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REVIEW 3 major objections 5 minor 84 references

Dynamical Models of the Milky Way in Action Space with LAMOST DR8 and GAIA EDR3

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read This paper constructs self-consistent action-based Milky Way models and shows that the three-dimensional kinematics of 86,109 K giant stars are fit by a galaxy with a virial mass of about 1.3×10^12 M⊙, a local stellar density of 0.0696 M⊙…

desk verdict Solid application of AGAMA action-based modeling to a valuable K-giant sample, but the headline virial mass is model-dependent rather than measured, and the paper's own tables show why. read the letter →

arxiv 2502.08164 v2 pith:INS4APQ5 submitted 2025-02-12 astro-ph.GA

Guang-Chen Sun , Qiao Wang , Shude Mao , Yichao Li , Richard J. Long , Ping-Jie Ding , Yougang Wang , Xin Zhang
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Xuelei Chen
This is my paper · ORCID
classification astro-ph.GA
keywords GalaxydynamicsMilkyWaymasskinematicsphysicsaction-baseddistributionfunctionsKgiantstars
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to build a self-consistent dynamical model of the Milky Way that reproduces the full three-dimensional velocity distribution of K giant stars, using proper motions from Gaia EDR3 and spectroscopy from LAMOST DR8. Its central claim is that the near-Sun kinematics of 86,109 K giants are consistent with an axisymmetric action-based model whose virial mass is about 1.3×$10^{12}$ M⊙, local stellar density 0.0696 M⊙ $pc^{-3}$, and local dark matter density 0.0115 M⊙ $pc^{-3}$. The model replaces the earlier torus-based model of Wang et al. (2017), which did not use Gaia proper motions and now fails the new proper-motion distributions. The best-fit disks are different from that earlier model: the thick disk is hotter and more extended, while the thin disk is cooler. Near the Sun the fit is good, but all models fail at 15–20 kpc, which the authors attribute to unmodeled structures such as spiral arms, the bar, or non-equilibrium features.

What carries the argument

The central object is a quasi-isothermal action-based distribution function f(J), written in terms of the three action integrals (J_R, J_z, J_φ) that describe radial, vertical, and azimuthal orbital motion in an axisymmetric potential. The argument is carried by the self-consistency loop: start from an initial density-potential pair, compute actions for a sample of orbits, integrate the distribution function to get a new density, solve Poisson's equation for the updated potential, and repeat until convergence. The fitted parameters are the disk surface-density scale lengths, scale heights, and the velocity-dispersion scales σ_r0, σ_z0, and R_σ for the thin and thick disks, plus the dark-matter halo parameters. Model predictions for line-of-sight velocity and both proper-motion components in 30 sky regions are compared with observations through a χ² statistic, and two optional ingredients—a contracted dark-matter halo and a circumgalactic medium—are built into some models.

What would settle it

Measure the local dark matter density independently with the vertical Jeans equation using Gaia RVS stars; if it differs from the paper's value of 0.0115 M⊙ $pc^{-3}$ by more than the quoted uncertainties, the fiducial axisymmetric model is falsified.

Watch

Extended reading notes

Core claim

On its own terms, this paper claims that a self-consistent, axisymmetric Milky Way model written as an action-based distribution function can simultaneously match the line-of-sight velocities and Gaia proper motions of K giants in the solar neighborhood, and that this requires a Milky Way with a virial mass of M200 = 1.31×$10^{12}$ M⊙ for the fiducial model (the abstract quotes 1.35×$10^{12}$ M⊙), a local stellar density of 0.0696 M⊙ $pc^{-3}$, and a local dark matter density of 0.0115 M⊙ $pc^{-3}$. The fiducial best-fit model, Mc17a, starts from the McMillan (2017) potential and is selected by the lowest reduced χ² in the inner sky regions. Compared with the earlier Wang et al. (2017) torus model, the fitted thick disk has a larger vertical velocity dispersion and scale length, and the thin disk has a smaller vertical velocity dispersion. The paper also reports that proper-motion data are what exclude the older model, and that all attempted models predict velocity distributions that are narrower than observed in the outer disk, signaling missing ingredients in the axisymmetric equilibrium picture.

