The Age-velocity Dispersion Relations of the Galactic Disk as Revealed by the LAMOST-Gaia Red Clump Stars

Biwei Jiang; Han Shen; Weixiang Sun; Xiaowei Liu

REVIEW 4 major objections 5 minor 2 cited by

The Age-velocity Dispersion Relations of the Galactic Disk as Revealed by the LAMOST-Gaia Red Clump Stars

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The Milky Way's thin and thick disks show opposite age-heating trends

desk verdict A useful radial extension of AVR measurements, but the uncharacterized stellar ages and the admitted age systematics leave the central beta–R gradients and the Sagittarius timing claim unsecured. read the letter →

arxiv 2412.07089 v2 pith:2PQYVVVB submitted 2024-12-10 astro-ph.GA

Weixiang Sun , Han Shen , Biwei Jiang , Xiaowei Liu This is my paper · ORCID

classification astro-ph.GA

keywords age-velocitydispersionrelationGalacticdiskredclumpstarsLAMOSTGaiaheatingthickSagittariusminormerger

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

Using nearly 230,000 red clump stars from LAMOST and Gaia (about 160,000 after quality cuts), this paper measures the age–velocity dispersion relation (AVR) of the Milky Way's disk out to 15 kpc and shows that the power-law slope β of the relation is not a universal number: it falls with Galactocentric radius for the thin disk and rises for the thick disk. The AVRs are fitted as $\sigma_v = \sigma_{v,0}(\tau+0.1)^{\beta_v}$, and the paper finds thin-disk $\beta_R$ and $\beta_Z$ decline exponentially with $R$ while $\beta_\phi$ stays nearly constant at 0.20–0.25, matching long-term heating by giant molecular clouds and spiral arms. The thick disk shows $\beta$ values that are globally small and increase with $R$, meaning its stars already have large velocity dispersions at all ages—evidence of violent heating through mergers or a turbulent, chaotic birth. The paper also interprets a flat $\sigma_\phi$ pattern for 3–7 Gyr stars in the outer disk as a recent minor merger, likely Sagittarius, within the last 3 Gyr. The central contribution is the radial behavior of $\beta$ as a population-specific observational constraint on disk heating and assembly.

What carries the argument

The central object is the exponent $\beta_v$ in the fitted AVR $\sigma_v = \sigma_{v,0}(\tau+0.1)^{\beta_v}$, where $\tau$ is stellar age in Gyr and the +0.1 floor accounts for the nonzero velocity dispersion at birth; $\beta_v$ measures how quickly velocity dispersion grows with age, so its radial gradient separates slow secular heating (large $\beta$) from rapid or early heating (small, flat $\beta$). The machinery includes the red clump sample itself—core-helium-burning giants whose nearly fixed luminosity makes them standard candles with ~5–10% distance errors—combined with Gaia DR3 astrometry and spectroscopy to compute 3D positions and velocities in Galactocentric cylindrical coordinates. A chemical separation of thin and thick disks on the [Fe/H]–[α/Fe] plane removes the 7–9 Gyr jump seen in the whole-sample AVRs, isolating each disk's heating history, and the paper fits $\beta(R)$ with exponentials for the thin disk and lines for the thick disk while using an outer-disk $\sigma_\phi$ comparison across age bins to date a recent heating event.

What would settle it

A re-analysis using asteroseismic ages (independent of spectral fitting) for the same stars would settle the matter: if the thin-disk $\beta_R$ and $\beta_Z$ still decline with $R$ while the thick-disk $\beta$ values still rise, and if the 1–3 Gyr stars at $R = 12$–14 kpc still have $\sigma_\phi$ larger than the 3–7 Gyr stars, the paper's claims stand; a monotonic AVR in the outer disk or washed-out radial gradients would falsify them.

