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Discs follow the same mass–dispersion scaling as bulges, and the thick-to-thin dispersion ratio is nearly mass-constant—but the size of the gap depends on how the split is defined.

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Thin and thick disc components follow parallel mass–velocity dispersion relations, with thick discs about 1.6 times hotter than thin discs under circularity-based definitions.

T0 review reviewed 2026-08-01 challenge →

load-bearing objection Useful, honest extension of the disc M*-sigma relation to thin/thick subcomponents, but the SAMI-NewHorizon agreement rests on equating two different circularity definitions and needs stronger uncertainty handling before it will convince. the 3 major comments →

arxiv 2607.22007 v1 pith:OEOIXD3P submitted 2026-07-24 astro-ph.GA

Kinematic scaling of thin and thick discs from SAMI to NewHorizon

Sree Oh , J. K. Jang , Giulia Santucci , Sukyoung K. Yi , Matthew Colless , Scott M. Croom , Yohan Dubois , Stefania Barsanti
show 3 more authors
Christophe Pichon S\'ebastien Peirani Madusha L. P. Gunawardhana
This is my paper
classification astro-ph.GA
keywords galaxy kinematicsvelocity dispersionthin discthick discscaling relationsorbital circularitySchwarzschild modelscosmological simulations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 sets out to extend the established stellar mass–velocity dispersion (M*–σe) relation—previously measured for bulges and ellipticals—to the thin and thick disc components of disc galaxies, using orbit-superposition models of 161 passive galaxies from the SAMI survey and particle kinematics of 31 massive disc galaxies from the NewHorizon simulation. It claims that discs obey a tight M*–σe relation nearly parallel to the bulge relation, that the thick disc is systematically hotter than the thin disc, and that the ratio σ_thick/σ_thin is almost independent of stellar mass, bulge fraction, and thick-disc fraction. The ratio depends on the classification scheme: circularity-based selection gives a median log ratio of ~0.20–0.23 (a factor of ~1.6), while age-based selection in the simulation gives only ~0.08 (a factor of ~1.2). The paper further claims that no single global age threshold reproduces the circularity-based split, because median stellar ages of all components rise with mass and the age distributions overlap. These results matter because they show a disc's kinematic state is predictable from mass, and they frame 'thin' versus 'thick' as dynamical, not simply age, categories.

Core claim

The paper's central claim is that thin and thick discs are each characterized by a well-defined stellar mass–velocity dispersion relation, with the thick disc offset to higher dispersion. Using the orbital circularity parameter λz with thresholds 0.5 and 0.8 to separate bulge, thick disc, and thin disc, the authors find a median log(σ_thick/σ_thin) of 0.20 in the observed SAMI sample and 0.23 in the NewHorizon simulation—nearly constant across mass and morphology, corresponding to a ratio about 1.6. When the simulated discs are instead split by stellar age into components older and younger than 8 Gyr, the contrast shrinks to a median log ratio of 0.08 (ratio ~1.2), and varying the age thresh

What carries the argument

The central tool is the orbital circularity parameter λz: for SAMI galaxies it is defined per orbit as Lz/(r·Vc) from Schwarzschild orbit-superposition models, and for NewHorizon star particles as Jz/Jc(E), the ratio of azimuthal angular momentum to the maximum angular momentum at a given binding energy. The paper uses the fixed thresholds λz<0.5, 0.5<λz<0.8, and λz>0.8 to define bulge, thick disc, and thin disc, respectively, in both datasets, and measures the flux-weighted (SAMI) or mass-weighted (NewHorizon) velocity dispersion within 1 effective radius for each component. This matched circularity decomposition is what allows the observed and simulated thin–thick dispersion ratios to be c

Load-bearing premise

The load-bearing premise is that the two circularity definitions—Lz/(r·Vc) from the Schwarzschild models and Jz/Jc(E) from the simulation—plus the same thresholds of 0.5 and 0.8 separate the same physical orbit families; if the normalisations select different populations, the 'matched selection' agreement between SAMI and NewHorizon is not established.

