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arxiv: 2605.16994 · v1 · pith:53ZZCU56new · submitted 2026-05-16 · 🌌 astro-ph.GA · astro-ph.CO

Determination of the best dark matter profile for the Milky Way with Gaia DR3 using Bayesian Model Comparison

Aryan Singh , Shantanu Desai This is my paper

Pith reviewed 2026-05-19 20:16 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords Milky Waydark matter profilesrotation curveBayesian model comparisonEinasto profileNFW profileGaia DR3MOND
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The pith

Bayesian comparison of Gaia rotation curves favors the Einasto dark matter profile over NFW.

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

The paper performs a Bayesian model comparison to identify which dark matter density profile best describes the Milky Way rotation curve using four recent Gaia DR3 compilations. It evaluates seven dark matter profiles paired with three different baryonic models for the visible matter. The Einasto profile emerges as the preferred fit over the NFW profile in most dataset and model combinations. Cored profiles generally outperform the cuspy NFW profile. MOND models with three interpolating functions fit worse than the leading dark matter options, and the different baryonic models show no decisive differences among themselves.

Core claim

Within the adopted modeling framework and Gaia-based rotation curve datasets, the Einasto profile provides the preferred phenomenological fit compared to the NFW profile across most combinations of datasets and baryonic models. We also find that the cored dark profiles are preferred over the (cuspy) NFW profile. MOND models provide poorer fits than the preferred dark matter profiles. Finally, among the different baryonic models considered, none is decisively favored over the others.

What carries the argument

Bayesian model comparison applied to Gaia DR3 rotation curve compilations, testing seven dark matter density profiles against three baryonic models.

Load-bearing premise

The compiled rotation curve velocities accurately trace the circular velocity field without substantial contamination from non-circular motions, streaming, or distance errors, and the chosen baryonic models correctly capture the visible matter contribution without large systematic offsets.

What would settle it

New rotation curve data that requires a steep central density cusp matching NFW but inconsistent with Einasto or cored profiles would undermine the reported preference for those alternatives.

read the original abstract

We carry out a Bayesian model comparison analysis to determine the dark matter model that best describes the Milky Way rotation curve, using four recent compilations of rotation-curve velocities with the Gaia data. We compare these data using three different baryonic models along with seven different dark matter models. Within the adopted modeling framework and Gaia-based rotation curve datasets, we find that the Einasto profile provides the preferred phenomenological fit compared to the NFW profile} across most combinations of datasets and baryonic models. We also find that the cored dark profiles are preferred over the (cuspy) NFW profile. We also test MOND using three different interpolating functions and find that, within the implementations considered, the models provide poorer fits than the preferred dark matter profiles. Finally, among the different baryonic models considered, none is decisively favored over the others.

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 manuscript performs a Bayesian model comparison of seven dark matter density profiles (including NFW, Einasto, and several cored variants) against four Gaia DR3-based Milky Way rotation-curve compilations, using three different baryonic models. It reports that the Einasto profile is preferred over NFW across most dataset/baryonic combinations, that cored profiles are favored over cuspy NFW, that MOND implementations yield poorer fits, and that none of the baryonic models is decisively preferred.

Significance. If the central modeling assumptions hold, the work supplies a systematic, multi-dataset ranking of phenomenological halo profiles that can inform both N-body simulations and indirect-detection forecasts. The explicit inclusion of MOND as a comparator and the use of several independent rotation-curve compilations are positive features that increase the robustness of the model-selection exercise.