Watch

Extended reading notes

Core claim

The paper claims that the age–velocity dispersion relation of the Galactic disk is well described by $\sigma_v = \sigma_{v,0}(\tau+0.1)^{\beta_v}$, and that the exponent $\beta_v$ carries the physical signal. For the whole sample, $\beta_R$, $\beta_\phi$, and $\beta_Z$ all decrease with $R$, following $\beta_R = 0.348 \exp(-(R-8.34)/4.936)$, $\beta_\phi = 0.354 \exp(-(R-8.34)/18.265)$, and $\beta_Z = 0.515 \exp(-(R-8.34)/8.695)$. Splitting the sample chemically, the thin disk shows $\beta_R$ and $\beta_Z$ decreasing exponentially with $R$ ($\beta_R$ from 0.23 at 8.5 kpc to 0.12 beyond 12.5 kpc; $\beta_Z$ from 0.46 to 0.40), while $\beta_\phi$ is nearly constant at 0.20–0.25 between 8.5 and 11.5 kpc; these values align with predictions of long-term heating by giant molecular clouds and spiral arms. The thick disk shows the opposite: $\beta_R$ rises from 0.05 at 7.5 kpc to 0.25 at 11.5 kpc, with weak increasing trends in $\beta_\phi$ and $\beta_Z$, and the overall small $\beta$ means thick-disk stars of all ages already move with large dispersions. The paper interprets this as rapid violent heating from merger and accretion, or formation in chaotic gas-rich mergers and turbulent interstellar medium, and it reads a non-monotonic $\sigma_\phi$ versus age in the outer disk ($R = 12$–14 kpc) as a Sagittarius-induced perturbation within the last 3 Gyr.

Load-bearing premise

The analysis assumes that the catalog stellar ages are unbiased enough in radius and [α/Fe] to serve as the independent variable of every fitted AVR, even though the paper never defines or characterizes these ages, quotes no age uncertainties, and removes young alpha-enhanced stars precisely because their ages are known to be underestimated.

Editorial extensions

If this is right

If the radial $\beta$ trends are real, disk heating models must reproduce the thin disk's exponentially declining $\beta_R$ and $\beta_Z$ with a nearly flat $\beta_\phi$, which points to giant molecular clouds and spiral arms as the dominant long-term heating agents.
The thick disk's small, radially rising $\beta$ implies its stars were heated rapidly or born hot, favoring merger, accretion, or turbulent-ISM origins over slow secular heating.
The non-monotonic $\sigma_\phi$ signal at $R = 12$–14 kpc places a Sagittarius-like minor merger within the last 3 Gyr, giving a timing anchor for the Milky Way's accretion history.
The disappearance of the 7–9 Gyr AVR jump in the chemically separated disks indicates the jump is a population effect—the presence of the thick disk—rather than a single universal heating event.
The flattening of $\beta_Z$–$R$ beyond 10.5 kpc links vertical heating in the outer disk to the thin-disk flare, implying structural flaring contributes to outer-disk kinematics.

Reading between the lines

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

The opposite radial gradients of $\beta$ between the two disks could be used as a diagnostic in galaxy simulations: the radius where the thick-disk $\beta_R$ stops rising may trace the radial extent of merger-heated stars.
A direct extension would be to compare the fitted scale length of the whole-sample $\beta_R$ decline (≈4.9 kpc) with the Milky Way's molecular gas scale length; a match would strengthen the GMC-heating interpretation, a mismatch would point elsewhere.
If a Sagittarius passage occurred within 3 Gyr, the same outer-disk stars should show phase-space substructure or chemical anomalies in Gaia data that could be searched for independently.
The removal of young alpha-enhanced stars because their catalog ages are underestimated suggests future AVR work at ages below about 6 Gyr should correct for binary mergers or use asteroseismic ages to avoid biasing the youngest bins.

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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

This paper gives the first radial profiles of the AVR slope β across the Galactic disk for a large red-clump sample, splitting thin and thick disks chemically. That's a real step beyond solar-neighborhood measurements. The fits are clearly presented, the solar-neighborhood values match earlier work, and the comparison with GMC/spiral-arm heating predictions is sensible. If the radial trends hold up, they are exactly the kind of constraint needed to separate slow heating from merger heating.

The soft spot is the stellar ages. Section 2 quotes uncertainties for radial velocities, T_eff, log g, [Fe/H], [α/Fe], and distances, but never for age, never names the age estimator or catalogue. Age is the independent variable in Eq. (1), so every fitted β depends on it. The only explicit statement about age reliability is the removal of young α-enhanced stars because their true ages are confirmed to be underestimated. That is an admission that the ages carry population-dependent systematics. If those systematics correlate with radius or chemistry, the β–R gradients and the Sagittarius timing inference are not secured. This is a load-bearing omission, not a cosmetic one.

The Sagittarius interpretation itself rests on a small feature in σ_phi at R > 11.5 kpc; it's plausible but not compelling on its own. The exponential versus linear functional forms for β–R are adopted post hoc; they are fine as descriptions but shouldn't be given physical weight beyond that.

Who should read this: Galactic dynamicists and anyone using AVRs as a heating probe. It deserves a serious referee. The age problem is fixable: state the age source, quote the uncertainties, propagate them into the fits, and test for radial and [α/Fe]-dependent bias. I would not cite the β–R gradients or the Sgr claim until that is done. But the data set and the quantitative trends, once age-characterized, would be a useful reference.

