise

The entire chemical conclusion depends on the assumption that cutting at $[\mathrm{Mg}/\mathrm{Fe}] < 0.1$ cleanly isolates the thin-disk population, so that the residual abundance differences between kinematic groups reflect stellar birthplaces rather than survey calibration systematics, remaining thick-disk contamination, or the arbitrary placement of kinematic group boundaries.

Editorial extensions

If this is right

  • If the claim holds, the solar neighbourhood contains stars born in the inner Galaxy, so local stellar samples can be used to probe the chemistry of the outer bar region.
  • The requirement that the formation mechanism transports stars from the inner Galaxy to the solar neighbourhood excludes purely local or circular-orbit scenarios and supports a resonant mechanism such as Trojan orbits at bar corotation.
  • The identification of Hercules III and IV as the youngest stars of the old sequence connects the Hercules group to the inner thick disc and implies that the old sequence extends into the outer bar.
  • The low-$L_Z$ patch becomes a testable population: infrared surveys of the inner Galaxy can check whether outer-bar stars share the same Ni, Na, and Al enhancements.
  • Consistent detection of the patch in both GALAH and APOGEE after the alpha cut suggests that survey differences in wavelength and stellar selection can be reconciled once thick-disk contamination is removed.

Reading between the lines

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

  • Beyond the paper: the same $[\mathrm{Mg}/\mathrm{Fe}] < 0.1$ selection could be applied to other kinematic groups to look for additional inner-Galaxy migrants, effectively turning the Hercules method into a general search tool.
  • If the outer bar is indeed Na/Al-rich, then Na and Al abundances in local stars could serve as a chemical tag for outer-bar membership, independent of kinematics.
  • The paper's argument implies that local chemical evolution models should account for a population of stars whose abundances reflect the inner disc rather than local enrichment, which would bias interpretations of the solar-neighbourhood abundance distribution if ignored.
  • A testable extension: if Trojan orbits are responsible, Hercules III and IV stars should show orbital librations around the bar's Lagrange points in Gaia astrometry, a prediction the authors' companion paper develops.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper investigates the chemical composition of the Hercules kinematic group in the solar neighbourhood using Gaia DR3 astrometry and GALAH DR4 and APOGEE DR17 spectroscopy. It defines kinematic groups in the LZ-VR plane, analyses [Mg/Fe]-[Fe/H] diagrams, and after applying a [Mg/Fe] < 0.1 cut to remove thick-disc stars, finds that the low angular momentum subgroups Hercules III and IV display enhanced iron-peak (Fe, Ni, Mn) and Odd-Z (Na, Al) abundances and slightly deficient alpha (O, Ca, Ti) abundances relative to kinematically local stars. The authors interpret this pattern as evidence that these stars originated in the outer thin bar in the inner Galaxy and were transported outward by a bar-related mechanism, to be discussed in a companion paper.

Significance. If the chemical signature is real, the paper would provide a valuable new constraint on the origin of the Hercules group, linking a specific kinematic substructure to the inner Galaxy and bar dynamics. The study makes good use of two independent spectroscopic surveys and presents a fairly complete elemental inventory, and the authors are transparent about inconsistencies between surveys and within element groups. However, the central claim depends on a post-hoc [Mg/Fe] cut that is the very step that makes the signal appear, and the reported abundance differences are not accompanied by significance tests or robustness checks. The strengths are the survey cross-checks and the explicit acknowledgment of degeneracies; the weakness is that the main conclusion currently rests on this single, not-fully-justified selection.