Load-bearing premise

The load-bearing premise is that the Milky Way can be treated as an axisymmetric galaxy in a steady state, so that every star's orbit is fully described by three conserved actions in a fixed potential; if the survey volume contains the bar, spiral arms, or phase spirals, the fitted distribution-function parameters and the inferred mass and densities are biased.

Editorial extensions

If this is right

  • If the fiducial model is right, the Milky Way's virial mass of about 1.3×10^12 M⊙ and local dark matter density of 0.0115 M⊙ pc^-3 are the values consistent with K-giant kinematics.
  • Proper motions are now a required constraint: any viable disk model must reproduce Gaia proper-motion distributions, not just line-of-sight velocities.
  • The thick disk is hotter and more extended while the thin disk is cooler, changing expectations for how the two disks formed and evolved.
  • The outer disk at 15–20 kpc is hotter than axisymmetric equilibrium models predict, implying missing non-axisymmetric or non-equilibrium components.
  • With contracted-halo models that include a circumgalactic medium, the virial mass can be as low as about 0.4×10^12 M⊙, so the outer halo mass remains uncertain even with good local kinematics.

Reading between the lines

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

  • Beyond the paper: The systematic failure in the outer disk means the fiducial mass and densities are effectively calibrated to the inner few kiloparsecs; a model that included the bar and spiral arms could redistribute velocity dispersion and shift the inferred local dark matter density.
  • Beyond the paper: The distance-calibration ratios D = D_Carlin/0.86 and D = D_Carlin/0.97 are load-bearing; a change in these scale factors would rescale the stellar densities and velocities and alter the fitted distribution-function parameters.
  • Beyond the paper: The spread of virial masses across the paper's models, from about 0.39 to 1.31×10^12 M⊙, shows that K-giant kinematics near the Sun do not by themselves determine the total halo mass; the outer halo mass is fixed by the assumed profile rather than by the data.
  • Beyond the paper: A testable extension is to fit the same action-based distribution function to Gaia RVS stars or red-clump stars with independent distances; if the derived local dark matter density changes by more than the quoted uncertainties, the axisymmetric steady-state assumption is the likely cause.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper constructs axisymmetric, self-consistent action-based distribution-function models of the Milky Way using the AGAMA code, fitted to the three-dimensional velocity distributions of 86,109 K giants from LAMOST DR8 and Gaia EDR3 in 30 sky regions. The authors vary disk and halo density and distribution-function parameters seeded by several published models (McMillan 2017, Cautun et al. 2020, Wang et al. 2017), iterate the potential to self-consistency, and compare the models by reduced chi-square. They report a best-fit local model with a Milky Way virial mass of 1.35e12 Msun, a local stellar density of 0.0696 Msun/pc3, and a local dark matter density of 0.0115 Msun/pc3, and conclude that the thick disk is hotter and more extended while the thin disk is cooler than in Wang et al. (2017). The paper acknowledges that the fits to the outer regions and the North Galactic Pole are poor, and attributes the discrepancies to missing structures such as spiral arms, the bar, and non-equilibrium features.

Significance. If the local results were robust, the paper would provide a useful update to Wang et al. (2017) by adding Gaia proper motions and a larger LAMOST sample. The use of a public, well-tested modeling code (AGAMA), explicit self-consistency iteration, and comparison against several published potentials are genuine strengths, as is the honest reporting of the poor outer-region fits. However, the headline virial mass is not a stable output of the data: the paper itself shows that models with M200 from 0.39 to 1.31e12 Msun fit comparably, and the fiducial selection is based on local chi-square only. The analysis is therefore more credible as a local dynamical calibration than as a global Milky Way mass measurement, and the abstract overstates the robustness of M200.