I'd send it to peer review with a request for major revision. My own priority would be the age characterization, not the astrophysical interpretation.

Referee Report

4 major / 5 minor

Summary. Using 159,752 red clump stars from LAMOST and Gaia after cuts (from an initial 228,820), the paper measures age–velocity dispersion relations (AVRs) in cylindrical radial bins over 5 ≤ R ≤ 15 kpc and |Z| ≤ 3 kpc. It fits σ_v = σ_{v,0}(τ+0.1)^β_v for the whole sample and for chemically selected thin and thick disk subsamples, and reports the best-fit exponents β_R, β_φ, β_Z as a function of R. The central claims are: (i) for the whole sample, all three exponents decline globally and approximately exponentially with R; (ii) for the thin disk, β_R and β_Z decline while β_φ ≈ 0.20–0.25 out to 11.5 kpc; (iii) for the thick disk, β_R, β_φ, β_Z increase with R; and (iv) a discontinuity in the outer-disk σ_φ AVR implies a Sagittarius-induced heating event within the last 3 Gyr. These trends are interpreted as evidence for long-term GMC/spiral heating in the thin disk and violent merger/accretion heating in the thick disk.

Significance. If the radial β–R trends are robust, they provide a new observational constraint on where and how disk heating operates, and the thin/thick disk comparison is a valuable population-level probe. The paper is strong in using RC standard candles and Gaia astrometry to build a large sample, and the solar-neighborhood β values agree with earlier work. The local AVR normalization is not the novelty, however; the new information lies in the radial gradients and the Sgr timing claim. Those rest on stellar ages, whose estimator and uncertainties are not stated, and on a qualitative reading of one σ_φ panel. With those points resolved, the paper could be an important empirical reference; in its current form the headline claims are not yet secured.

major comments (4)

[Section 2, Eq. (1)] The independent variable τ of every fit is never defined. The paper quotes uncertainties for Vr, Teff, logg, [α/Fe], and [Fe/H], and states distance errors of 5–10%, but gives no age-estimation method, no age catalogue, and no age uncertainty. This is load-bearing: in a power-law fit with noisy ages, β is attenuated, and if the age bias varies with R or [α/Fe], the fitted β–R gradients in Figs. 3 and 5 shift directly. The paper itself admits in Section 2 that young [α/Fe]-enhanced stars are removed 'since their true ages are confirmed have been underestimated,' i.e., age systematics exist for a chemically distinct population. Please state the age estimator and its uncertainties, propagate age errors into β, and provide a robustness test (e.g., repeat the fits without the young α-enhanced cut, or cross-check ages against an independent catalogue such as asteroseismic ages).
[Section 3.1, Fig. 2] The claim that the Sagittarius perturbation occurred within 3.0 Gyr is inferred from the σ_φ AVR at R = 12–14 kpc, where stars younger than ∼3 Gyr are said to show 'obviously larger' σ_φ than stars at 6–7 Gyr. No significance test, no uncertainty on the σ_φ values in those bins, and no model of the expected Sgr perturbation is provided. Alternative explanations (e.g., a radial selection effect, the warp/flare, or spiral-arm transients) are not quantitatively excluded. Please add a statistical comparison of the age slices and, ideally, a simple model or literature comparison for the Sgr-induced heating signature.
[Section 3.2, Fig. 5] The thin/thick disk separation is imported from Sun et al. (2023, 2024a) but the boundary definitions in the [Fe/H]–[α/Fe] plane are not given in this paper. Because all population-specific claims—constant β_φ in the thin disk, increasing β in the thick disk—are comparisons between these two subsamples, the reader needs the selection boundaries and a test of how the results change when the boundary is shifted by a reasonable amount.
[Section 3.1 and Section 4] The abstract and conclusions describe a 'global exponential decreasing trend' of β with R, but Eq. (2) is fitted only for R ≥ 8.5 kpc for β_R and β_Z and only for 8.5 ≤ R ≤ 11.5 kpc for β_φ, and the thin-disk β_φ and thick-disk profiles are fitted with linear functions instead. No goodness-of-fit or model comparison (e.g., exponential vs. linear vs. broken power law) is reported. Please temper the 'global exponential' wording to match the fitted ranges, or justify the choice of fitting window and form with quantitative model selection.

minor comments (5)