major comments (4)
  1. [§3.4–3.5, Figs. 9–12] The main chemical signal of Hercules III/IV is only present after applying the [Mg/Fe] < 0.1 cut, and the cut is not robustly tested. The paper's own APOGEE Mg-binning (Fig. 10) shows that the low-Lz patch is nearly absent at [Mg/Fe] < -0.02 (nH = 13%) and appears progressively as the threshold approaches 0.1 (19%, 21%, 30%). This means the APOGEE enhancement in Fig. 12 is driven by stars with -0.02 < [Mg/Fe] < 0.1, i.e., stars immediately below the cut rather than by the most alpha-poor thin-disc population. The threshold 0.1 is chosen 'based on the analysis in Sec. 3.4' but no alternative thresholds (e.g., 0.0, 0.05, 0.15) are explored. Without such robustness checks, the claim that the low-alpha population carries the iron-peak and Odd-Z enhancement is not established; the signal could be an artifact of residual thick-disc contamination or of the arbitrary kinematic boundaries.
  2. [Tables 4 and 5] The paper states abundances are 'significantly enhanced' but provides only medians with quartile ranges, without any statistical significance test. For instance, in Table 4, [Fe/H] for Hercules III is +0.12 (+0.23/−0.01) versus LSR −0.01 (+0.09/−0.12); the quartile ranges show large overlap. Similarly, [Na/Fe] for Hercules III is 0.09 (+0.15/+0.02) versus LSR 0.02 (+0.08/−0.04). Given the broad distributions and the modest sample sizes after the cut, a bootstrap or rank-sum test is needed to support the qualitative description. The lack of such tests is load-bearing because the central claim is a differential abundance pattern.
  3. [§3.4, Figs. 9–10] The GALAH and APOGEE data disagree on the behaviour of the Hercules fraction with [Mg/Fe]: nH is roughly constant across Mg bins in GALAH (27%, 26%, 25%, 30%) but rises monotonically in APOGEE (13%, 19%, 21%, 30%). The paper resolves this by 'favouring' APOGEE because of better bimodality separation, but no quantitative test or explanation is offered. This discrepancy is directly relevant to the post-cut interpretation: it suggests that the APOGEE low-alpha patch is an emergent feature of the binning near 0.1 dex, while the GALAH data do not show the same emergence, so the cross-survey agreement claimed for Fig. 12 is not actually a confirmation of a single low-alpha population.
  4. [§4] The interpretation of the chemical pattern as evidence for an outer thin bar origin is an inference from literature radial metallicity gradients, not a quantitative comparison with inner-Galaxy abundance data. The paper itself notes that 'the direct way to verify the origin... is to compare the abundances in the inner disc' and that such data are scarce. As a result, the claim 'these chemical signatures support their origin from the outer thin bar' goes beyond what the data alone can establish; alternative origins (e.g., radial migration from a range of radii, or different bar models) are not considered quantitatively. This is not an error, but it is a limitation that should be stated more carefully in the abstract and conclusions.
minor comments (4)
  1. [§1, §2] There are several typos, e.g., 'refered to' in §1, 'associtated' in §1, and 'the the' in the first sentence of §2. A careful proofreading pass is recommended.
  2. [Figs. 6 and 7] The colour scales and binning are not identical between panels in Figs. 6 and 7, making visual comparisons across elements difficult; a common scale or a clearer description of the colour mapping would aid the reader.
  3. [Abstract, §4–5] The paper uses 'outer thin bar' in the abstract but 'inner disc' and 'inner Galaxy' in §4–5; the precise spatial region intended (e.g., R ~ 4–6 kpc from Wylie et al.) should be stated consistently throughout.
  4. [Table 1] The table caption notes that the APOGEE Hercules IV peak is the thick-disc peak; this is helpful, but the corresponding low-alpha peak should also be listed (or explicitly omitted) so that the comparison with the low-alpha analysis in Tables 4 and 5 is transparent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Hercules III/IV chemical signature is measured within a common [Mg/Fe]<0.1 sample, and the outer-bar interpretation rests on external gradient results, not on this paper's fitted parameters.

full rationale

The derivation chain is self-contained in the relevant sense. The paper identifies kinematic groups from Gaia overdensity contours, then measures abundances in those groups. The Fe-peak and Odd-Z enhancements of Hercules III and IV are already visible before the alpha cut in Figs. 4 and 5 and Table 1, so they are not manufactured by the subsequent selection. The [Mg/Fe]<0.1 threshold in Sec. 3.5 is a uniform selection applied to all kinematic groups, not a parameter fitted to the particular abundance contrast being claimed; the abstract's 'deficiency in alpha elements' is based on O, Ca, and Ti, which are not the selection variable, and is evaluated relative to kinematically local stars inside the same low-alpha sample. The outer-bar interpretation is an inference from external, independently published radial metallicity gradient results (Wegg et al. 2015; Wylie et al. 2021; Lian et al. 2023; Guiglion et al. 2024), not from a result derived in this paper. Self-references to the companion paper II (Li et al. 2024) are forward references to future dynamical work, not evidence used to force the chemical conclusion. Co-authorship overlap with Owusu et al. (2024) and Wylie et al. (2021) does not make those citations circular, because their content is externally falsifiable and the present paper's central claim does not reduce to those citations. The threshold sensitivity noted by the skeptic is a legitimate selection-robustness concern, but it is not a circularity: no equation equates the claimed prediction to an input, and no fitted parameter is renamed as a prediction. Verdict: no significant circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on literature assumptions about solar kinematics and the inner Galaxy's metallicity gradient, plus one author-introduced threshold ([Mg/Fe] < 0.1). No new physical entities are proposed.

free parameters (1)
  • [Mg/Fe] thick-disc threshold = 0.1 dex
    Chosen in §3.4 after inspecting the data and applied in §3.5. This cut defines the low-alpha sample in which the paper's main chemical signature is measured.
assumptions (4)
  • domain assumption Solar position and motion parameters (R_GC = 8.2 kpc, LSR tangential velocity 235 km/s, solar peculiar motion (11.1, 12.24, 7.25) km/s).
    Adopted in §2 to transform Gaia astrometry into Galactocentric cylindrical kinematics.
  • domain assumption Inner Galaxy has a positive radial metallicity gradient peaking around R ~ 4-6 kpc, associated with the outer bar.
    Cited from Wylie et al. 2021, Lian et al. 2023, and Guiglion et al. 2024; used in §4 to interpret Fe-rich stars as originating from the outer bar region.
  • ad hoc to paper Stars with [Mg/Fe] >= 0.1 are thick disk stars that contribute little to kinematic structures.
    The threshold is chosen in §3.4 after showing the high-alpha population is near-uniform in the LZ-VR plane; it is applied in §3.5 to define the low-alpha sample. The cutoff is a modeling choice specific to this paper.
  • domain assumption Na and Al enhancements identify the old sequence in the inner disc.
    Based on Nissen et al. 2020 and Owusu et al. 2024; used in §4 to argue the low-LZ Hercules stars are the youngest stars of the old sequence.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On the origin of the Hercules group: I. chemical signatures indicating the outer bar origin." pith.science (2026). https://pith.science/paper/YM42UYS6

