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REVIEW 4 major objections 6 minor 52 references

Variable gravitational potential of Milky Way analogues in HESTIA suite

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Local Group mass shapes the Milky Way's potential beyond 100 kpc, and ignoring it introduces over 20 percent quadrupole errors.

desk verdict Main claim—environment matters for MW-like potentials beyond ~100 kpc—holds up across all 14 realizations; the abstract overclaims both the 20% quadrupole figure and the universality of the growth trend. read the letter →

arxiv 2412.18880 v2 pith:EXBB7MA4 submitted 2024-12-25 astro-ph.GA astro-ph.CO

Naira R. Arakelyan , Sergey V. Pilipenko , Stefan Gottlöber , Noam I. Libeskind , Gustavo Yepes , Yehuda Hoffman This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords MilkyWaypotentialsphericalharmonicsLocalGroupenvironmentconstrainedsimulationsdarkmatterhalosatelliteorbitsgravitational
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

This paper argues that the Milky Way's gravitational potential is not an isolated, static object out to large radii: at 100 kpc and beyond, the non-spherical part of the potential is measurably shaped by the Local Group environment. The authors analyze the spherical-harmonic expansion of the potential in fourteen constrained simulations of Milky Way analogues over the last six billion years. They find that truncating the mass distribution at the virial radius produces errors greater than 20 percent in the potential quadrupole at these distances, and that including the environment changes the angular momenta of test particles on 100–150 kpc orbits. If the result transfers to the real Galaxy, accurate models of the Galactic potential used to interpret Gaia-era orbits of streams and satellites must include M31 and other Local Group galaxies as time-dependent contributors.

What carries the argument

The central object is the multipole expansion of the gravitational potential, $\Phi(r,\theta,\varphi) = \sum_{\ell,m} a_{\ell m}(r) Y_{\ell m}(\theta,\varphi)$, with coefficients computed from the simulated particle distribution. The orientation-independent amplitude $c_\ell^2 = \sum_m a_{\ell m}^2$ isolates the degree of non-sphericity. The argument works by comparing expansions with a maximum radius $r_{\mathrm{max}} = r_{\mathrm{vir}}$ against expansions with $r_{\mathrm{max}} = 3$ Mpc, and by cross-correlating the full potential's harmonics with harmonics of nearby galaxies and satellites treated as point masses. This machinery turns a particle distribution into a time-dependent, radially resolved description of the potential shape, making the environmental contribution quantifiable.

What would settle it

Measure the quadrupole of the real Milky Way potential at 100–500 kpc using outer-halo tracers such as the Sagittarius stream or distant halo stars; if the non-sphericity does not grow with distance beyond the virial radius, or if the quadrupole is fully explained by mass inside $r_{\mathrm{vir}}$, the predicted environmental effect fails.

Watch

Extended reading notes

Core claim

In the paper's own terms, the central discovery is that the non-spherical part of the gravitational potential of Milky Way analogues at $r \ge 100$ kpc carries a clear environmental signature. The quadrupole amplitude does not converge when the expansion is limited to matter within the virial radius; extending the expansion to about 1 Mpc changes the harmonic amplitudes by more than 20 percent at $r \approx 150$ kpc. The same environmental mass drives the time evolution of the harmonics at $r \ge 30$ kpc: the correlation between the full particle potential and a potential reconstructed from nearby galaxies as point masses reaches $\xi \approx 0.77$–$0.87$, while using only satellites inside the virial radius gives much weaker or no significant correlation. Nearly all realizations show non-sphericity growing monotonically with radius between roughly 200 and 700 kpc, which leads the authors to predict that the real Milky Way's potential becomes increasingly non-spherical from the virial radius out to about 500 kpc.

Load-bearing premise

The constrained simulations faithfully reproduce the real Milky Way's Local Group environment, so that the trends seen across the fourteen realizations, such as the growth of non-sphericity with radius beyond the virial radius, apply to the actual Galaxy.

Editorial extensions

If this is right

  • Static, isolated Milky Way potential models will mispredict orbits whose apocenters lie at or beyond 100 kpc.
  • Adding the Large Magellanic Cloud alone is not enough: Local Group galaxies must be included to keep quadrupole errors below roughly 20 percent at 150 kpc.
  • The non-sphericity of the real Milky Way potential is expected to grow with distance in the range $r_{\mathrm{vir}} < r < 500$ kpc.
  • The potential harmonics vary on timescales from about 0.2 Gyr to several Gyr, so time-dependent models are needed for accurate orbit reconstruction.