[Header] The header reads 'A CCEPTED DECEMBER 09, 2024'; this appears to be a spacing typo in the source file.
[Table 1 caption] The caption says 'The properties of thin and thin disk populations' and should read 'thin and thick disk populations.'
[Section 3.1] The sentence 'The global trends of β – R in our results are obviously' is incomplete and should be finished.
[Eq. (2)] Please define R0 immediately before or after Eq. (2) as R0 = 8.34 kpc, rather than only in the following paragraph.
[Section 2] Please report how many stars are removed by each individual cut, especially the young α-enhanced cut, since the total drops from 228,820 to 159,752 and the effect of this particular cut is central to the age-systematics concern.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the AVR slopes are empirical fits to survey data, and the self-citations support sample-cleaning choices rather than the derived conclusions.

full rationale

The paper's central quantities are the power-law exponents beta_R, beta_phi, and beta_Z obtained by fitting equation (1) to binned LAMOST-Gaia red clump stars, and the radial trends obtained by fitting those exponents with equation (2). These are descriptive fits to the data, not predictions derived from the fitted parameters themselves, so there is no construction by which an output equals an input. The use of equation (1) with the (tau + 0.1) offset is a standard empirical form motivated by a published, external study (Sharma et al. 2021), not by an unpublished ansatz of the present authors. The self-citations to Sun et al. (2020, 2023, 2024a) support the removal of young alpha-enhanced stars and the thin/thick disk separation; these are published, externally checkable results used as input sample definitions, and they do not assume the paper's conclusions. The radial-break interpretation involving Sagittarius is an interpretive step based on the shape of the fitted AVRs, not a circular reduction. The main weakness is that the stellar-age estimator is not described and age uncertainties are not propagated, which is a completeness and robustness concern rather than a circularity; it does not make the measurement equivalent to its inputs by definition. Accordingly, the circularity score is 0.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central claims are empirical fits that inherit several assumptions: standard Galactocentric constants, the standard-candle nature of RC stars, reliable stellar ages, a chemical separation of thin and thick disks, and an assumed power-law AVR form. The exponential and linear beta-R profiles are additional ad hoc functional choices. No new physical entities are introduced.

free parameters (6)

Per-bin AVR exponents beta_R, beta_phi, beta_Z = e.g., beta_R=0.333 +/- 0.011, beta_phi=0.362 +/- 0.010, beta_Z=0.537 +/- 0.013 in the solar neighborhood; values at…
Free slopes of Eq. (1) fitted to velocity dispersion versus age in each radial bin; these are the main measured quantities.
Per-bin AVR normalizations sigma_v,0 = not tabulated; depends on R and component
Normalization of Eq. (1) fitted alongside beta, absorbing the overall velocity scale of each population.
Exponential beta-R parameters for combined sample = beta_R0=0.348, R_R=4.936 kpc; beta_phi0=0.354, R_phi=18.265 kpc; beta_Z0=0.515, R_Z=8.695 kpc
Parameters of Eq. (2) fitted to the per-bin beta values, used to claim a global exponential decreasing trend.
Thin disk beta-R parameters = beta_R=0.237 exp(-(R-8.34)/7.241); beta_phi=0.005 R+0.184; beta_Z=0.440 exp(-(R-8.34)/36.937)
Fitted profiles used to characterize the thin disk radial dependence.
Thick disk beta-R parameters = beta_R=0.034 R-0.148; beta_phi=0.014 R-0.065; beta_Z=0.013 R+0.057
Linear fits used to characterize the thick disk radial increase.
Age offset tau0 in Eq. (1) = 0.1 Gyr (fixed)
Chosen a priori following Sharma et al. 2021 to represent the birth velocity dispersion epoch; not fitted but affects the beta slopes.

assumptions (7)

domain assumption Galactocentric constants: R_sun=8.34 kpc, Vc,0=238 km/s, solar motion (13.00,12.24,7.24) km/s.
Standard values from cited astrometric and kinematic references; used to convert observed coordinates and velocities into Galactocentric cylindrical components.
domain assumption RC stars are standard candles with distance errors below about 10% after cuts.
The Data section states a typical distance error of 5% to 10%; the kinematic accuracy depends on this.
domain assumption Stellar ages used as the independent variable are accurate enough for AVR fitting.
The paper never states how ages are estimated or their uncertainties; all AVR slopes depend on ages.
domain assumption Chemical thin and thick disk separation on the [Fe/H]-[alpha/Fe] plane isolates populations with distinct heating histories.
The split follows Sun et al. 2023 and 2024a and is used to interpret the different beta-R trends.
domain assumption Young alpha-enhanced stars (age <= 6 Gyr, [alpha/Fe] >= 0.15) have underestimated ages and are excluded.
Selection based on Sun et al. 2020; removes stars that would otherwise flatten the young-age AVR, but also biases the young end if the assumption is wrong.
domain assumption The AVR follows sigma_v = sigma_v0 (tau + 0.1)^beta_v.
Standard power-law model from the literature (e.g., Lacey 1984; Sharma et al. 2021), not derived here; all beta values are conditional on this form.
ad hoc to paper The beta-R profiles follow exponential (Eq. 2) or linear functional forms.
The exponential form is chosen after inspecting the data and is fitted only over limited radial ranges; no model comparison is provided.