@misc{pith2026241119085,
  author       = {Pith},
  title        = {Pith review of: On the origin of the Hercules group: I. chemical signatures indicating the outer bar origin},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YM42UYS6}},
  note         = {Machine review of arXiv:2411.19085}
}
read the original abstract

The Hercules kinematic group is a kinematic anomaly of stars observed in the solar neighbourhood (SNd). In this series of papers, we present a comprehensive study of this structure. This paper focuses on its chemical signatures over several groups of elements. The next paper discusses its kinematical properties. While studies suggested a non-native origin of Hercules stars due to the distinct chemical and kinematic features, previous studies focussed mainly on the Fe abundances. We adopt chemical data with abundances of elements from GALAH and APOGEE to seek further chemical implications on the origin. Our analysis reveals that the low alpha population of the low angular momentum Hercules group is significantly enhanced in iron-peak (Fe, Ni, Mn) and Odd-Z (Na, Al) elements, and slightly deficient in alpha elements (O, Ca, Ti) compared to kinematically local stars. The super enhancement in iron-peak elements and deficiency in alpha elements support their origin from the outer thin bar in the inner Galaxy. Moreover, the enhancement in Na and Al indicates these stars as the youngest stars in the old sequence from the inner thick disc. Hence, the origin of these stars can be related to the outer bar region. These chemical signatures require the underlying dynamical mechanism that forms the Hercules group to be capable of transporting stars in the inner Galaxy out to the SNd. The next paper will consider the Trojan orbits as the favoured mechanism.

Figures

Figures reproduced from arXiv: 2411.19085 by the authors.

Figure 1
Figure 1. The distribution of stars in the SNd in three surveys in the planar angular momentum-radial velocity plane. The kinematic groups appear as overdensity structures in the plane, consistently throughout three surveys. Left: 8.9 million Gaia stars in the SNd. The yellow asterisk and the white cross mark the solar and the LSR kinematics, respectively. The Hercules structure, subdivided into four subgroups, is enclosed in… view at source ↗
Figure 2
Figure 2. Distribution of stars with Galactic |𝑧 | < 1 kpc in the surveys, projected onto the Galactic plane in Cartesian 𝑋-𝑌 coordinates. The Sun and the solar neighbourhood are located 25◦ above the bar’s major axis, marked by the yellow asterisk and the dashed black circle. The Galactic bar is marked by the black, semi-transparent ellipse in the centre. Left: 16.7 million stars in Gaia DR3, and the super-thin outer bar is … view at source ↗
Figure 3
Figure 3. The selection of stars into kinematic group samples in the local 𝐿𝑍 -𝑉𝑅 kinematic space. The dashed magenta contour lines show density structures in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The [Mg/Fe]-[Fe/H] distribution of GALAH stars for the eight kinematic groups in the SNd (see [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: The [Mg/Fe]-[Fe/H] distribution of APOGEE stars in eight samples of the SNd kinematic groups and background. Same as [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The 𝐿𝑍 -𝑉𝑅 kinematics space coloured by 15 reliable element abundances and age for the GALAH DR4 sample. While many kinematic groups appear as peaks or anti-peaks in many abundances, the inconsistency of trends in the Fe-peak elements (top row) challenges the reliabili…
Figure 7
Figure 7. Figure 7: The 𝐿𝑍 -𝑉𝑅 kinematics space coloured by 9 reliable element abundances in APOGEE DR17. Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: The fraction of high alpha stars ([Mg/Fe] > 0.1) in the 𝐿𝑍 -𝑉𝑅 kinematic space in GALAH. The fraction of high alpha thick disc stars rises significantly from 25.4 per cent at 𝐿𝑍 = 1600 kpc km s−1 to 70.9 per cent at 𝐿𝑍 = 1200 kpc km s−1 , whereas the high 𝐿𝑍 groups aro…
Figure 9
Figure 9. Figure 9: The 2D histogram of four intervals of four GALAH abundances and isochrone age in the SNd. The high alpha, low Fe thick disc population appears to be a near-flat distribution that contributes little to the kinematic structures. Top row: [Fe/H]; second row: [Mg/Fe]; thir…
Figure 10
Figure 10. Figure 10: The kinematics of four intervals of two APOGEE abundances in the SNd. Similar to [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: The 𝐿𝑍 -𝑉𝑅 kinematics space coloured by 15 reliable chemical abundances and age in GALAH DR4 with [Mg/Fe] < 0.1. Same to [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 12
Figure 12. Figure 12: The 𝐿𝑍 -𝑉𝑅 kinematics space coloured by 9 reliable element abundances in APOGEE DR17 stars with [Mg/Fe] < 0.1. Same to [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13: The [Na/Fe]-Age distribution of the SNd GALAH stars in the alpha-deficient kinematic group samples. While the high 𝐿𝑍 kinematic groups occupy similar regions in the diagram, Hercules III and IV include a significant number of intermediate-aged and Na-enhanced stars. T…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the origin of the Hercules group: II. the Trojan quasi-periodic identity on the orbital level

    astro-ph.GA 2024-11 conditional novelty 5.0 of 10

    Quasi-periodic orbits trapped around L4/L5 Trojan orbits of a slowly rotating long Galactic bar reproduce the Hercules kinematic group's position and shape in the solar neighbourhood velocity plane and can transport i...