major comments (2)
  1. [§3] §3 (Data compilation and likelihood): The analysis treats the compiled rotation-curve velocities as faithful tracers of the circular-speed field. No quantitative assessment of possible radius-dependent biases from non-circular motions, streaming, or distance-scale systematics is presented, nor is a covariance matrix for the velocity uncertainties included in the likelihood. Because such systematics can shift the evidence ratios between cuspy and cored profiles, this assumption is load-bearing for the reported ranking.
  2. [§4.2] §4.2 (Prior specification): The priors on the halo scale parameters (rs, ρ0) and on the baryonic-model parameters are stated only in broad terms. Without explicit functional forms or boundary values, it is impossible to verify that the reported Bayes factors are insensitive to reasonable prior variations, which directly affects the claimed preference for Einasto and cored profiles.
minor comments (2)
  1. [Table 2] Table 2: The caption does not indicate whether the quoted uncertainties on the evidence values include only statistical or also systematic contributions from the baryonic models.
  2. [Figure 3] Figure 3: The legend is too small to distinguish the seven dark-matter models clearly; adding a supplementary table of best-fit parameters would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We respond to each major comment below and indicate the revisions we will implement.

read point-by-point responses

  1. Referee: [§3] §3 (Data compilation and likelihood): The analysis treats the compiled rotation-curve velocities as faithful tracers of the circular-speed field. No quantitative assessment of possible radius-dependent biases from non-circular motions, streaming, or distance-scale systematics is presented, nor is a covariance matrix for the velocity uncertainties included in the likelihood. Because such systematics can shift the evidence ratios between cuspy and cored profiles, this assumption is load-bearing for the reported ranking.

    Authors: We agree that potential systematics in the rotation-curve data represent an important consideration that could affect the model ranking. The four compilations employed are based on Gaia DR3 and have been validated in the source papers, yet we acknowledge that non-circular motions, streaming, and distance-scale effects are not quantitatively assessed here. In the revised manuscript we will add a dedicated paragraph in §3 discussing these possible biases and their likely direction of influence on the evidence ratios between cuspy and cored profiles. The published compilations do not furnish a full covariance matrix, so we will explicitly note that our likelihood assumes independent Gaussian uncertainties and will state this as a limitation of the present analysis. revision: partial

  2. Referee: [§4.2] §4.2 (Prior specification): The priors on the halo scale parameters (rs, ρ0) and on the baryonic-model parameters are stated only in broad terms. Without explicit functional forms or boundary values, it is impossible to verify that the reported Bayes factors are insensitive to reasonable prior variations, which directly affects the claimed preference for Einasto and cored profiles.

    Authors: We thank the referee for highlighting this omission. Although the priors were chosen to be broad and weakly informative, we agree that explicit functional forms and boundary values are required for reproducibility and for assessing prior sensitivity. In the revised manuscript we will provide the precise prior distributions (including uniform or log-uniform ranges for rs and ρ0, and the specific forms adopted for all baryonic parameters) together with their boundary values. We will also report a short prior-sensitivity test confirming that the preference ordering among the dark-matter profiles remains unchanged under reasonable variations of these priors. revision: yes

Circularity Check

0 steps flagged

No circularity in Bayesian model comparison of standard DM profiles against external Gaia rotation curves

full rationale

The paper performs Bayesian model comparison by fitting parameters of seven standard dark matter profiles (including NFW and Einasto) and three baryonic models to four independent compilations of Gaia-based rotation curve velocities. Model preference is determined via Bayesian evidence computed from the likelihood on these external datasets. No derivation step reduces the ranking or central claim (Einasto preferred, cored profiles over cuspy NFW) to a quantity defined solely in terms of the fitted parameters themselves, nor does the provided text invoke self-citations for uniqueness theorems, ansatzes, or load-bearing premises. The analysis remains self-contained with external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard galactic dynamics assumptions and phenomenological density profiles whose parameters are constrained by data; no new particles or forces are introduced.

free parameters (2)
  • halo scale parameters (e.g., rs, rho0 for each profile)
    Each of the seven dark matter profiles contains one or more scale parameters that are fitted or marginalized over during the Bayesian analysis.
  • baryonic model parameters
    Parameters describing the three baryonic models are adjusted to the data within the joint fit.
axioms (2)
  • domain assumption The observed rotation curve is produced by the sum of baryonic and dark matter gravitational potentials under Newtonian gravity.
    Standard assumption invoked when fitting dark matter halo models to rotation curves.
  • domain assumption Bayesian evidence correctly ranks models given the chosen priors and likelihood.
    Core assumption of the model comparison method used throughout the paper.

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