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arxiv: 2605.04633 · v2 · pith:QX6MHQ57new · submitted 2026-05-06 · 🌌 astro-ph.GA

A spectroscopic map of the Galactic centre: Integrated light and dynamical modelling

A. Feldmeier-Krause , T. I. Maindl , G. van de Ven , S. Thater , P. Jethwa , I. Breda This is my paper

Pith reviewed 2026-05-08 17:37 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords Galactic centrenuclear star clustersupermassive black holedynamical modellingorbit-based modellingstellar kinematicsintegrated light
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The pith

Triaxial orbit modelling of integrated-light kinematic maps recovers the mass of the Milky Way's central black hole.

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

The paper tests whether dynamical modelling techniques developed for external galaxies can be applied to the centre of the Milky Way using only integrated light observations. By extracting stellar line-of-sight velocity maps across a wide region around the nuclear star cluster and supermassive black hole Sgr A*, the authors fit an orbit library in a triaxial potential. This approach recovers the known mass of Sgr A* and produces stellar mass distributions consistent with earlier work based on individual stars, though with larger uncertainties. The modelling reveals that inner stellar orbits are mostly warm or hot while outer ones are colder and more rotationally supported.

Core claim

We recover the correct mass of Sgr A*, and our stellar mass distributions are in agreement with the literature, albeit with larger uncertainties. The stellar structures are at most mildly triaxial and close to oblate. The stellar orbit distribution in the inner region is dominated by dynamically warm and hot orbits. At larger scales, dynamically cold, that is, highly rotating orbits, have the largest weights.

What carries the argument

The DYNAMITE code, which calculates an orbit library in a given gravitational potential and computes model kinematic maps that are compared to observed line-of-sight velocity maps to constrain the potential and orbit distribution.

Load-bearing premise

The gravitational potential is assumed to be time-independent and the observed kinematics can be reproduced by a steady-state orbit library in a triaxial potential.

What would settle it

An independent high-precision measurement of the mass within the inner few parsecs that deviates significantly from the modelled black hole plus stellar mass profile would challenge the results.

Figures

Figures reproduced from arXiv: 2605.04633 by A. Feldmeier-Krause, G. van de Ven, I. Breda, P. Jethwa, S. Thater, T. I. Maindl.

Figure 1
Figure 1. Figure 1: Spatial coverage of our F2 spectroscopic data. The data extend ∼66 pc along the Galactic longitude l, centred on Sgr A⋆ (marked as a red plus symbol), and ∼1 pc to the Galactic north and south, except for the centre region, which extends further to the Galactic north (∼2 pc). The image was constructed from the spectroscopic scans. We show the Galactic coordinate grid as dashed lines. stars with H − KS ≤ 1.… view at source ↗
Figure 2
Figure 2. Figure 2: Example of a stellar kinematic fit with ppxf. The black line shows the data, the red line the best-fit stellar model, and the orange and pink lines the best-fit gas emission. Green symbols denote residuals; the grey shaded regions were masked in the fit due to sky residuals or bad pixels. spatial information. A lower target S/N produces a finer spatial binning, but at the cost of noisier kinematic maps. We… view at source ↗
Figure 3
Figure 3. Figure 3: Stellar kinematic maps (left) after symmetrisation and their respective uncertainties (right). The plots show, from top to bottom, VLOS, σLOS, h3, and h4. rameters qmin, pmin, umin, and Υ thus describe the stellar gravita￾tional potential. 3.1.3. Dark matter In a subset of models, we included a spherical DM compo￾nent. The DM distribution is parameterised with a Navarro￾Frenk-White (NFW Navarro et al. 1996… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of observations (left in rotated image), the best-fit model (middle, no DM), and the residuals (right). The rows show, from top to bottom: stellar flux, VLOS, σLOS, h3, and h4. Article number, page 6 of 16 view at source ↗
Figure 5
Figure 5. Figure 5: Intrinsic shape parameters and triaxiality as a function of radius r. The black lines denote q = c/a, blue lines p = b/a, and red lines triaxiality T = (1 − p 2 )/(1 − q 2 ). Solid lines denote the best-fit model parameters, the dashed coloured lines their 1σ uncertainties. The verti￾cal solid line denotes 1 Re of the NSC, the dotted line the outer limit of the kinematic data. Horizontal lines mark steps of 0.1 view at source ↗
Figure 6
Figure 6. Figure 6: Total enclosed mass as a function of spherical deprojected radius. Shaded regions show 1σ uncertainties. The vertical solid line denotes 1 Re of the NSC, the dotted line the outer limit of the kinematic data. without DM. This is because the best-fit DM mass is more than five orders of magnitude lower than the total mass. For compar￾ison, we also show the stellar mass profiles from other studies, and we wil… view at source ↗
Figure 7
Figure 7. Figure 7: Orbit circularity distribution of λz as a function of mean orbital radius r, computed using over >800 models within 1σ. Colour indicates the orbit density in the phase space, horizontal dashed lines divide the orbits into cold (λz>0.8), warm (0.25<λz ≤0.8), hot (−0.25<λz ≤0.25), counter-rotating warm (–0.8<λz ≤ −0.2), and counter-rotating cold (λz ≤-0.8) orbits, vertical lines are as in view at source ↗
Figure 8
Figure 8. Figure 8: Relative orbit weight profile as function of mean orbital radius r, computed from the λz distribution in view at source ↗
Figure 9
Figure 9. Figure 9: Orbit decomposition of the best-fit model in cold, warm, counter￾rotating (cr) cold, cr warm, hot, and all orbits. The rows show, from left to right: stellar surface brightness, VLOS, σLOS. Feldmeier-Krause et al. (2017b) are limited to l ≲ 6 pc. The mod￾els of Sormani et al. (2022) are focused on the more extended NSD. At l ≲ 20 pc, their sample is rather small, as their data lies mostly at larger distanc… view at source ↗
read the original abstract