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Cite this review

Pith. "Pith review of The Age-velocity Dispersion Relations of the Galactic Disk as Revealed by the LAMOST-Gaia Red Clump Stars." pith.science (2026). https://pith.science/paper/2PQYVVVB

@misc{pith2026241207089,
  author       = {Pith},
  title        = {Pith review of: The Age-velocity Dispersion Relations of the Galactic Disk as Revealed by the LAMOST-Gaia Red Clump Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2PQYVVVB}},
  note         = {Machine review of arXiv:2412.07089}
}

abstract

Using nearly 230,000 red clump (RC) stars selected from LAMOST and Gaia, we conduct a comprehensive analysis of the stellar age-velocity dispersion relations (AVRs) for various disk populations, within 5.0 $\leq$ $R$ $\leq$ 15.0 kpc and $|Z|$ $\leq$ 3.0 kpc. The AVRs of the whole RC sample stars are accurately described as $\sigma_{v}$ = $\sigma_{v,0}$ ($\tau$ + 0.1)$^{\beta_{v}}$, with $\beta_{R}$, $\beta_{\phi}$ and $\beta_{Z}$ displaying a global exponential decreasing trend with $R$, which may point to the difference in spatial distributions of various disk heating mechanisms. The measurements of $\beta$ $-$ $R$ for various disks suggest that the thin disk exhibits a radial dependence, with a global exponential decreasing trend in $\beta_{R}$ $-$ $R$ and $\beta_{Z}$ $-$ $R$, while $\beta_{\phi}$ remains a nearly constant value (around 0.20$\sim$0.25) within 8.5 $\leq$ $R$ $\leq$ 11.5 kpc. The thick disk displays a global increasing trend in $\beta_{R}$ $-$ $R$, $\beta_{\phi}$ $-$ $R$ and $\beta_{Z}$ $-$ $R$. These results indicate that the thin disk stars are likely heated by long-term heating from GMCs and spiral arms, while thick disk stars are likely heated by some violent heating process from merger and accretion, and/or formed by the inside-out and upside-down star formation scenarios, and/or born in the chaotic mergers of gas-rich systems and/or turbulent ISM. Our results also suggest that the disk perturbation by a recent minor merger from Sagittarius may have occurred within 3.0 Gyr.

Figures

Figures reproduced from arXiv: 2412.07089 by the authors.

**Figure 1.** Spatial distribution in the R - Z plane, of the sample stars, colorcoded by the mean stellar ages. There are no less than 8 stars in each bin, with spaced 0.1 kpc in both axes. The top panel displays histograms of fraction number density (f = Ni/Ntot) distributions along the radial direction. Here, Ni represents the number of stars in each radial bin, and Ntot denotes the total number of stars in the whole sample.… view at source ↗

**Figure 2.** The AVRs of the whole RC sample stars at different R bins, color-coded by mean R. From left to right represent respectively the AVR of σR, σϕ and σZ . The dashed lines represent the best fit with equation (1) for various R bins. The best fits of AVRs are plotted by dashed lines in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** The best fit parameter (β) of Equation (1) as a function of R of the whole RC sample stars, with the βR, βϕ and βZ are plotted by different colors. ilar value in σϕ, meaning those stars are likely to be rapidly heated to such large azimuthal velocity dispersion in a short time-scale by a violent event. Considering that the σϕ of stars with age younger than ∼3.0 Gyr obviously larger than that of stars with age = 6.0∼… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Similar to [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: Similar to [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Works this paper leans on

93 extracted references · 58 canonical work pages · cited by 2 Pith papers

[1]

G., Navarro, J

Abadi, M. G., Navarro, J. F., Steinmetz, M., Eke, V. R.\ 2003, , 597, 21

2003
[2]

Antoja, T., Helmi, A., Dehnen, W., et al.\ 2014, , 563, A60

2014
[3]

Antoja, T., Helmi, A., Romero-G \'o mez, M., et al.\ 2018, , 561, 360

2018
[4]

Aumer, M., Binney, J., & Sch \"o nrich, R.\ 2016a, , 459, 3326
[5]