Reference graph

Works this paper leans on

91 extracted references · 13 canonical work pages · cited by 1 Pith paper

  1. [1]

    Abdurro'uf et al., 2022, @doi [ ] 10.3847/1538-4365/ac4414 , https://ui.adsabs.harvard.edu/abs/2022ApJS..259...35A 259, 35

    doi:10.3847/1538-4365/ac4414 2022

  2. [2]

    Antoja T., et al., 2014, @doi [ ] 10.1051/0004-6361/201322623 , https://ui.adsabs.harvard.edu/abs/2014A&A...563A..60A 563, A60

    doi:10.1051/0004-6361/201322623 2014

  3. [3]

    Antoja T., et al., 2017, @doi [ ] 10.1051/0004-6361/201629387 , https://ui.adsabs.harvard.edu/abs/2017A&A...601A..59A 601, A59

    work page doi:10.1051/0004-6361/201629387 2017

  4. [4]

    Astropy Collaboration et al., 2013, @doi [ ] 10.1051/0004-6361/201322068 , https://ui.adsabs.harvard.edu/abs/2013A&A...558A..33A 558, A33

    doi:10.1051/0004-6361/201322068 2013

  5. [5]

    Astropy Collaboration et al., 2018, @doi [ ] 10.3847/1538-3881/aabc4f , https://ui.adsabs.harvard.edu/abs/2018AJ....156..123A 156, 123

    doi:10.3847/1538-3881/aabc4f 2018

  6. [6]

    Astropy Collaboration et al., 2022, @doi [ ] 10.3847/1538-4357/ac7c74 , https://ui.adsabs.harvard.edu/abs/2022ApJ...935..167A 935, 167

    doi:10.3847/1538-4357/ac7c74 2022

  7. [7]

    A., P \'e rez-Villegas A., L \'e pine J

    Barros D. A., P \'e rez-Villegas A., L \'e pine J. R. D., Michtchenko T. A., Vieira R. S. S., 2020, @doi [ ] 10.3847/1538-4357/ab59d1 , https://ui.adsabs.harvard.edu/abs/2020ApJ...888...75B 888, 75

    doi:10.3847/1538-4357/ab59d1 2020

  8. [8]

    W., Graham J

    Basri G., Marcy G. W., Graham J. R., 1996, @doi [ ] 10.1086/176842 , https://ui.adsabs.harvard.edu/abs/1996ApJ...458..600B 458, 600

    work page doi:10.1086/176842 1996

Show all 91 references
  1. [9]

    Baumann P., Ram \' rez I., Mel \'e ndez J., Asplund M., Lind K., 2010, @doi [ ] 10.1051/0004-6361/201015137 , https://ui.adsabs.harvard.edu/abs/2010A&A...519A..87B 519, A87

    2010 doi

  2. [10]

    S., 2014, @doi [ ] 10.1051/0004-6361/201322631 , https://ui.adsabs.harvard.edu/abs/2014A&A...562A..71B 562, A71

    Bensby T., Feltzing S., Oey M. S., 2014, @doi [ ] 10.1051/0004-6361/201322631 , https://ui.adsabs.harvard.edu/abs/2014A&A...562A..71B 562, A71

    2014 doi

  3. [11]

    Bernet M., Ramos P., Antoja T., Famaey B., Monari G., Al Kazwini H., Romero-G \'o mez M., 2022, @doi [ ] 10.1051/0004-6361/202244070 , https://ui.adsabs.harvard.edu/abs/2022A&A...667A.116B 667, A116

    2022 doi

  4. [12]

    Binney J., 2020, @doi [ ] 10.1093/mnras/staa1103 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.495..895B 495, 895

    2020 doi

  5. [13]

    C., Kazantzidis S., Weinberg D

    Bird J. C., Kazantzidis S., Weinberg D. H., Guedes J., Callegari S., Mayer L., Madau P., 2013, @doi [ ] 10.1088/0004-637X/773/1/43 , https://ui.adsabs.harvard.edu/abs/2013ApJ...773...43B 773, 43

    2013 doi

  6. [14]

    V., Bajkova A

    Bobylev V. V., Bajkova A. T., Myll \"a ri A. A., 2010, @doi [Astronomy Letters] 10.1134/S1063773710010044 , https://ui.adsabs.harvard.edu/abs/2010AstL...36...27B 36, 27

    2010 doi

  7. [15]

    W., 2010, @doi [ ] 10.1088/0004-637X/717/2/617 , https://ui.adsabs.harvard.edu/abs/2010ApJ...717..617B 717, 617