What would settle it

A concrete check would be to recompute the NewHorizon circularity using the SAMI-style normalisation Lz/(r·Vc) (with the same reference circular speed) and re-measure the median σ_thick/σ_thin; if the ratio shifts by more than the ~0.03 dex difference between the two samples, the matched-selection claim is contradicted. Alternatively, applying both the SAMI and NewHorizon circularity definitions to the same set of simulated galaxies and showing they classify the same particles would directly verify the assumption.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Disc velocity dispersion at one effective radius can be predicted from stellar mass alone, with a tight scatter comparable to the bulge relation; this adds a mass-based anchor alongside rotation-based Tully–Fisher scalings.
  • The circularity-based ratio σ_thick/σ_thin ≈ 1.6 is nearly independent of stellar mass, bulge fraction, and thick-disc fraction; galaxy formation models that produce substantially different ratios would be inconsistent with the data.
  • Age-based selections yield a weaker contrast (~1.2), implying that surveys or models equating 'old population' with 'thick disc' will underestimate the kinematic separation and misclassify components as a function of mass.
  • The observation–simulation offset in absolute σe (NewHorizon is ~0.25 dex colder at fixed mass) is a known systematic, but the thin–thick ratio remains comparable; this suggests the ratio is a more robust benchmark for simulations than the absolute normalization.

Where Pith is reading between the lines

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

  • Editorial inference: if secular heating in vertical equilibrium sets the baseline, then at fixed circularity thresholds the thick-to-thin ratio should grow with galaxy age; observing this ratio in high-redshift discs (e.g., with future IFU surveys) would directly test the heating model.
  • Editorial inference: the tightness of the disc M*–σe relation suggests that σe could be used as a mass proxy for disc-dominated galaxies in samples where photometric masses are uncertain, provided the ~0.25 dex observation–simulation offset is calibrated.
  • Editorial inference: the decoupling of age and circularity implies that chemical tagging of the thick disc (using [α/Fe]) will not recover the kinematic thin–thick split one-to-one; combining orbit models with stellar-population maps in external galaxies could measure the [α/Fe]–λz relation directly.
  • Editorial inference: the smaller scatter in NewHorizon compared to SAMI may reflect an undersampling of rare heating events; a sharper test would be to compare the scatter in σ_thick/σ_thin itself (not just the mean) between simulations with different feedback prescriptions.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. This paper revisits the stellar mass–velocity dispersion (M*–σe) relation for disc galaxies and extends it to thin and thick subcomponents. Using Schwarzschild orbit-superposition models for 161 passive SAMI galaxies and the NewHorizon cosmological simulation for 31 disc galaxies, the authors classify bulge/thin/thick components by orbital circularity (λz) in both datasets and, in NewHorizon, also by stellar age. They report three main results: (1) disc components follow a tight M*–σe relation nearly parallel to the bulge relation; (2) the thick-disc component is systematically hotter than the thin-disc component, with a circularity-based median σ_thick/σ_thin ≈ 1.6 (SAMI) and ≈ 1.7 (NewHorizon), only weakly dependent on mass; age-based definitions give a smaller ratio ≈ 1.2, indicating that age and circularity do not map one-to-one; (3) Schwarzschild-based disc dispersions are systematically higher than spectroscopic decompositions, and simulated discs have lower σe at fixed mass than observed. The paper includes sensitivity tests to circularity threshold (0.7, 0.8, 0.9) and age threshold (4, 6, 8 Gyr) and interprets the results in terms of vertical equilibrium and secular heating.

Significance. If the central claims hold, the paper provides a valuable component-resolved extension of the disc M*–σe relation, using a state-of-the-art dynamical modelling technique on the observational side and a high-resolution simulation on the theoretical side. The explicit sensitivity analysis (Figs. 7–8), the use of an age-based control (Fig. 6g–i), and the candid discussion of method-dependent offsets (§5.1–5.2) are strengths. The result that age-selected components are less distinct kinematically than circularity-selected components is an important, testable message for disc classification. However, the headline SAMI–NH agreement depends on the unquantified equivalence of two different circularity definitions, and the quantitative M*–σe slopes are quoted without uncertainties. These issues are repairable but need to be addressed before the paper can be accepted.