Reading between the lines

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

  • If the environmental effect is real, orbit fits of distant stellar streams and satellite galaxies should improve when a Local Group perturbation is added to a standard Milky Way model; that is a testable prediction for Gaia data.
  • The same logic should apply to Andromeda: its outer potential is probably shaped by the Milky Way, so models of M31 satellites may need an analogous environmental term.
  • A practical route suggested by the paper is to use observed Local Group galaxy positions and masses to build a time-dependent perturbation on top of an axisymmetric Milky Way model, then check whether known stream orbits become more consistent.
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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

4 major / 6 minor

Summary. The paper uses 14 constrained hydrodynamical simulations of Local Group analogues from the HESTIA suite to study the spherical-harmonic expansion of the gravitational potential of Milky Way analogues. It computes a_lm coefficients with AGAMA over the last 6 Gyr, tests convergence in resolution and snapshot cadence, and examines the role of mass outside the virial radius by comparing expansions truncated at rvir with those extending to 3 Mpc. The authors report that the environment significantly affects the quadrupole at r >= 100 kpc, with >20% errors if mass outside rvir is ignored, that including the environment changes test-particle angular momenta at 100-150 kpc, that the harmonics vary strongly over 6 Gyr, and that the non-sphericity grows with radius in the range rvir < r < 500 kpc in the simulated analogues, which they extrapolate to the real Milky Way.

Significance. If established, the main result is important: it implies that accurate dynamical modeling of streams and satellites at 100-150 kpc requires including the Local Group galaxies and other external mass, not just the MW halo and LMC. The paper's strengths are the use of constrained simulations of the real LG environment, the explicit convergence tests in Appendix C, the systematic lmax/rmax checks, and the public release of the multipole coefficients. The main caveats are that the quantitative headline statements are currently based on a subset of realizations and that the analytic point-mass estimate in Appendix A contains an error; these need to be addressed before the claims can be accepted at face value.

major comments (4)
  1. [Abstract and Appendix A (Fig. 6)] The abstract's statement that 'ignoring the mass distribution outside the virial radius of the MW results in >20% errors in the potential quadrupole at these distances' is supported only by Fig. 6, which is explicitly for one realization (09 18). No multi-realization distribution of the rmax-truncation error is shown, so the unconditional wording in the abstract overstates the evidence. Please provide the same rmax-vs-rvir comparison for all 14 realizations, or preferably a histogram of the quadrupole error at r = 100-150 kpc, and adjust the abstract and conclusions to the actual fraction.
  2. [Abstract and Appendix B (Fig. 8)] The abstract claims that 'all realizations of simulated MW-like objects' show growing non-sphericity in rvir < r < 500 kpc, but Appendix B states that the rise 'is seen for almost all the realizations' and that there are exceptions when a large infalling satellite is near the virial radius. Because the prediction for the real Milky Way rests on this universality, the paper should quantify the fraction of realizations that exhibit the growth, define the criterion used to identify it, and discuss how the exceptions affect the forward prediction.
  3. [Appendix A, Eq. (A1)] Equation (A1) states c_l ∝ M r^l / d^{2l+2} for the multipole coefficients of a point mass at distance d. Since a_lm are potential coefficients in Eq. (1), the correct scaling for an external point mass is c_l ∝ M r^l / d^{l+1}. Moreover, with the values used in the text (M_M31 = 2e12 Msun at 750 kpc; M_LMC = 2e11 Msun at 50 kpc), the claim that the M31-like mass dominates for l = 1 at r > 140 kpc is not reproduced by either scaling; the LMC-like mass remains much larger at all r < 750 kpc. This analytic estimate therefore does not support the 'LG comparable to LMC' motivation, and the rmax > 1 Mpc choice should be justified from the simulation results in Fig. 6 rather than from Eq. (A1).
  4. [Section IV, Fig. 2] The text states that 'in all the realizations the addition of the environment makes the difference of the angular momentum larger' for 100 and 150 kpc, but Fig. 2 shows only the mean and 10-90% scatter over realizations. Please provide per-realization values, for example the median or mean of |ΔL|/|L_init| for rmax = 3 Mpc and rmax = rvir, so the reader can verify the claimed universality.
minor comments (6)
  1. [References] References [40] and [41] are identical; [41] should be replaced with the correct source for the description of the 13 realizations.
  2. [Throughout] There are several typographical errors: 'wether' in Section IV should be 'whether', 'the the angular momenta' in Section IV should be 'the angular momenta', and 'fictious' should be 'fictitious'.
  3. [Fig. 8 caption] The caption says 'color shades' but the figure likely uses line styles or colors to distinguish the 14 realizations; please clarify the legend or line coding.
  4. [Ref. [44]] The GitHub URL in Ref. [44] contains 'HESITA' instead of 'HESTIA'.
  5. [Section III A] The choice rmin = 5 kpc while analyzing r >= 10 kpc could be clarified: including particles between 5 and 10 kpc affects the potential at 10 kpc, but the sentence as written is confusing.
  6. [Eq. (3)] The averaging in the correlation coefficient ξ is not explicitly defined; please state that it is over snapshots and realizations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's claims are direct measurements from HESTIA simulations, not derivations from fitted parameters or self-citation chains.