    Bovy J., Hogg D. W., 2010, @doi [ ] 10.1088/0004-637X/717/2/617 , https://ui.adsabs.harvard.edu/abs/2010ApJ...717..617B 717, 617

    2010 doi

  8. [16]

    Buder S., et al., 2021, @doi [ ] 10.1093/mnras/stab1242 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.506..150B 506, 150

    2021 doi

  9. [17]

    arXiv:2409.19858

    Buder S., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2409.19858 , https://ui.adsabs.harvard.edu/abs/2024arXiv240919858B p. arXiv:2409.19858

    2024 doi arXiv

  10. [18]

    Chiappini C., Matteucci F., Romano D., 2001, @doi [ ] 10.1086/321427 , https://ui.adsabs.harvard.edu/abs/2001ApJ...554.1044C 554, 1044

    2001 doi

  11. [19]

    Chiba R., Friske J. K. S., Sch \"o nrich R., 2021, @doi [ ] 10.1093/mnras/staa3585 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.500.4710C 500, 4710

    2021 doi

  12. [20]

    R., Grand R

    Ciuc a I., Kawata D., Miglio A., Davies G. R., Grand R. J. J., 2021, @doi [ ] 10.1093/mnras/stab639 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.503.2814C 503, 2814

    2021 doi

  13. [21]

    Cui X.-Q., et al., 2012, @doi [Research in Astronomy and Astrophysics] 10.1088/1674-4527/12/9/003 , https://ui.adsabs.harvard.edu/abs/2012RAA....12.1197C 12, 1197

    2012 doi

  14. [22]

    Aguerri J

    D'Onghia E., L. Aguerri J. A., 2020, @doi [ ] 10.3847/1538-4357/ab6bd6 , https://ui.adsabs.harvard.edu/abs/2020ApJ...890..117D 890, 117

    2020 doi

  15. [23]

    D'Orazi V., Magrini L., Randich S., Galli D., Busso M., Sestito P., 2009, @doi [ ] 10.1088/0004-637X/693/1/L31 , https://ui.adsabs.harvard.edu/abs/2009ApJ...693L..31D 693, L31

    2009 doi

  16. [24]

    J., Wyse R

    Daniel K. J., Wyse R. F. G., 2015, @doi [ ] 10.1093/mnras/stu2683 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.447.3576D 447, 3576

    2015 doi

  17. [25]

    J., Wyse R

    Daniel K. J., Wyse R. F. G., 2018, @doi [ ] 10.1093/mnras/sty199 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.476.1561D 476, 1561

    2018 doi

  18. [26]

    B., Fox A

    De Cia A., Jenkins E. B., Fox A. J., Ledoux C., Ramburuth-Hurt T., Konstantopoulou C., Petitjean P., Krogager J.-K., 2021, @doi [ ] 10.1038/s41586-021-03780-0 , https://ui.adsabs.harvard.edu/abs/2021Natur.597..206D 597, 206

    2021 doi

  19. [27]

    M., Freeman K

    De Silva G. M., Freeman K. C., Bland-Hawthorn J., Asplund M., Bessell M. S., 2007, @doi [ ] 10.1086/510131 , https://ui.adsabs.harvard.edu/abs/2007AJ....133..694D 133, 694

    2007 doi

  20. [28]

    Dehnen W., 1998, @doi [ ] 10.1086/300364 , https://ui.adsabs.harvard.edu/abs/1998AJ....115.2384D 115, 2384

    1998 doi

  21. [29]

    Dehnen W., 2000, @doi [ ] 10.1086/301226 , https://ui.adsabs.harvard.edu/abs/2000AJ....119..800D 119, 800

    2000 doi

  22. [30]

    J., 1950, @doi [ ] 10.1086/145240 , https://ui.adsabs.harvard.edu/abs/1950ApJ...111...65E 111, 65

    Eggen O. J., 1950, @doi [ ] 10.1086/145240 , https://ui.adsabs.harvard.edu/abs/1950ApJ...111...65E 111, 65

    1950 doi

  23. [31]

    J., 1958, @doi [ ] 10.1093/mnras/118.2.154 , https://ui.adsabs.harvard.edu/abs/1958MNRAS.118..154E 118, 154

    Eggen O. J., 1958, @doi [ ] 10.1093/mnras/118.2.154 , https://ui.adsabs.harvard.edu/abs/1958MNRAS.118..154E 118, 154

    1958 doi

  24. [32]

    J., 1983, @doi [ ] 10.1086/113352 , https://ui.adsabs.harvard.edu/abs/1983AJ.....88..642E 88, 642

    Eggen O. J., 1983, @doi [ ] 10.1086/113352 , https://ui.adsabs.harvard.edu/abs/1983AJ.....88..642E 88, 642

    1983 doi

  25. [33]

    J., 1996, @doi [ ] 10.1086/118126 , https://ui.adsabs.harvard.edu/abs/1996AJ....112.1595E 112, 1595

    Eggen O. J., 1996, @doi [ ] 10.1086/118126 , https://ui.adsabs.harvard.edu/abs/1996AJ....112.1595E 112, 1595

    1996 doi

  26. [34]