major comments (3)
  1. [§3.1, Eq. (1)–(2), Fig. 6] The SAMI–NH cross-check equates Eq. (1) λz,SAMI = Lz/(r Vc) with Eq. (2) λz,NH = Jz/Jc(E) and applies identical 0.5/0.8 thresholds. The paper itself notes (Sec. 3.1.1) that λz,SAMI is 'a proxy for rotational support rather than the circularity of a literal circular orbit in a non-axisymmetric potential.' These two normalisations are not equivalent in general: r Vc(r) is not Jc(E) unless the potential is spherical and the orbit is at the circular-orbit radius for its energy. Because the central agreement in Fig. 6(a,d) (median 0.20 vs 0.23) is offered as evidence of a common mapping, the equivalence must be demonstrated, e.g. by computing both definitions for NH particles and comparing component assignments and the resulting ratio, or by re-deriving the SAMI thresholds under a common definition. Without such a test, the agreement could be a threshold coincidence.
  2. [§4.2, Figs. 4 and 5] Best-fit slopes and intercepts for the M*–σe relations are quoted without uncertainties (e.g., 'log σ_disc = 0.35 log(M*/10^10 M_sun) + 1.86' in Fig. 4b; same for Fig. 5). The claims that the disc relation is 'nearly parallel' to the bulge and the comparison with the equilibrium expectations in §5.4 (slope ∼0.33 vs ∼0.45) require error bars. Please provide uncertainties on all fitted parameters and, if feasible, the intrinsic scatter. This is necessary to assess whether the SAMI and NH slopes are actually consistent with each other and with the theoretical baselines.
  3. [§2.3 and §4.2/Fig. 6] The 'matched selection' claim for the SAMI–NH comparison is not supported by the actual samples. The SAMI Schwarzschild sample is 161 passive, predominantly bulge-dominated galaxies, while the NH sample is 31 disc galaxies with B/T<0.5. Fig. 6(a,d) compares the full SAMI sample against NH. The flat slope with B/T in Fig. 6(b,e) mitigates but does not establish invariance of the median ratio to sample selection. I recommend repeating the median log(σ_thick/σ_thin) for the SAMI subsample with M*>10^10 M_sun and B/T<0.5 (28 galaxies by the authors' count), or explicitly reframing the comparison as population-level with unmodelled selection differences.
minor comments (3)
  1. [Fig. 8 caption] The caption states that panels (a,b), (c,d), and (e,f) use thresholds of 6, 8, and 10 Gyr, but the panel labels and §4.4 indicate 4, 6, and 8 Gyr. Please correct this inconsistency.
  2. [Fig. 7 caption] The caption lists thresholds in the order 0.7, 0.8, 0.9, but the panels are presented as 0.9, 0.8, 0.7. Please align the caption with the actual panel order.
  3. [§4.2 and §5.3] The caveat that the circularity-based ratio is not independent of the chosen thresholds appears only in §5.3. State this explicitly when the ratio is first introduced in §4.2 so readers do not overinterpret the value 1.6 as a universal physical constant.

Circularity Check

1 steps flagged

Circularity-based 'thick disc is hotter' is largely built into the lambda selection, but the paper's independent age-based split and weak-mass-dependence results keep the central claim from being fully circular.

specific steps
  1. self definitional [§3.1.1, §4.2, §5.3 (Eq. 1; Figs 5–6)]
    "We adopt the circularity criteria suggested by Du et al. (2019) to categorise orbital components into hot (λz,SAMI <0.5), warm (0.5< λz,SAMI <0.8), and cold (λz,SAMI >0.8) components, which serve as proxies for the bulge, thick disc, and thin disc, respectively. ... Because the separation is defined kinematically, this ratio is not independent of the adopted circularity thresholds (Figure 7)."

    The 'thick' and 'thin' disc samples are defined by cuts in the orbital circularity lambda, a kinematic/rotational-support parameter derived from the same Schwarzschild models used to produce the velocity-dispersion maps. Ranking orbits as cold (lambda>0.8) and warm (0.5<lambda<0.8) already orders them by rotational support, so the statement that the thick (warm) component has higher sigma than the thin (cold) component is substantially a restatement of the selection rule rather than an independent empirical discovery. The paper concedes the ratio changes with threshold. However, the age-based classification (lambda>0.5 with age split) is an independent definition and also yields a hotter thick disc, providing genuine support for the direction and preventing full circularity.

full rationale

The one explicit definitional reduction is the circularity-based thin/thick decomposition: because the components are chosen from a kinematic circularity parameter, the qualitative result that the warm/thick component is hotter than the cold/thin component is partly built into the selection. The paper is transparent about this, stating that the dispersion ratio is not independent of the circularity thresholds. The main quantitative claims that are not forced are (i) the weak mass dependence of the ratio, (ii) the 'no single global age threshold' result, and (iii) the age-based contrast of ~1.2, which uses stellar age rather than circularity to separate the two discs and thus provides an independent check. The SAMI-NH agreement in the circularity-based ratio depends on an untested equivalence between Eq. (1) and Eq. (2), but that is a methodological assumption/risk, not a circular reduction: applying identical thresholds to differently normalised circularity parameters could in principle produce agreement for non-physical reasons, yet this is a falsifiable calibration issue rather than an equation reducing to itself. The cited age threshold (Haywood et al. 2013) and the Schwarzschild models (Santucci et al. 2022) are external inputs, not self-citations carrying the argument. Overall score 4 reflects one acknowledged definitional component in the headline result, with independent age-based support preventing a higher score.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The paper introduces no new particles, forces, or invented physical entities. Its free parameters are the adopted circularity and age thresholds plus literature empirical scalings used in the equilibrium slope argument. The main loaded assumptions are the equivalence of the two circularity definitions across observation and simulation, the transferability of a Milky Way age cut, and comparability of mass-weighted simulation dispersions to flux-weighted observed dispersions.

