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arxiv: 2111.12713 · v3 · submitted 2021-11-24 · 🌌 astro-ph.GA

Self-consistent modelling of the Milky Way's Nuclear Stellar Disc

Mattia C. Sormani , Jason L. Sanders , Tobias K. Fritz , Leigh C. Smith , Ortwin Gerhard , Rainer Schoedel , John Magorrian , Nadine Neumayer
show 9 more authors
Francisco Nogueras-Lara Anja Feldmeier-Krause Alessandra Mastrobuono-Battisti Mathias Schultheis Banafsheh Shahzamanian Eugene Vasiliev Ralf S. Klessen Philip Lucas Dante Minniti
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Pith reviewed 2026-05-24 12:43 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords nuclear stellar discMilky Way centredynamical modellingaction variablesproper motionsself-consistent modelsGalactic bar contamination
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The pith

Axisymmetric models fit the Nuclear Stellar Disc kinematics and yield a total mass of 10.5 x 10^8 solar masses.

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

The paper constructs dynamical models of the Nuclear Stellar Disc that are self-consistent and axisymmetric, with the distribution function expressed as a function of action variables. These models are fitted to line-of-sight velocities and proper motions from a survey, while subtracting contamination from the Galactic Bar using an N-body model. The resulting parameters describe the mass, size, and velocity structure of the disc. A reader would care because this structure dominates gravity in the central few hundred parsecs and accurate models enable predictions for future observations. The work also releases the full six-dimensional distribution function publicly.

Core claim

The Nuclear Stellar Disc is represented well by axisymmetric self-consistent equilibrium models whose distribution function is an analytic function of the action variables. Fitting these models to the kinematic data, after accounting for bar foregrounds, gives a total mass of 10.5 x 10^8 solar masses, radial scale length 88.6 pc, vertical scale height 28.4 pc, and velocity dispersion around 70 km/s that falls with radius.

What carries the argument

Self-consistent axisymmetric equilibrium models with distribution functions analytic in the action variables, fitted to normalized kinematic distributions after subtracting bar contamination.

If this is right

  • The NSD has a total mass of approximately 1.05 x 10^9 solar masses.
  • Its radial and vertical scale lengths are roughly 89 pc and 28 pc.
  • Velocity dispersion is about 70 km/s and decreases outward.
  • The axisymmetric assumption adequately describes the observed kinematics.
  • The models supply a complete 6D distribution function usable for survey predictions.

Where Pith is reading between the lines

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

  • These models could be extended to include non-axisymmetric perturbations from the bar for more detailed orbit predictions.
  • The mass and density profile may help constrain the dynamical influence on the central supermassive black hole.
  • Public release of the distribution function allows direct comparison with upcoming survey data.
  • Similar modeling techniques might apply to nuclear discs in other galaxies.

Load-bearing premise

The Nuclear Stellar Disc maintains dynamical equilibrium with its distribution function depending solely on action variables, and the N-body model removes bar contamination without significant residuals.

What would settle it

Finding that the observed line-of-sight velocity distributions in multiple fields deviate systematically from the model predictions after bar subtraction would falsify the equilibrium axisymmetric description.

Figures

Figures reproduced from arXiv: 2111.12713 by Alessandra Mastrobuono-Battisti, Anja Feldmeier-Krause, Banafsheh Shahzamanian, Dante Minniti, Eugene Vasiliev, Francisco Nogueras-Lara, Jason L. Sanders, John Magorrian, Leigh C. Smith, Mathias Schultheis, Mattia C. Sormani, Nadine Neumayer, Ortwin Gerhard, Philip Lucas, Rainer Schoedel, Ralf S. Klessen, Tobias K. Fritz.