    Famaey B., Jorissen A., Luri X., Mayor M., Udry S., Dejonghe H., Turon C., 2005, @doi [ ] 10.1051/0004-6361:20041272 , https://ui.adsabs.harvard.edu/abs/2005A&A...430..165F 430, 165

    2005 doi

  27. [35]

    Feltzing S., Holmberg J., 2000, , https://ui.adsabs.harvard.edu/abs/2000A&A...357..153F 357, 153

    2000

  28. [36]

    Fragkoudi F., et al., 2019, @doi [ ] 10.1093/mnras/stz1875 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.488.3324F 488, 3324

    2019 doi

  29. [37]

    GRAVITY Collaboration et al., 2019, @doi [ ] 10.1051/0004-6361/201935656 , https://ui.adsabs.harvard.edu/abs/2019A&A...625L..10G 625, L10

    2019 doi

  30. [38]

    GRAVITY Collaboration et al., 2021, @doi [ ] 10.1051/0004-6361/202040208 , https://ui.adsabs.harvard.edu/abs/2021A&A...647A..59G 647, A59

    2021 doi

  31. [39]

    Gaia Collaboration et al., 2023, @doi [ ] 10.1051/0004-6361/202243940 , https://ui.adsabs.harvard.edu/abs/2023A&A...674A...1G 674, A1

    2023 doi

  32. [40]

    Gilmore G., Reid N., 1983, @doi [ ] 10.1093/mnras/202.4.1025 , https://ui.adsabs.harvard.edu/abs/1983MNRAS.202.1025G 202, 1025

    1983 doi

  33. [41]

    Grisoni V., Matteucci F., Romano D., Fu X., 2019, @doi [ ] 10.1093/mnras/stz2428 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.489.3539G 489, 3539

    2019 doi

  34. [42]

    Guiglion G., et al., 2019, @doi [ ] 10.1051/0004-6361/201834203 , https://ui.adsabs.harvard.edu/abs/2019A&A...623A..99G 623, A99

    2019 doi

  35. [43]

    Guiglion G., et al., 2024, @doi [ ] 10.1051/0004-6361/202347122 , https://ui.adsabs.harvard.edu/abs/2024A&A...682A...9G 682, A9

    2024 doi

  36. [44]

    R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    Harris C. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    2020 doi

  37. [45]

    Hattori K., Gouda N., Tagawa H., Sakai N., Yano T., Baba J., Kumamoto J., 2019, @doi [ ] 10.1093/mnras/stz266 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.484.4540H 484, 4540

    2019 doi

  38. [46]

    R., et al., 2015, @doi [ ] 10.1088/0004-637X/808/2/132 , https://ui.adsabs.harvard.edu/abs/2015ApJ...808..132H 808, 132

    Hayden M. R., et al., 2015, @doi [ ] 10.1088/0004-637X/808/2/132 , https://ui.adsabs.harvard.edu/abs/2015ApJ...808..132H 808, 132

    2015 doi

  39. [47]

    Hunt J. A. S., Bovy J., 2018, @doi [ ] 10.1093/mnras/sty921 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.3945H 477, 3945

    2018 doi

  40. [48]

    Hunt J. A. S., Hong J., Bovy J., Kawata D., Grand R. J. J., 2018, @doi [ ] 10.1093/mnras/sty2532 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.481.3794H 481, 3794

    2018 doi

  41. [49]

    D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    Hunter J. D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    2007 doi

  42. [50]

    J., 1991, in Sundelius B., ed., Dynamics of Disc Galaxies

    Kalnajs A. J., 1991, in Sundelius B., ed., Dynamics of Disc Galaxies. p. 323

    1991

  43. [51]

    Khoperskov S., Gerhard O., 2022, @doi [ ] 10.1051/0004-6361/202141836 , https://ui.adsabs.harvard.edu/abs/2022A&A...663A..38K 663, A38

    2022 doi

  44. [52]

    I., Lugaro M., 2020, @doi [ ] 10.3847/1538-4357/abae65 , https://ui.adsabs.harvard.edu/abs/2020ApJ...900..179K 900, 179

    Kobayashi C., Karakas A. I., Lugaro M., 2020, @doi [ ] 10.3847/1538-4357/abae65 , https://ui.adsabs.harvard.edu/abs/2020ApJ...900..179K 900, 179

    2020 doi

  45. [53]

    Kushniruk I., Bensby T., 2019, @doi [ ] 10.1051/0004-6361/201935234 , https://ui.adsabs.harvard.edu/abs/2019A&A...631A..47K 631, A47

    2019 doi

  46. [54]

    L., Feuillet D., Casagrande L., 2020, @doi [ ] 10.1051/0004-6361/202037923 , https://ui.adsabs.harvard.edu/abs/2020A&A...638A.154K 638, A154

    Kushniruk I., Bensby T., Feltzing S., Sahlholdt C. L., Feuillet D., Casagrande L., 2020, @doi [ ] 10.1051/0004-6361/202037923 , https://ui.adsabs.harvard.edu/abs/2020A&A...638A.154K 638, A154

    2020 doi

  47. [55]

    W., Bovy J., Mackereth J

    Leung H. W., Bovy J., Mackereth J. T., Hunt J. A. S., Lane R. R., Wilson J. C., 2023, @doi [ ] 10.1093/mnras/stac3529 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.519..948L 519, 948