Aumer, M., Binney, J., & Sch \"o nrich, R.\ 2016b, , 462, 1697
[6]

J.\ 2009, , 397, 1286

Aumer, M., Binney J. J.\ 2009, , 397, 1286

2009
[7]

Aumer, M., White, S. D. M.\ 2013, , 428, 1055

2013
[8]

Barbanis, B., Woltjer, L.\ 1967, , 150, 461

1967

Show all 93 references

[9]

W., et al.\ 2018, , 478, 611

Belokurov, V., Erkal, D., Evans, N. W., et al.\ 2018, , 478, 611

2018
[10]

C., Loebman, S

Bird, J. C., Loebman, S. R., Weinberg, D. H., et al.\ 2021, , 503, 1815

2021
[11]

Bissantz, N., Englmaier, P., & Gerhard, O.\ 2003, , 340, 949

2003
[12]

Bland-Hawthorn, J., Gerhard, O.\ 2016, , 54, 529

2016
[13]

B., Kawata, D., Gibson, B

Brook, C. B., Kawata, D., Gibson, B. K., & Freeman, K. C.\ 2004, , 612, 894

2004
[14]

K.\ 2007, , 658, 60

Brook, C., Richard, S., Kawata, D., Martel, H., & Gibson, B. K.\ 2007, , 658, 60

2007
[15]

B., Stinson, G

Brook, C. B., Stinson, G. S., Gibson, B. K., et al.\ 2012, , 426, 690

2012
[16]

Carrillo, I., Minchev, I., Steinmetz, M., et al.\ 2019, , 490 797

2019
[17]

Casagrande, L., Sch \"o nrich, R., Asplund, M., et al.\ 2011, , 530, A138

2011
[18]

Combes, F.\ 2014, in Structure and Dynamics of Disk Galaxies, eds. M. S. Seigar, & P. Treuthardt, ASP Conf. Ser., 480, 211

2014
[19]

Q., Zhao, Y

Cui, X. Q., Zhao, Y. H., Chu, Y. Q., et al.\ 2012,\ RAA, 12, 1197

2012
[20]

De Simone, R., Wu, X., & Tremaine, S.\ 2004, , 350, 627

2004
[21]

J., Belokurov, V., Koposov, S

Deason, A. J., Belokurov, V., Koposov, S. E., et al.\ 2018, , 862, 1D

2018
[22]

Dehnen, W.\ 1998, , 115, 2384

1998
[23]

Dehnen, W.\ 2000, , 119, 800

2000
[24]

C., Newberg, H

Deng, L. C., Newberg, H. J., Liu, C., et al.\ 2012,\ RAA, 12, 735

2012
[25]

Fuchs, B.\ 2001, , 325, 1637

2001
[26]

L., Sarro, L

Gaia Collaboration, Creevey, O. L., Sarro, L. M., Lobel, A., et al. et al.\ 2023a, , 674, A39
[27]

Gaia Collaboration, Recio-Blanco, A., Kordopatis, G., et al.\ 2023b, ,, 674, A38
[28]

A., Minchev, I., Villalobos, A., O'Shea, B

G \'o mez, F. A., Minchev, I., Villalobos, A., O'Shea, B. W., & Williams, M. E. K. 2012, , 419, 2163

2012
[29]

A., Minchev, I., O'Shea, B

G \'o mez, F. A., Minchev, I., O'Shea, B. W., et al., 2012, , 423, 3727

2012
[30]

Grand, R. J. J., Springel, V., G \'o mez, F. A., et al.\ 2016, , 459, 199

2016
[31]

H \"a nninen, J., Flynn, C.\ 2002, , 337, 731

2002
[32]

R., Bland-Hawthorn, J., Sharma, S., et al.\ 2020, , 493, 2952

Hayden, M. R., Bland-Hawthorn, J., Sharma, S., et al.\ 2020, , 493, 2952

2020
[33]

H., et al.\ 2018, , 563, 85

Helmi, A., Babusiaux, C., Koppelman, H. H., et al.\ 2018, , 563, 85

2018
[34]

Holmberg, J., Nordstr \"o m, B., Andersen, J.\ 2009, , 501, 941

2009
[35]

L.; Brook, C

House, E. L.; Brook, C. B.; Gibson, B. K., et al.\ 2011, , 415, 2652

2011
[36]

W., Yuan, H

Huang, Y., Liu, X. W., Yuan, H. B., et al.\ 2016, , 463, 2623

2016
[37]

W., et al.,\ 2018, , 864, 129

Huang, Y., Sch \"o nrich, R., Liu, X. W., et al.,\ 2018, , 864, 129

2018
[38]