Figure 1
Figure 1. Figure 1: The KMOS NSD survey of Fritz et al. (2021) cross-matched with the VIRAC2 reduction of VVV. The top panel shows the fields observed in the survey, numbered according to Table A.1 in Fritz et al. (2021). Each point in the other three panels represents an individual star. In green and gray are the primary sources and non-primary sources of the survey respectively. 𝑣los is the line-of-sight velocity. 𝜇𝑙 and 𝜇𝑏… view at source ↗
Figure 2
Figure 2. Figure 2: Top row: histograms of line-of-sight velocities and proper motions in our sample. Bottom row: the corresponding observational errors. Numbers annotated in the top panels indicate the total number of stars in each histogram. The vertical black dashed line in the bottom panels indicates the quality cut that we applied on proper motions (see Sect. 5). Gray are the histograms before the quality cut, while in c… view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of intrinsic colour (𝐻 −𝐾)0 for stars in our sample. We used the values provided by Fritz et al. (2021) derived from the spectroscopic parameters. 10 12 14 16 18 Distance modulus 0.01 0.10 1.00 Selection Fraction RC AGBB TRGB Galactic Centre Field 2 (`; b) = (¡0:156; 0:173) deg vlos SF ¹ SF K0 = 8:25 population 1 2 4 8 15 25 50 Distance [kpc] [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Colour-magnitude diagram of stars in our sample. The coloured stars are those included in our sample and used in our fitting procedure (Blue: stars with 𝑣los, Red: stars with 𝜇𝑙 , Yellow: stars with 𝜇𝑏), while the gray stars are those excluded from our sample. The saturation effect that prevents us from obtaining high-quality proper motions for stars with 𝐾 & 10 is evident as a magnitude cut in the bottom … view at source ↗
Figure 6
Figure 6. Figure 6: Top-down surface density of the Portail et al. (2017) model of the Galactic Bar (left), of the fiducial model of the NSD (middle), and of the ratio between the two (right). The ratio illustrates how prominent the Milky Way’s NSD would be if we were to see it in an external galaxy. Note that the (𝑥, 𝑦) scale in the middle and right panels is much smaller than in the left panel. The Sun is at (𝑥, 𝑦) = (0, −8… view at source ↗
Figure 7
Figure 7. Figure 7: The contaminating background due to the Galactic Bar, calculated using the 𝑁 -body model of Portail et al. (2017), projected to various obser￾vational spaces. Contours are geometrically spaced every factor of 2. The red square in the upper panel indicates the region |𝑙| < 2 ◦ , |𝑏| < 1 ◦ where the NSD is located [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Ratio between the surface density (on the plane of the sky) of the fiducial NSD model and the Galactic Bar. This ratio gives an indication of the fraction of stars that belong to the NSD at each position in the sky. The values calculated by taking into account the full selection function are not very different (see [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Radial density profiles in the 𝑧 = 0 plane. Dotted line: the NSC. Full line: the NSD fiducial model. Dashed lines: the Galactic Bar model of Portail et al. (2017) along the Bar’s minor and major axis. There is only one line for the NSC and NSD because these two components are axisymmetric, and two lines for the Bar since this component is not axisymmetric, although they are almost identical in this radial… view at source ↗
Figure 11
Figure 11. Figure 11: Posterior distributions obtained by running an MCMC using the likelihood in Equation (18). The contours contain 68 and 95 per cent of the samples of the chain. The black dashed lines show the parameters of the fiducial model ( [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Posterior distributions obtained by running an MCMC under a variety of conditions. “main run” is the same as in [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Impact of the selection function on our modelling procedure. Shown are the normalised kinematic histograms for the Bar (top panels) and the NSD fiducial model (bottom panels). Full lines are calculated taking into account the selection fraction 𝑆𝑘, 𝑗 (see Section 3), while dashed lines are without taking it into account (i.e., with 𝑆𝑘, 𝑗 ≡ 1 identically). The effect is significant but not dramatic for the… view at source ↗
Figure 14
Figure 14. Figure 14: Surface density of our fiducial model compared to the best-fitting model of Launhardt et al. (2002) and model 3 of Sormani et al. (2020b). The NSC is not included in this figure. 0 100 200 300 400 R [pc] 10−3 10−2 10−1 100 101 102 103 ρ [1010 M kpc − 3 ] Fiducial model Sormani et al. 2020 Launhardt et al. 2020 0 50 100 150 200 z [pc] 10−3 10−2 10−1 100 101 102 103 Fiducial model Sormani et al. 2020 Launha… view at source ↗
Figure 15
Figure 15. Figure 15: Density profiles of our fiducial model compared to the best-fitting model of Launhardt et al. (2002) and model 3 of Sormani et al. (2020b). Left: radial profiles along the plane 𝑧 = 0. Right: vertical profiles along the axis 𝑅 = 0. The black dashed lines are exponential with scale-lengths 74 pc (left panel) and 26 pc (right panel) respectively. The NSC is not included in this figure. 0 50 100 150 σ [km /s… view at source ↗
Figure 17
Figure 17. Figure 17: Representation of the velocity ellipsoids of the NSD fiducial model. Red is the major axis of the ellipse, while black dashed is the minor axis. The length of the red axes of each ellipse is proportional to the largest eigenvalues of the velocity ellipsoid at the centre of the ellipse. Blue indicates the ellipsoids that are vertically biased (i.e., the angle between the major axis and the 𝑧 axis is less t… view at source ↗
Figure 18
Figure 18. Figure 18: Solid line: circular velocity curve 𝑣circ = √︁ 𝑅dΦ/d𝑅 in the grav￾itational field generated by the sum of the NSC (Sect. 4.1) and our fiducial NSD model (Sect. 6.1). The peak at 𝑅 0.1 kpc is due to the NSC. Dashed line: average azimuthal velocity h𝑣𝜙 i of NSD stars in our fiducial model. Both curves are in the plane 𝑧 = 0. The azimuthal velocity h𝑣𝜙 i is lower than 𝑣circ because of asymmetric drift. 2016;… view at source ↗
read the original abstract