    2023 doi

  48. [56]

    arXiv:2411.19097

    Li Y., Freeman K., Jerjen H., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2411.19097 , https://ui.adsabs.harvard.edu/abs/2024arXiv241119097L p. arXiv:2411.19097

    2024 doi arXiv

  49. [57]

    R., 2023, @doi [Nature Astronomy] 10.1038/s41550-023-01977-z , https://ui.adsabs.harvard.edu/abs/2023NatAs...7..951L 7, 951

    Lian J., Bergemann M., Pillepich A., Zasowski G., Lane R. R., 2023, @doi [Nature Astronomy] 10.1038/s41550-023-01977-z , https://ui.adsabs.harvard.edu/abs/2023NatAs...7..951L 7, 951

    2023 doi

  50. [58]

    Liang X., Yoon S.-J., Zhao J., Li Z., Zhang J., Wu Y., 2023, @doi [ ] 10.3847/1538-4357/acf295 , https://ui.adsabs.harvard.edu/abs/2023ApJ...956..146L 956, 146

    2023 doi

  51. [59]

    Lindegren L., et al., 2021, @doi [ ] 10.1051/0004-6361/202039709 , https://ui.adsabs.harvard.edu/abs/2021A&A...649A...2L 649, A2

    2021 doi

  52. [60]

    arXiv:1510.06123

    Liu C., et al., 2015, @doi [arXiv e-prints] 10.48550/arXiv.1510.06123 , https://ui.adsabs.harvard.edu/abs/2015arXiv151006123L p. arXiv:1510.06123

    2015 doi arXiv

  53. [61]

    E., Andrievsky S

    Luck R. E., Andrievsky S. M., Kovtyukh V. V., Gieren W., Graczyk D., 2011, @doi [ ] 10.1088/0004-6256/142/2/51 , https://ui.adsabs.harvard.edu/abs/2011AJ....142...51L 142, 51

    2011 doi

  54. [62]

    A., L \'e pine J

    Michtchenko T. A., L \'e pine J. R. D., P \'e rez-Villegas A., Vieira R. S. S., Barros D. A., 2018, @doi [ ] 10.3847/2041-8213/aad804 , https://ui.adsabs.harvard.edu/abs/2018ApJ...863L..37M 863, L37

    2018 doi

  55. [63]

    arXiv:1306.2632

    Monari G., Antoja T., Helmi A., 2013, @doi [arXiv e-prints] 10.48550/arXiv.1306.2632 , https://ui.adsabs.harvard.edu/abs/2013arXiv1306.2632M p. arXiv:1306.2632

    2013 doi arXiv

  56. [64]

    Monari G., Kawata D., Hunt J. A. S., Famaey B., 2017, @doi [ ] 10.1093/mnrasl/slw238 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.466L.113M 466, L113

    2017 doi

  57. [65]

    Monari G., Famaey B., Siebert A., Wegg C., Gerhard O., 2019, @doi [ ] 10.1051/0004-6361/201834820 , https://ui.adsabs.harvard.edu/abs/2019A&A...626A..41M 626, A41

    2019 doi

  58. [66]

    F., Helmi A., Freeman K

    Navarro J. F., Helmi A., Freeman K. C., 2004, @doi [ ] 10.1086/381751 , https://ui.adsabs.harvard.edu/abs/2004ApJ...601L..43N 601, L43

    2004 doi

  59. [67]

    F., Przybilla N., 2012, @doi [ ] 10.1051/0004-6361/201118158 , https://ui.adsabs.harvard.edu/abs/2012A&A...539A.143N 539, A143

    Nieva M. F., Przybilla N., 2012, @doi [ ] 10.1051/0004-6361/201118158 , https://ui.adsabs.harvard.edu/abs/2012A&A...539A.143N 539, A143

    2012 doi

  60. [68]

    E., 2015, @doi [ ] 10.1051/0004-6361/201526269 , https://ui.adsabs.harvard.edu/abs/2015A&A...579A..52N 579, A52

    Nissen P. E., 2015, @doi [ ] 10.1051/0004-6361/201526269 , https://ui.adsabs.harvard.edu/abs/2015A&A...579A..52N 579, A52

    2015 doi

  61. [69]

    E., Christensen-Dalsgaard J., Mosumgaard J

    Nissen P. E., Christensen-Dalsgaard J., Mosumgaard J. R., Silva Aguirre V., Spitoni E., Verma K., 2020, @doi [ ] 10.1051/0004-6361/202038300 , https://ui.adsabs.harvard.edu/abs/2020A&A...640A..81N 640, A81

    2020 doi

  62. [70]

    K., Buder S., Ruiter A

    Owusu E. K., Buder S., Ruiter A. J., Seitenzahl I. R., Rodr \' guez-Segovia N., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2405.00315 , https://ui.adsabs.harvard.edu/abs/2024arXiv240500315O p. arXiv:2405.00315

    2024 doi arXiv

  63. [71]

    Pagel B. E. J., Edmunds M. G., 1981, @doi [ ] 10.1146/annurev.aa.19.090181.000453 , https://ui.adsabs.harvard.edu/abs/1981ARA&A..19...77P 19, 77