W., et al.\ 2020, ApJS, 249, 29

Huang, Y., Sch \"o nrich, R., Zhang, H. W., et al.\ 2020, ApJS, 249, 29

2020
[39]

Hunt, J. A. S., Bovy, J., P \'e rez-Villegas, A., et al.\ 2018, , 474, 95

2018
[40]

Jenkins A., Binney J.\ 1990, , 245, 305

1990
[41]

Jenkins, A.\ 1992, , 257, 620

1992
[42]

J \'o nsson, V. H. & McMillan, P. J.\ 2024, , 688, A38

2024
[43]

J.\ 1991, Dynamics of Disc Galaxies, 323

Kalnajs, A. J.\ 1991, Dynamics of Disc Galaxies, 323

1991
[44]

Kawata, D., Grand, R. J. J., Gibson, B. K., et al.\ 2017, , 464, 702

2017
[45]

S., Zentner, A

Kazantzidis, S., Bullock, J. S., Zentner, A. R., et al.\ 2008, , 688, 254

2008
[46]

Khanna, S., Yu, J., Drimmel, R., et al.\ 2024, arXiv:2410.22036

2024
[47]

Kruijssen, J. M. D., Pfeffer, J. L., Reina-Campos, M., et al.\ 2019, , 486, 3180

2019
[48]

G.\ 1984, , 208, 687

Lacey, C. G.\ 1984, , 208, 687

1984
[49]

Laporte, C. F. P., G \'o mez, F. A., Besla, G., Johnston, K. V., & Garavito-Camargo, N.\ 2018, , 473, 1218

2018
[50]

Liu, X., Tian, H., Cui, W., et al.\ 2024, RAA, 24, 065005

2024
[51]

W., Yuan, H

Liu, X. W., Yuan, H. B., Huo, Z. Y., et al.\ 2014, in IAU Symp. 298, Setting the Scene for Gaia and LAMOST (Cambridge: Cambridge Univ. Press), 310

2014
[52]

T., Bovy, J., Schiavon, R

Mackereth, J. T., Bovy, J., Schiavon, R. P., et al.\ 2017, , 471, 3057

2017
[53]

T., Bovy, J., Leung, H

Mackereth, J. T., Bovy, J., Leung, H. W., et al.\ 2019, , 489, 176

2019
[54]

J., Petersson, J., Tepper-Garcia, T., et al.\ 2022, , 516, 4988

McMillan, P. J., Petersson, J., Tepper-Garcia, T., et al.\ 2022, , 516, 4988

2022
[55]

Minchev, I., Chiappini, C., & Martig, M.\ 2013, , 558, A9

2013
[56]

Minchev, I., Chiappini, C., Martig, M., et al.\ 2014, , 781, L20

2014
[57]

Minchev, I., Martig, M., Streich, D., et al.\ 2015, , 804, L9

2015
[58]

Nordstr \"o m, B., Mayor, M., Andersen, J., et al.\ 2004, , 418, 989

2004
[59]

J., Hernquist, L., & Fullagar, D

Quinn, P. J., Hernquist, L., & Fullagar, D. P.\ 1993, , 403, 74

1993
[60]

C., & Garnett, D

Quillen, A. C., & Garnett, D. R. 2001, in ASP Conf. Ser. 230, Galaxy Disks and Disk Galaxies, ed. J. G. Funes & E. M. Corsini (San Francisco, CA: ASP), 87

2001
[61]

A., et al.\ 2023, , 674, A29

Recio-Blanco, A., de Laverny, P., Palicio, P. A., et al.\ 2023, , 674, A29

2023
[62]

J., & Brunthaler, A.\ 2004, , 616, 872

Reid, M. J., & Brunthaler, A.\ 2004, , 616, 872

2004
[63]

J., Menten, K

Reid, M. J., Menten, K. M., Brunthaler, A., et al.\ 2014, , 783, 130

2014
[64]

P., Brooks, A

Ro s kar, R., Debattista, V. P., Brooks, A. M., et al.\ 2010, , 408, 783

2010
[65]

L., Das, P.\ 2018, , 481, 4093

Sanders, J. L., Das, P.\ 2018, , 481, 4093

2018
[66]

Sch \"o nrich, R., Binney, J., & Dehnen, W.\ 2010, , 403, 1829

2010
[67]

Sch \"o nrich, R.\ 2012, , 427, 274

2012
[68]

J.\ 2017, , 467, 1154

Sch \"o nrich, R., & McMillan, P. J.\ 2017, , 467, 1154

2017
[69]