major comments (3)
  1. [Abstract; Section 4.4; Section 4.5; Table 2; Table 3] The reported virial mass is not robustly constrained and is internally inconsistent. The abstract states 1.35e12 Msun, but Table 2 gives M200=1.31e12 for the fiducial 'Mc17a'; the value 1.35e12 corresponds to 'Mc17b'. More importantly, Section 4.4 selects 'Mc17a' solely because it has the smallest chi2_in, while Table 3 shows chi2_tot/dof = 9.97 for Ca20e (best overall), 10.36 for Mc17a, and 12.54 for Ca20d, with M200 values of 0.84, 1.31, and 0.39e12 Msun, respectively. The differences in reduced chi-square among these models are small (0.4-3) and are dwarfed by the overall poor fit (reduced chi-square ~10), so the data do not discriminate among halo models. The virial mass is an extrapolation from local kinematics that depends strongly on the assumed halo profile, baryonic contraction, and CGM treatment (Sections 3.4-3.5 and 4.5). Section 4.2 states that MCMC sampling was performed and that uncertainties are generally below 10%, but no MCMC results, posteriors, or convergence diagnostics are shown. The paper should either provide the MCMC confidence intervals or remove the virial mass from the abstract and present it explicitly as a model-dependent extrapolation.
  2. [Table 3; Section 4.4; Section 4.6] The global fit quality is poor, so the model cannot support global conclusions. The fiducial model has chi2_tot/dof = 10.36, chi2_out/dof = 27.10 for regions 21-24, and chi2_pole/dof = 21.91 for regions 25-26; even the best global model, Ca20e, has chi2_tot/dof = 9.97. Section 4.6 states that all models fail in the outer regions and that the predicted velocities are narrower than observed, and Section 4.4 notes that proper-motion fits are 2-5 times worse than line-of-sight fits. The statement that 'our model aligns well with observations near the Sun' is defensible only for the 16 local regions (chi2_in = 5.84), but even this value is substantially larger than 1 and indicates unmodeled variance in the local volume. The conclusions about a hotter, more extended thick disk and a cooler thin disk are based on fits that fail to describe a large fraction of the fitted volume; the paper should either restrict these conclusions to the local region or extend the model (e.g., with non-axisymmetric components, flaring, or a warp) and refit before presenting them as main results.
  3. [Section 3.2; Section 4.6; Section 5] The axisymmetric, steady-state assumption is load-bearing and is explicitly acknowledged to be violated. The model assumes a steady-state axisymmetric system with three conserved actions (Section 3.2), yet Section 4.6 invokes the bar, spiral arms, phase spirals, and the flared/warped outer disk to explain the poor fits. These structures are inside the fitted volume: regions 21-24 reach the Galactic anticenter at 3-12 kpc and cross the Perseus arm, and Section 4.4 notes that regions 02, 03, and 14 include the Local Arm. If non-axisymmetric perturbations bias the inferred distribution-function parameters, then the quoted local densities and masses are also biased. The paper should quantify the impact of this assumption, for example by repeating the fit with regions containing known spiral-arm or bar-affected stars removed, or by explicitly stating that the quoted parameters are conditional on strict axisymmetry and are not intended as unbiased estimates.
minor comments (5)
  1. [Section 3.1, Eq. (5)] Equation (5) defines pdata_n as the 'observed velocity dispersion', but the text describes fitting binned histograms of vLOS, mu_alpha, and mu_delta; please clarify the notation and define how the degrees of freedom are counted for each region and how the region-averaged reduced chi-square is justified as a global comparison statistic.
  2. [Section 2.1] The distance corrections D = DCarlin/0.86 in the disk direction and D = DCarlin/0.97 toward the pole are adopted from Ding et al. (2021) with a small change; please state explicitly whether these factors are fixed or fitted, and whether their uncertainties are propagated into the model parameter uncertainties.
  3. [Table 2] There is a typographical issue in Table 2: the row labeled 'Mv17i' appears to be a typo for 'Mc17i', and there are two rows with similar 'Mc17i' labels but different parameter values; please disambiguate the model names.
  4. [Table 3] The caption for Table 3 states that chi2_pole is 'estimated from sky regions 25-16', which should presumably read '25 and 26'; please correct this typo.
  5. [Section 4.2] The sentence 'we employed MCMC sampling to estimate the uncertainties in the fitted parameters' followed by 'specific MCMC results are not included in this paper' is not verifiable; either provide the chains, a corner plot, or a clear statement that these are preliminary and model-dependent, or remove the claim of small (<10%) uncertainties.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the mass and density estimates are outputs of a self-consistent fit to LAMOST/Gaia kinematic histograms, not re-scaled inputs; the virial mass is model-dependent but not circularly derived.