    1981

  64. [72]

    E., 2007, @doi [Computing in Science and Engineering] 10.1109/MCSE.2007.53 , 9, 21

    P\'erez F., Granger B. E., 2007, @doi [Computing in Science and Engineering] 10.1109/MCSE.2007.53 , 9, 21

    2007 doi

  65. [73]

    P \'e rez-Villegas A., Portail M., Wegg C., Gerhard O., 2017, @doi [ ] 10.3847/2041-8213/aa6c26 , https://ui.adsabs.harvard.edu/abs/2017ApJ...840L...2P 840, L2

    2017 doi

  66. [74]

    Portail M., Gerhard O., Wegg C., Ness M., 2017, @doi [ ] 10.1093/mnras/stw2819 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.465.1621P 465, 1621

    2017 doi

  67. [75]

    C., et al., 2018, @doi [ ] 10.1093/mnras/sty865 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.478..228Q 478, 228

    Quillen A. C., et al., 2018, @doi [ ] 10.1093/mnras/sty865 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.478..228Q 478, 228

    2018 doi

  68. [76]

    Raboud D., Grenon M., Martinet L., Fux R., Udry S., 1998, @doi [ ] 10.48550/arXiv.astro-ph/9802266 , https://ui.adsabs.harvard.edu/abs/1998A&A...335L..61R 335, L61

    1998 doi arXiv

  69. [77]

    J., Brunthaler A., 2004, @doi [ ] 10.1086/424960 , https://ui.adsabs.harvard.edu/abs/2004ApJ...616..872R 616, 872

    Reid M. J., Brunthaler A., 2004, @doi [ ] 10.1086/424960 , https://ui.adsabs.harvard.edu/abs/2004ApJ...616..872R 616, 872

    2004 doi

  70. [78]

    S \'a nchez-Bl \'a zquez P., et al., 2014, @doi [ ] 10.1051/0004-6361/201423635 , https://ui.adsabs.harvard.edu/abs/2014A&A...570A...6S 570, A6

    2014 doi

  71. [79]

    Sch \"o nrich R., Binney J., Dehnen W., 2010, @doi [ ] 10.1111/j.1365-2966.2010.16253.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.403.1829S 403, 1829

    2010

  72. [80]

    A., Binney J

    Sellwood J. A., Binney J. J., 2002, @doi [ ] 10.1046/j.1365-8711.2002.05806.x , https://ui.adsabs.harvard.edu/abs/2002MNRAS.336..785S 336, 785

    2002

  73. [81]

    M., 1979, @doi [ ] 10.1086/157039 , https://ui.adsabs.harvard.edu/abs/1979ApJ...229.1046T 229, 1046

    Tinsley B. M., 1979, @doi [ ] 10.1086/157039 , https://ui.adsabs.harvard.edu/abs/1979ApJ...229.1046T 229, 1046

    1979 doi

  74. [82]

    M., 1980, @doi [ ] 10.48550/arXiv.2203.02041 , https://ui.adsabs.harvard.edu/abs/1980FCPh....5..287T 5, 287

    Tinsley B. M., 1980, @doi [ ] 10.48550/arXiv.2203.02041 , https://ui.adsabs.harvard.edu/abs/1980FCPh....5..287T 5, 287

    1980 doi arXiv

  75. [83]

    Virtanen P., et al., 2020, @doi [Nature Methods] 10.1038/s41592-019-0686-2 , https://rdcu.be/b08Wh 17, 261

    2020 doi

  76. [84]

    Wallerstein G., 1962, @doi [ ] 10.1086/190067 , https://ui.adsabs.harvard.edu/abs/1962ApJS....6..407W 6, 407

    1962 doi

  77. [85]

    X., et al., 2024, @doi [ ] 10.1093/mnras/stae385 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.5394W 528, 5394

    Wang E. X., et al., 2024, @doi [ ] 10.1093/mnras/stae385 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.5394W 528, 5394

    2024 doi

  78. [86]

    Wegg C., Gerhard O., Portail M., 2015, @doi [ ] 10.1093/mnras/stv745 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.4050W 450, 4050

    2015 doi

  79. [87]

    Wegg C., Rojas-Arriagada A., Schultheis M., Gerhard O., 2019, @doi [ ] 10.1051/0004-6361/201936779 , https://ui.adsabs.harvard.edu/abs/2019A&A...632A.121W 632, A121

    2019 doi

  80. [88]

    M., Gerhard O

    Wylie S. M., Gerhard O. E., Ness M. K., Clarke J. P., Freeman K. C., Bland-Hawthorn J., 2021, @doi [ ] 10.1051/0004-6361/202140990 , https://ui.adsabs.harvard.edu/abs/2021A&A...653A.143W 653, A143

    2021 doi

  81. [89]

    Yoshii Y., 1982, , https://ui.adsabs.harvard.edu/abs/1982PASJ...34..365Y 34, 365

    1982

  82. [90]

    da Costa-Luis C., et al., 2024, tqdm: A fast, Extensible Progress Bar for Python and CLI , @doi 10.5281/zenodo.595120

    2024 doi

  83. [91]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

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