Sch \"o nrich, R., & Dehnen, W.\ 2018, , 478, 3809

2018
[70]

M., Gilmore, G.\ 2007, , 380, 1348

Seabroke, G. M., Gilmore, G.\ 2007, , 380, 1348

2007
[71]

Sharma, S., Steinmetz, M., & Bland-Hawthorn, J.\ 2012, , 750, 107

2012
[72]

Sharma, S., Bland-Hawthorn, J., Binney, J., et al.\ 2014, , 793, 51

2014
[73]

R., Bland-Hawthorn, J., et al.\ 2021, , 506, 1761

Sharma, S., Hayden, M. R., Bland-Hawthorn, J., et al.\ 2021, , 506, 1761

2021
[74]

V., et al.\ 2008, , 480, 91

Soubiran, C., Bienaym \'e , O., Mishenina, T. V., et al.\ 2008, , 480, 91. doi:10.1051/0004-6361:20078788

2008 doi
[75]

Spitzer Lyman J., Schwarzschild M.\ 1951, , 114, 385

1951
[76]

Spitzer Lyman J., Schwarzschild M.\ 1953, , 118, 106

1953
[77]

Str \"o mberg, G.\ 1946, , 104, 12

1946
[78]

X., Huang, Y., Wang, H

Sun, W. X., Huang, Y., Wang, H. F., et al.\ 2020, , 903, 12

2020
[79]

X., Shen, H., Liu, X

Sun, W. X., Shen, H., Liu, X. W.\ 2023, , 952, 163

2023
[80]

X., Huang, Y., Shen, H., et al.\ 2024a, , 961, 141

Sun, W. X., Huang, Y., Shen, H., et al.\ 2024a, , 961, 141
[81]

X., Shen, H., Jiang, B

Sun, W. X., Shen, H., Jiang, B. W., & Liu, X. W. .\ 2024b, , 272, 8
[82]

X., Shen, H., Jiang, B

Sun, W. X., Shen, H., Jiang, B. W., & Liu, X. W. .\ 2024c, , 965, L9
[83]

X., Shen, H., Jiang, B

Sun, W. X., Shen, H., Jiang, B. W., & Liu, X. W. .\ 2024d, arXiv:2412.12876

arXiv
[84]

& Rix, H.-W.\ 2019, , 878, 21

Ting, Y.-S. & Rix, H.-W.\ 2019, , 878, 21

2019
[85]

Uppal, N., Ganesh, S., & Schultheis, M.\ 2024, , 527, 4863

2024
[86]

J., Shen, J

Vickers, J. J., Shen, J. T., Li, Z. Y.\ 2021, , 922, 189

2021
[87]

Villalobos, \'A ., & Helmi, A.\ 2008, , 391, 1806

2008
[88]

Wang, C., Huang, Y., Zhou, Y., et al.\ 2023, , 675, A26

2023
[89]

Wielen, R.\ 1977, , 60, 263

1977
[90]

M., Wuyts, S., et al.\ 2015, , 799, 209

Wisnioski, E., F \"o rster Schreiber, N. M., Wuyts, S., et al.\ 2015, , 799, 209

2015
[91]

S., Liu, X

Xiang, M. S., Liu, X. W., Yuan, H. B., et al.\ 2017, , 467, 1890

2017
[92]

C., Liu, C.\ 2018, , 475, 1093

Yu, J. C., Liu, C.\ 2018, , 475, 1093

2018
[93]

B., Liu, X

Yuan, H. B., Liu, X. W., Huo, Z. Y., et al.\ 2015, , 448, 855

2015

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

G., Navarro, J

Abadi, M. G., Navarro, J. F., Steinmetz, M., Eke, V. R.\ 2003, , 597, 21

2003

[2] [2]

Antoja, T., Helmi, A., Dehnen, W., et al.\ 2014, , 563, A60

2014

[3] [3]

Antoja, T., Helmi, A., Romero-G \'o mez, M., et al.\ 2018, , 561, 360

2018

[4] [4]

Aumer, M., Binney, J., & Sch \"o nrich, R.\ 2016a, , 459, 3326

[5] [5]

Aumer, M., Binney, J., & Sch \"o nrich, R.\ 2016b, , 462, 1697

[6] [6]

J.\ 2009, , 397, 1286

Aumer, M., Binney J. J.\ 2009, , 397, 1286

2009

[7] [7]

Aumer, M., White, S. D. M.\ 2013, , 428, 1055

2013

[8] [8]

Barbanis, B., Woltjer, L.\ 1967, , 150, 461

1967