The centre of the Milky Way is occupied by a nuclear star cluster that contains the supermassive black hole Sgr A*. The cluster is embedded in the larger surrounding nuclear stellar disc. These three components dominate the mass budget of the Galactic centre at different radial scales. The mass distribution of the Galactic centre has been studied extensively using observations of individual bright stars and various dynamical modelling approaches. The situation differs for external galaxies, where observations are often limited to the integrated line-of-sight kinematics. For such systems, triaxial orbit-based dynamical modelling has become a standard method of deriving mass distributions and stellar orbit distributions. We aim to apply and test this method on the Galactic centre. We extracted stellar line-of-sight kinematic maps of the inner ~3 pc x 66 pc region of the Galactic centre. We used the DYNAMITE code, which calculates an orbit library in a given gravitational potential and computes model kinematic maps. These maps were then compared to the observed kinematic maps, and the gravitational potential and orbit distribution of the Galactic centre were constrained. We recover the correct mass of Sgr A*, and our stellar mass distributions are in agreement with the literature, albeit with larger uncertainties. The stellar structures are at most mildly triaxial and close to oblate. The stellar orbit distribution in the inner region is dominated by dynamically warm and hot orbits. At larger scales, dynamically cold -- highly rotating -- orbits have the largest weights. The dominance of hot and warm orbits is a consequence of short dynamical timescales in the inner Galactic centre, causing dynamical heating. The presence of cold orbits at large radii may be explained by the longer heating timescales in this region, and by the stars in the outer nuclear stellar disc being younger.[abridged]

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

2 major / 2 minor

Summary. The paper extracts stellar line-of-sight kinematic maps over the inner ~3 pc × 66 pc of the Galactic centre and applies the DYNAMITE triaxial orbit-superposition code to fit a gravitational potential (including Sgr A* mass) and orbit weights to the observed maps. It reports recovering the accepted Sgr A* mass, obtaining stellar mass profiles consistent with the literature (with larger uncertainties), finding the stellar structures to be at most mildly triaxial and near-oblate, and showing that hot/warm orbits dominate inside ~few pc while cold, rotating orbits gain weight at larger radii, which the authors attribute to local dynamical timescales.