free parameters (3)
  • Circularity thresholds lambda_z = 0.5 and 0.8 = 0.5 and 0.8
    Used to separate hot (bulge), warm (thick disc), and cold (thin disc) orbits. Adopted from Du et al. (2019). The median sigma_thick/sigma_thin changes from 0.18 to 0.34 as the thin-disc cut moves from 0.7 to 0.9 (§4.3).
  • Age threshold for thin/thick disc split = 8 Gyr (fiducial), with 4 and 6 Gyr tested
    Chosen from Milky Way results (Haywood et al. 2013; Hayden et al. 2017). Affects the age-based dispersion contrast, which remains near 0.08–0.09 dex across tested thresholds (§4.4).
  • Structural scaling exponents used to predict M-sigma slope = alpha=0.25, beta=0.17, Tully-Fisher slope=0.3
    Adopted from van der Wel et al. (2014), Tsukui et al. (2025), and a stellar-mass Tully-Fisher relation to compute expected equilibrium slopes of ~0.33 and ~0.45 (§5.4). Not fitted in this paper, but load-bearing for the 'consistent with vertical equilibrium' interpretation.
axioms (5)
  • domain assumption Vertical Jeans equilibrium for an exponential disc: sigma_z^2 ≈ pi G Sigma_star h_z (Eq. 3).
    Used in §5.4 as the baseline physical model for the disc M-sigma relation.
  • domain assumption Toomre stability with Q ≈ 1, giving sigma_R ∝ Sigma_star / kappa (Eq. 4).
    Used in §5.4 to motivate a second mass–dispersion scaling and interpret the NH slope.
  • ad hoc to paper lambda_z,SAMI and lambda_z,NH measure the same physical orbital circularity despite different normalisations.
    The SAMI definition uses L_z/(r Vc) while NH uses J_z/Jc(binding energy); treating them as equivalent under the same thresholds underlies the matched SAMI–NH comparison in §§3.1 and 4.2.
  • domain assumption An 8 Gyr age threshold inferred from the Milky Way is transferable to external galaxies and to the NewHorizon simulation.
    The age-based thin/thick split in §3.2 rests on this MW-motivated threshold; the authors test 4 and 6 Gyr and find weak sensitivity.
  • domain assumption Simulated mass-weighted velocity dispersions within 1 Re are comparable to observed flux-weighted dispersions.
    Stated in §4.1: the simulation uses sigma_e = sqrt((sigma_r^2+sigma_t^2+sigma_z^2)/3) rather than a flux-weighted analogue, and the paper discusses but cannot remove the resulting weighting bias.

reviewed 2026-08-01 · how reviews work

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Cite this review

Pith. "Pith review of Kinematic scaling of thin and thick discs from SAMI to NewHorizon." pith.science (2026). https://pith.science/paper/OEOIXD3P

@misc{pith2026260722007,
  author       = {Pith},
  title        = {Pith review of: Kinematic scaling of thin and thick discs from SAMI to NewHorizon},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OEOIXD3P}},
  note         = {Machine review of arXiv:2607.22007}
}
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read the original abstract

We revisit the relation between disc stellar mass and disc velocity dispersion (M_*-\sigma_e) and extend it to thin and thick subcomponents using orbit-based dynamical models of 161 SAMI galaxies and counterpart measurements for 31 disc galaxies in the NewHorizon simulation. On the observational side, we apply Schwarzschild orbit superposition to recover orbital circularity distributions and component kinematics. On the simulation side, we sample thin and thick discs by circularity and, separately, by stellar age to test classification dependence. Our analysis reveals three main results. (1) Discs follow a tight M_*-\sigma_e relation, nearly parallel to the bulge relation. (2) For both circularity- and age-based definitions, the thick-disc component is systematically hotter than the thin-disc component, and the thin-thick dispersion ratio varies only weakly with mass. However, age cuts yield a smaller kinematic contrast, indicating that stellar age and orbital circularity do not map one-to-one and that no single global age threshold reproduces the circularity-based split. (3) Method and data systematics are present, with Schwarzschild modelling returning slightly higher disc \sigma_e than spectroscopic bulge-disc decompositions, and simulated discs showing lower \sigma_e at fixed mass than observed. All these results are consistent with a baseline set by vertical-equilibrium scalings, with secular heating accumulating over time and modulating the dispersion at fixed mass. Occasional minor interactions may add localised heating but do not appear to be essential for explaining the qualitative, global trends reported here. Future tests with chemo-dynamical modelling and higher-resolution, chemistry-tracking simulations will provide stronger constraints on disc substructures in external galaxies.