full rationale

The paper's derivation chain is a forward-modeling fit, not a tautology. The free parameters (Table 2, columns 2-9 and 11-17) are the density-profile and quasi-isothermal DF parameters, adjusted to match the observed binned velocity distributions (vLOS, mu_alpha, mu_delta) in 30 sky regions via Eq. (5). The reported virial mass, local stellar density, and local dark matter density (Table 4) are computed from the fitted potential and DF through Poisson's equation (Eq. 6) and Eq. (1); they are not supplied as constraints in the chi-squared. Therefore the headline quantities are statistically dependent on the fitted parameters, which is normal for model outputs, not circular. The selection of Mc17a by smallest chi2_in (Section 4.4) is an internal model comparison, and the paper explicitly acknowledges in Section 4.5 that M200 ranges from 0.39 to 1.31e12 Msun across similarly fitting models, so the virial mass is not forced by construction. External rotation-curve comparisons (Figure 17) use independent data (Eilers et al. 2019; Ablimit et al. 2020; Wang et al. 2023). The self-citations (Wang et al. 2017 as an initial/comparison model, Ding et al. 2021 as the data catalog, Sun et al. 2023 for cluster checks) are not load-bearing uniqueness or theorem citations. The paper also flags its own limitations: Section 4.6 admits all models fail in the outer disk, and Section 4.2 omits the MCMC uncertainty results; these are evidentiary gaps and model-dependence caveats, not circular steps. The abstract's 1.35e12 vs Table 2's 1.31e12 is a reporting inconsistency, not a circularity.

Assumptions & free parameters 17 free parameters · 11 assumptions · 0 invented entities

The central claim rests on 15 fitted model parameters plus two phenomenological distance corrections calibrated on the same dataset, and on the axisymmetric steady-state assumption. The mass and density outputs are derived from these fitted parameters, not independently measured. External comparisons with rotation curve data and independent local density estimates provide some validation.