full rationale

The central results are obtained by directly expanding simulated particle distributions into spherical harmonics with AGAMA and comparing truncations at rmax=rvir versus rmax=3 Mpc. The '>20%' quadrupole error is read from Fig. 6 as a measured difference between a converged value and the value at rmax=rvir; this is a controlled numerical experiment, not a fitted input renamed as a prediction. The reconstruction attempt with a_model = A*a_gal in Eq. (4) fits a constant A, but the paper uses it only to show that the linear model fails (Q never drops below 0.45), so no successful prediction is being manufactured from that fit. The HESTIA and AGAMA citations, including co-authored HESTIA papers, are used as provenance for the simulation suite and the numerical tool; they are not invoked as an unverified uniqueness theorem or as a premise that already contains the target claim. The abstract's 'all realizations' phrasing is stronger than the text's 'almost all the realizations' in Appendix B, and the headline quadrupole error is shown for one realization in Appendix A; these are concerns about statistical support and generalization, not about circularity, because the measurements themselves are not equivalent to their inputs by construction. No step in the derivation chain reduces to the paper's own definitions or to a self-citation in the sense forbidden by the circularity criteria.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the fidelity of the HESTIA constrained simulations and the convergence of the AGAMA multipole expansion. No new physical entities are introduced; the free parameters are numerical choices with convergence justifications.

free parameters (3)
  • rmax (maximum radius for potential expansion) = 3 Mpc
    Chosen from convergence tests (Appendix A). The central claim that environment matters depends on using rmax well beyond the virial radius; this is a modeling choice supported by convergence, not a fit to the target result.
  • lmax (spherical harmonic truncation) = 4
    Chosen based on Sanders et al. 2020 and verified by comparing with lmax=8, giving <5% difference in angular momentum. Numerical setting, not fitted to a target.
  • A (amplitude in galaxy-based potential reconstruction) = varied 0.5 to 3.0
    Scaling constant in Eq. (4) used to test whether galaxy positions can reconstruct the full potential. It is fitted but the result is negative (Q stays above 0.45), so it does not support any positive claim.
assumptions (4)
  • domain assumption Lambda-CDM cosmology with Planck parameters
    The HESTIA simulations are run within this cosmological model; all results are contingent on it. Invoked in Section II.
  • domain assumption HESTIA constrained initial conditions reproduce the real Local Group environment
    The paper relies on this to extrapolate trends from 14 realizations to the real Milky Way, citing Libeskind et al. 2020. Stated in Section II.
  • domain assumption AGAMA multipole expansion with lmax=4, n=40, rmax=3 Mpc converges to the true potential
    The analysis uses AGAMA's potential constructor; convergence is tested in Appendices A and C, but the adequacy of the expansion is an assumption.
  • standard math Spherical harmonics expansion and Poisson equation are valid standard mathematics
    Used without proof as the basis for the potential expansion in Section III A.

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Cite this review

Pith. "Pith review of Variable gravitational potential of Milky Way analogues in HESTIA suite." pith.science (2026). https://pith.science/paper/EXBB7MA4

@misc{pith2026241218880,
  author       = {Pith},
  title        = {Pith review of: Variable gravitational potential of Milky Way analogues in HESTIA suite},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EXBB7MA4}},
  note         = {Machine review of arXiv:2412.18880}
}
abstract

Investigations of trajectories of various objects orbiting the Milky Way (MW) halo with modern precision, achievable in observations by Gaia, requires sophisticated, non-stationary models of the Galactic potential. In this paper we analyze the evolution of the spherical harmonics expansion of MW analogues potential in constrained simulations of the Local Group (LG) from the HESTIA suite. We find that at distances $r\ge 100$~kpc the non-spherical part of the potential demonstrates a significant impact of the environment: ignoring the mass distribution outside the virial radius of the MW results in $>$20\% errors in the potential quadrupole at these distances. {Account of the environment results in a noticeable change of the angular momenta of objects orbiting MW analogues}. Spherical harmonics vary significantly during the last 6 Gyr. We attribute variations of the potential at $r\ge 30$~kpc to the motions of MW satellites and LG galaxies. We also predict that the non-sphericity of the real MW potential should grow with distance in the range $r_\mathrm{vir}<r<500$~kpc, since all realizations of simulated MW-like objects demonstrate such a trend.

Figures

Figures reproduced from arXiv: 2412.18880 by the authors.

Figure 1
Figure 1. FIG. 1. Amplitudes of spherical harmonics as a function of time along four radii. Colors from dark to light correspond to radii [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Distribution of the change in test particle angular momentum after 6 Gyr of evolution for three initial radii (50, 100 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Impact of MW satellite galaxies and LG galaxies on the evolution of the potential harmonics [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Ratio of the total mass in simulation particles to the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Positions of M31 analogs in 14 LG realizations (cir [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Amplitude of spherical harmonics for the realization 09 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Left panel: Contributions to harmonics with [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Coefficients [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Expansion coefficients [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Potential expansion coefficients [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Potential expansion coefficients [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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