Figures

Figures reproduced from arXiv: 2607.22007 by Christophe Pichon, Giulia Santucci, J. K. Jang, Madusha L. P. Gunawardhana, Matthew Colless, Scott M. Croom, S\'ebastien Peirani, Sree Oh, Stefania Barsanti, Sukyoung K. Yi, Yohan Dubois.

Figure 1
Figure 1. Figure 1: The stellar mass and 𝐵/𝑇 distributions of the 161 SAMI and 31 NH galaxies. While the majority of the SAMI sample are massive and bulge-dominated, the sample also includes galaxies with low 𝐵/𝑇 values, indicating substantial disc components. The NH sample consists of massive disc galaxies. On the other hand, galaxies in the NH simulation are predomi￾nantly disc-dominated and reside in relatively sparse envi… view at source ↗
Figure 2
Figure 2. Figure 2: Example flux, stellar velocity, and velocity dispersion maps for (a) SAMI observation (ID 278802; log(𝑀∗/𝑀⊙ ) = 10.85, 𝐵/𝑇 = 0.33), (b) the Schwarzschild model reconstruction, and components sampled based on the circularity parameter: (c) bulge, (d) disc, (e) thick disc, and (f) thin disc. 3.2 NH: Age In addition to the sampling based solely on orbital circularity, we also implement a hybrid method in the … view at source ↗
Figure 4
Figure 4. Figure 4: Bulge and disc 𝑀∗–𝜎e relations based on: (a) the SAMI spectro￾scopic decomposition method from Oh et al. (2020); (b) the SAMI circularity parameter derived from Schwarzschild modelling; and (c) the circularity pa￾rameter from the New Horizon simulation. In all cases, the total stellar mass is shown, and 𝜎e is measured separately for each component. In panel (a), bulges and discs are spectroscopically separ… view at source ↗
Figure 5
Figure 5. Figure 5: Thin (diamonds) and thick (circles) disc 𝑀∗–𝜎e relations based on: (a) the circularity parameter derived from Schwarzschild modelling of the SAMI sample; (b) the circularity parameter from the New Horizon simulation; and (c) the stellar age of the particles in the New Horizon simulation. In all cases, the total stellar mass is presented. The solid lines indicate the best-fit 𝑀∗–𝜎e relations for each compon… view at source ↗
Figure 6
Figure 6. Figure 6: Logarithmic ratio of thick-to-thin disc velocity dispersions as a function of stellar mass (left), bulge-to-total luminosity ratio (middle), and thick-to-disc luminosity ratio (right). Panels (a–c) show results based on the circularity parameter from Schwarzschild modelling of the SAMI sample; (d–f) use the circularity parameter from the New Horizon simulation; and (g–i) are based on stellar age from the N… view at source ↗
Figure 7
Figure 7. Figure 7: Thin and thick disc 𝑀∗–𝜎e relations, together with the corre￾sponding log(𝜎thick/𝜎thin ) values as a function of thick-to-disc luminosity ratio, for different circularity thresholds. Details are the same as in Figures 5 and 6. Panels (a) and (b), (c) and (d), and (e) and (f) show the results for 𝜆z,NH,cut = 0.7, 0.8 (fiducial), and 0.9, respectively. In each case, the thick disc is defined by 0.5 < 𝜆z,NH <… view at source ↗
Figure 9
Figure 9. Figure 9: Median stellar age versus stellar mass in the New Horizon sim￾ulation for bulge (triangles), thick disc (circles), and thin disc (diamonds) components, with discs defined by orbital circularity. The dotted, solid, and dashed lines show least-squares fits to the bulge, thick-disc, and thin-disc se￾quences, respectively. Error bars indicate the typical 1 𝜎 distribution in age for each component. Note that th… view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 1, 2026.