free parameters (17)
  • thin disk central surface density Sigma0,thin = 8.95e8 M_sun/kpc^2
    Fitted to velocity distributions; listed in Table 2, controls thin disk surface density normalization.
  • thin disk scale radius Rd,thin = 2.48 kpc
    Fitted; radial scale length of thin disk.
  • thin disk scale height h_thin = 0.30 kpc
    Fitted; vertical scale height of thin disk.
  • thick disk central surface density Sigma0,thick = 1.87e8 M_sun/kpc^2
    Fitted; listed in Table 2.
  • thick disk scale radius Rd,thick = 3.05 kpc
    Fitted; radial scale length of thick disk.
  • thick disk scale height h_thick = 0.92 kpc
    Fitted; vertical scale height of thick disk.
  • dark halo density normalization rho0,halo = 8.52e6 M_sun/kpc^3
    Fitted; normalization of the spheroidal dark matter halo.
  • dark halo scale radius r0,halo = 19.25 kpc
    Fitted; scale radius of the dark matter halo.
  • solar distance to Galactic center d_sun = 8.11 kpc
    Fitted; initial value from Gravity Collaboration 2019 was 8.178 kpc, best-fit value is 8.11 kpc.
  • thin disk radial velocity dispersion at center sigma_r0,thin = 63.99 km/s
    Fitted DF parameter controlling velocity dispersion profile.
  • thin disk vertical velocity dispersion at center sigma_z0,thin = 30.22 km/s
    Fitted DF parameter; notably smaller than the Wang17 value, supporting a cooler thin disk.
  • thin disk dispersion scale length R_sigma,thin = 12.52 kpc
    Fitted; merged radial and vertical scale lengths by setting R_sigma,r = R_sigma,z = R_sigma (Section 3.3).
  • thick disk radial velocity dispersion at center sigma_r0,thick = 82.82 km/s
    Fitted DF parameter for the thick disk.
  • thick disk vertical velocity dispersion at center sigma_z0,thick = 132.99 km/s
    Fitted DF parameter; supports a hotter, more extended thick disk.
  • thick disk dispersion scale length R_sigma,thick = 18.73 kpc
    Fitted; merged radial and vertical scale lengths for the thick disk.
  • photometric distance scale factor in disk direction = 0.86
    Chosen so that corrected distance D = D_Carlin / 0.86 matches parallax distances; 2% different from the 0.842 used in Ding et al. (2021). Section 2.1.
  • photometric distance scale factor toward the pole = 0.97
    Chosen for the north Galactic pole direction; Section 2.1, based on comparison between photometric and parallax distances.
assumptions (11)
  • standard math Poisson equation relates potential to density: Laplace operator on Phi equals 4 pi G rho
    Used in Eq. 6 for the iterative density-potential construction in AGAMA.
  • standard math Strong Jeans theorem: equilibrium DF is a function of three isolating integrals, and actions J are such integrals
    Foundation of the action-based DF approach in Section 3.1.
  • domain assumption The Milky Way is axisymmetric and in a steady state
    Explicitly assumed in Section 3.2: 'The MW model adopted in this paper is assumed to be axisymmetrical'. The paper's own poor outer fits in Section 4.6 suggest this assumption is not fully valid.
  • domain assumption Quasi-isothermal DF describes the stellar disks
    Adopted in Section 3.3, Eq. 10, following Binney and McMillan; the paper argues suitability from the low eccentricities of most disk giants (Figure 5).
  • domain assumption Density profiles: exponential disks with sech^2 vertical profile for gas, and power-law spheroids with exponential cutoff for bulge and halo
    Standard parametric forms from Vasiliev (2019a), used in Eqs. 7-8 in Section 3.2.
  • domain assumption Dark matter halo contraction model of Cautun et al. (2020) with its quoted parameters
    Used in Section 3.4 to construct contracted halo variants (Ca20d, Ca20e, Mc17k).
  • domain assumption CGM density profile with ACGM = 0.190 and beta_CGM = -1.46
    Taken from Cautun et al. (2020), Section 3.5; included in Ca20 models.
  • ad hoc to paper R_sigma,r = R_sigma,z = R_sigma for both disks
    Imposed to reduce free parameters; Section 3.3 states tests show small differences, but this is a modeling choice.
  • ad hoc to paper sigma_min = 1% of (sigma_r0 + sigma_z0)/2
    Set in Section 3.3 to prevent the DF from reaching unphysical values at extreme J_phi.
  • domain assumption Systematic LAMOST velocity offset of 5.7 km/s
    Applied to line-of-sight velocities following Tian et al. (2015), Section 2.
  • domain assumption Solar parameters R_sun = 8.178 kpc, z_sun = 20.8 pc, and solar motion vector from literature
    Used in the coordinate transformation in Section 2; taken from Gravity Collaboration 2019, Bennett & Bovy 2019, and Schoenrich et al. 2010.

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Pith. "Pith review of Dynamical Models of the Milky Way in Action Space with LAMOST DR8 and GAIA EDR3." pith.science (2026). https://pith.science/paper/INS4APQ5

@misc{pith2026250208164,
  author       = {Pith},
  title        = {Pith review of: Dynamical Models of the Milky Way in Action Space with LAMOST DR8 and GAIA EDR3},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/INS4APQ5}},
  note         = {Machine review of arXiv:2502.08164}
}
abstract