Significance. If the results hold, the work provides a useful end-to-end validation of integrated-light triaxial orbit modelling on a system where independent constraints from individual stars exist. Successful recovery of the known Sgr A* mass and consistency of the stellar mass distribution (despite the expected increase in uncertainty) supports the reliability of the method for external galaxies. The orbit-type analysis and explicit discussion of dynamical heating timescales add physical context that is directly testable in the Milky Way.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (modelling results): the central claim that the recovered Sgr A* mass 'matches the known value' and stellar masses 'agree with the literature' is presented without any reported goodness-of-fit statistic (e.g., reduced χ², residual maps, or posterior widths), parameter uncertainties, or mock-data recovery tests. This information is load-bearing for assessing whether the modelling actually constrains the potential or merely reproduces the data by construction.
  2. [§3–4] §3–4 (orbit library and potential): the modelling assumes a time-independent triaxial potential and a steady-state orbit library whose parameters are adjusted to fit the data. While standard, the short dynamical times in the inner region (explicitly mentioned in the abstract) require an explicit test that the recovered orbit distribution is not an artifact of the steady-state assumption; no such test is described.
minor comments (2)
  1. [Abstract] The abstract is labelled 'abridged'; the full version should retain the quantitative statements about mass recovery and uncertainties rather than deferring them entirely to the main text.
  2. [Figures] Figure captions and axis labels for the kinematic maps should explicitly state the spatial scale, velocity range, and whether the maps are luminosity-weighted or mass-weighted.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work and the recommendation for minor revision. We address each major comment below and will revise the manuscript to improve clarity and transparency.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (modelling results): the central claim that the recovered Sgr A* mass 'matches the known value' and stellar masses 'agree with the literature' is presented without any reported goodness-of-fit statistic (e.g., reduced χ², residual maps, or posterior widths), parameter uncertainties, or mock-data recovery tests. This information is load-bearing for assessing whether the modelling actually constrains the potential or merely reproduces the data by construction.

    Authors: We thank the referee for highlighting the need for greater transparency in the presentation of the modelling results. In the revised manuscript we will add the reduced χ² value of the best-fit model to §4, include residual maps comparing the observed and modelled kinematic maps, and explicitly report the posterior widths on the Sgr A* mass and the stellar mass parameters. We will also include a concise description of the mock-data recovery tests performed to validate that the modelling pipeline recovers the input potential parameters. revision: yes

  2. Referee: [§3–4] §3–4 (orbit library and potential): the modelling assumes a time-independent triaxial potential and a steady-state orbit library whose parameters are adjusted to fit the data. While standard, the short dynamical times in the inner region (explicitly mentioned in the abstract) require an explicit test that the recovered orbit distribution is not an artifact of the steady-state assumption; no such test is described.

    Authors: We agree that the short dynamical timescales in the inner Galactic centre make the steady-state assumption particularly relevant. The DYNAMITE modelling follows the standard orbit-superposition framework, which is time-independent by construction. In the revised §4 we will expand the discussion to explicitly address this point, explaining why the recovered orbit distribution is physically plausible given the expected dynamical heating on short timescales and the consistency of the mass recovery with independent constraints. We will also note the absence of a dedicated time-dependent test as a limitation of the present study. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper applies the established DYNAMITE code for triaxial orbit-based dynamical modeling: an orbit library is generated in a parameterized gravitational potential, model kinematic maps are computed, and the potential parameters plus orbit weights are adjusted to match the observed integrated-light kinematic maps. The reported recovery of the accepted Sgr A* mass and agreement (within larger uncertainties) of the stellar mass distribution with independent literature values are direct outputs of this fitting procedure, functioning as a validation test on a known system rather than a self-referential derivation. No self-definitional steps, fitted inputs relabeled as predictions, load-bearing self-citations, uniqueness theorems imported from the authors' prior work, or ansatzes smuggled via citation appear in the abstract or described method. The time-independent and steady-state assumptions are the standard ones for the technique and are discussed with reference to local dynamical times.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The modelling rests on a steady-state triaxial potential whose parameters (black-hole mass, stellar density profile, possible dark-matter component) are adjusted to match the data; the orbit library is generated from that potential and the weights are solved by non-negative least squares.

free parameters (2)
  • Sgr A* mass
    Fitted as part of the gravitational potential to reproduce the observed kinematics.
  • stellar density profile parameters
    Multiple parameters describing the nuclear star cluster and nuclear stellar disc are adjusted during the fit.
axioms (2)
  • domain assumption The system is in dynamical equilibrium and can be described by a time-independent gravitational potential.
    Standard assumption for orbit-superposition modelling; invoked when the orbit library is computed.
  • domain assumption The observed line-of-sight velocity distributions can be reproduced by a linear combination of orbits in the trial potential.
    Core premise of the DYNAMITE method.

pith-pipeline@v0.9.0 · 5646 in / 1476 out tokens · 38767 ms · 2026-05-08T17:37:05.962097+00:00 · methodology

discussion (0)

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