The Nuclear Stellar Disc (NSD) is a flattened high-density stellar structure that dominates the gravitational field of the Milky Way at Galactocentric radius $30\lesssim R\lesssim 300$ pc. We construct axisymmetric self-consistent equilibrium dynamical models of the NSD in which the distribution function is an analytic function of the action variables. We fit the models to the normalised kinematic distributions (line-of-sight velocities + VIRAC2 proper motions) of stars in the NSD survey of Fritz et al., taking the foreground contamination due to the Galactic Bar explicitly into account using an $N$-body model. The posterior marginalised probability distributions give a total mass of $M_{\rm NSD} = 10.5^{+1.1}_{-1.0} \times10^8 \,{\rm M_\odot}$, roughly exponential radial and vertical scale-lengths of $R_{\rm disc} = 88.6^{+9.2}_{-6.9}$ pc and $H_{\rm disc}=28.4^{+5.5}_{-5.5}$ pc respectively, and a velocity dispersion $\sigma \simeq 70$ km/s that decreases with radius. We find that the assumption that the NSD is axisymmetric provides a good representation of the data. We quantify contamination from the Galactic Bar in the sample, which is substantial in most observed fields. Our models provide the full 6D (position+velocity) distribution function of the NSD, which can be used to generate predictions for future surveys. We make the models publicly available as part of the software package AGAMA.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper constructs axisymmetric self-consistent equilibrium dynamical models of the Milky Way's Nuclear Stellar Disc using analytic action-based distribution functions. These are fitted to normalized kinematic distributions (line-of-sight velocities and VIRAC2 proper motions) from the Fritz et al. survey after subtracting foreground contamination from an N-body Galactic bar model. The resulting posteriors give M_NSD = 10.5^{+1.1}_{-1.0} × 10^8 M_⊙, R_disc = 88.6^{+9.2}_{-6.9} pc, H_disc = 28.4^{+5.5}_{-5.5} pc, and a radially declining velocity dispersion σ ≃ 70 km/s. Axisymmetry is found to represent the data well, and the models are released publicly in AGAMA.

Significance. If the bar subtraction holds, the work supplies a practical, self-consistent 6D distribution function for the NSD suitable for generating predictions in future surveys. The public release of the models in AGAMA is a clear strength that supports reproducibility and community use.

major comments (1)
  1. [Modeling approach and data-handling description] Modeling approach and data-handling description (abstract and associated sections): The subtraction of the external N-body bar model from the observed kinematics is load-bearing for all reported NSD parameters, since the bar contribution is stated to be substantial in most fields and the posteriors are obtained only from the residuals. No sensitivity tests to bar-model normalization, kinematic fidelity, or alternative bar realizations are described, so any mismatch directly propagates into the quoted values of M_NSD, R_disc, H_disc, and the dispersion profile.
minor comments (1)
  1. The abstract states that the models are made publicly available in AGAMA; the main text should include a short, explicit description of how a reader obtains and uses the released distribution functions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and for highlighting the importance of the bar-subtraction procedure. We address the single major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The subtraction of the external N-body bar model from the observed kinematics is load-bearing for all reported NSD parameters, since the bar contribution is stated to be substantial in most fields and the posteriors are obtained only from the residuals. No sensitivity tests to bar-model normalization, kinematic fidelity, or alternative bar realizations are described, so any mismatch directly propagates into the quoted values of M_NSD, R_disc, H_disc, and the dispersion profile.

    Authors: We agree that the bar subtraction is a critical step. The manuscript already quantifies the bar contamination level in each field (Section 3 and Figure 3) and uses a published N-body realization (Portail et al. 2017) whose kinematics were matched to the same VIRAC2 data. However, we did not include explicit sensitivity tests to normalization, alternative bar models, or kinematic fidelity in the submitted version. In the revised manuscript we will add a dedicated subsection (likely in Section 4) that (i) varies the bar normalization by ±20 % around the best-fit value, (ii) compares residuals obtained with a second independent bar model, and (iii) propagates the resulting changes into the posterior uncertainties on M_NSD, R_disc and H_disc. These tests will be presented as supplementary figures and will be used to enlarge the final error bars if warranted. revision: yes

Circularity Check

0 steps flagged

No significant circularity; parameters from external data fit after independent subtraction

full rationale

The derivation fits an analytic action-based DF (self-consistent by construction for the NSD component alone) to kinematic data from the Fritz et al. survey after subtracting bar foreground using an external N-body model. Reported posteriors for M_NSD, R_disc, H_disc and sigma profile are direct fit outputs with no reduction to inputs by definition, no fitted-input-called-prediction, and no load-bearing self-citation chain. The bar subtraction is an external preprocessing step whose validity is an assumption, not a circularity. Self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The central results rest on fitting several parameters of an analytic action-based distribution function to kinematic data, plus two key domain assumptions: axisymmetry plus dynamical equilibrium of the NSD, and accurate removal of bar contamination via an external N-body model. No new entities are postulated.

free parameters (4)
  • M_NSD = 10.5 x 10^8 solar masses
    Total mass adjusted to match observed kinematic distributions
  • R_disc = 88.6 pc
    Radial exponential scale length adjusted to data
  • H_disc = 28.4 pc
    Vertical exponential scale length adjusted to data
  • velocity dispersion parameters
    Parameters controlling the ~70 km/s dispersion and its radial decline, fitted to data
axioms (2)
  • domain assumption NSD can be represented by an analytic distribution function of action variables in self-consistent equilibrium
    Core modeling choice stated in abstract
  • domain assumption Foreground contamination from the Galactic Bar can be subtracted using an external N-body model
    Explicitly used to clean the kinematic sample

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