This work explores dynamical models of the Milky Way (MW) by analyzing a sample of 86,109 K giant stars selected through cross-matching the LAMOST DR8 and Gaia EDR3 surveys. Our earlier torus models in Wang et al. (2017) did not include Gaia data, making them incompatible with the new proper motion distributions of samples. Here, we refine the construction of action-based, self-consistent models to constrain the three-dimensional velocity distribution of K giants over a larger parameter space, drawing on a series of existing MW models. This approach produces several new MW models. Our best-fit model for the local kinematics near the Sun indicates a MW virial mass of 1.35 $\times 10^{12} M_\odot$, a local stellar density of 0.0696 $\rm M_\odot pc^{-3}$, and a local dark matter density of 0.0115 $\rm M_\odot pc^{-3}$. Our main conclusion supports a thicker and more extended thick disk, alongside a cooler thin disk, compared to the best-fitting model in Wang et al. (2017). Near the Sun, our model aligns well with observations, but is less satisfactory at distances far from the Galactic center, perhaps implying unidentified structures. Further high-precision observations will be critical for understanding the dynamics in these outer Galactic regions, and will require a more realistic model.

Figures

Figures reproduced from arXiv: 2502.08164 by the authors.

Figure 1
Figure 1. The projected distribution in the x-y plane (upper left), x-z plane (lower left), VR-Vϕ plane (upper right), and VR-VZ plane (lower right) for all 607,833 K giants in our sample. The red stars in the left panels indicate the position of the Sun. The color map￾ping represents the observed density of K giants, calculated using the kernel-density estimation method with Gaussian kernels. It is important to note that thi… view at source ↗
Figure 3
Figure 3. The selected sky regions. The figure is similar to Fig￾ure 1 in Wang et al. (2017). The labels denote the region identifier. Following the symbol ‘#’ is the number of K giants in the region. Regions 01–16 encompass giants within 2 kpc from the Sun. Re￾gions 17, 18, 19, and 20 cover the same directions as 06, 07, 10, and 11, respectively, but extend to a depth of 2–3 kpc . Regions 21, 22, 23, and 24 cover a 20◦×, 20◦… view at source ↗
Figure 2
Figure 2. The comparison between photometric distance (DCarlin) and parallax distance (Dϖ) within the specified range reveals in￾teresting trends. In the direction of the Galactic anticenter (up￾per panel), we observe DCarlin/Dϖ=0.86, incorporating approx￾imately 160,000 high-precision parallax measurements for K gi￾ants. Conversely, toward the north Galactic pole, this ratio is DCarlin/Dϖ=0.97, based on observations of appro… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Flowchart for constructing the best-fitting dynamical model. The left and bottom parts are the scheme for our calculating [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: The distribution of recognized orbital eccentricities for 531,521 disk K giants. The horizontal axis represents the eccentric￾ity values, while the vertical axis indicates the corresponding count of giants. representation of the galaxy’s mass distribution within the ΛC…
Figure 6
Figure 6. Figure 6: The mass distribution at different stages of the iteration process for the model is depicted. Various colors denote different stages of iteration, showcasing the mass distribution from the initial to the final iteration. ‘ini’ represents the model constructed with the …
Figure 8
Figure 8. Figure 8: The probability distribution function of proper motion along the right ascension (µα) for sky regions 01-16, as defined in [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: The probability distribution function of the line-of-sight velocity (vLOS) for sky regions 17-20, as defined in [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: The probability distribution function of proper motion in the declination direction (µδ) for sky regions 21-24, as defined in [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: The right ascension direction proper motion (µα) prob￾ability distribution function for sky regions 25 and 26, as defined in [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: The probability distribution function of proper motion in the declination direction (µδ) for sky regions 27-30, as defined in [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 14
Figure 14. Figure 14: Similar to [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 15
Figure 15. Figure 15: From left to right, the radial distributions of the velocity dispersions σR, σz, and σϕ are presented. The color scheme is consistent with that used in [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: Surface density distribution of disk stars for differ￾ent models. The red, blue and green lines are the results for ‘Mc17a’,‘Ca20d’ and ‘Ca20e’ models, respectively. 86,109 K-type giant stars. The combination of observational data from LAMOST DR8 and Gaia EDR3 provide…
Figure 18
Figure 18. Figure 18: Mean steaming velocities of the thick (solid lines) and the thin disk (dashed lines) in the mid-plane for different Models. cannot be entirely ruled out. Additionally, the thin disk is generally found to be thinner and cooler (smaller σz0,thin). (iv) Our best-fitting …

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