🔭 astrophysics

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

Using Gaia DR3 data and Bayesian model comparison, this study finds that the Einasto dark matter profile provides a superior fit to the Milky Way's rotation curve compared to the NFW profile and MOND, while no single baryonic model is decisively favored.

Original authors: Aryan Singh, Shantanu Desai

Published 2026-05-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Aryan Singh, Shantanu Desai

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Milky Way galaxy as a giant, spinning cosmic carousel. For decades, astronomers have been trying to figure out exactly how fast the stars on the outer edges of this carousel are moving. According to the laws of physics we learned in school (Newton's laws), if you know how much visible stuff is on the carousel (stars, gas, dust), you should be able to predict exactly how fast the outer stars should spin.

But here's the mystery: The outer stars are moving much faster than the visible stuff alone should allow. It's like a child on the very edge of a merry-go-round spinning so fast that, without a giant invisible hand holding them, they would fly off into space.

This "invisible hand" is what scientists call Dark Matter. But what shape does this invisible hand take? Is it a fuzzy cloud? A dense core? A sharp spike?

This paper is like a massive "Taste Test" or a "Reality Check" to find the best recipe for this invisible hand, using the most precise data we have ever collected from the Gaia satellite (a space telescope that maps the positions and speeds of billions of stars).

The Setup: The Contestants

The authors set up a competition with three main categories of "contestants" to explain the galaxy's spin:

The Baryonic Models (The Visible Stuff): These are different ways of calculating the weight of the visible stars, dust, and gas. Think of these as three different ways of weighing the passengers on the carousel.
The Dark Matter Models (The Invisible Hand): They tested seven different shapes for the invisible dark matter.
- NFW: The "Standard Model." It's like a sharp, pointy spike in the center that gets thinner quickly.
- Einasto: A smoother, more rounded curve. Imagine a gentle hill rather than a sharp spike.
- Burkert & Beta: "Cored" models. These are like a flat plateau in the center, not a spike.
- Others: Various other mathematical shapes (Isothermal, gNFW, Hernquist).
MOND (The "No Invisible Hand" Option): This is a radical idea suggesting that maybe we don't need invisible matter at all, but that our laws of gravity are slightly broken at low speeds. They tested three different ways to "fix" the gravity laws.

The Method: The Bayesian Scorecard

How did they decide the winner? They didn't just guess. They used a statistical tool called Bayesian Model Comparison.

Think of this like a judge scoring a talent show. The judge looks at the data (the actual speed of the stars) and asks: "If I assume this specific model is true, how likely is it that I would see the data I'm looking at?"

If a model fits the data perfectly, it gets a high score.
If a model is a bad fit, it gets a low score.
They compared every model against the "Standard Model" (NFW Dark Matter). If a new model scored 100 times better than the standard, it was declared a decisive winner.

The Results: Who Won?

1. The Smooth Hill Wins (Einasto Profile)
The big winner was the Einasto profile. In almost every test, this "smooth hill" shape fit the data better than the "sharp spike" (NFW) shape.

The Metaphor: Imagine trying to fit a glove to a hand. The NFW model was like a glove with a sharp, stiff thumb that didn't quite match the curve of the hand. The Einasto model was a soft, flexible glove that hugged the hand perfectly.
The "Core" Discovery: The results suggest the center of the Milky Way's dark matter isn't a sharp spike (a "cusp"), but rather a softer, flatter region (a "core"). This is good news for the "Core-Cusp" problem, a long-standing headache in astronomy.

2. The "No Invisible Hand" Option Lost (MOND)
The models that tried to explain the spin without dark matter (MOND) performed very poorly.

The Metaphor: It was like trying to explain why a car is speeding up by saying "the engine is broken" when the car is actually being pushed by a giant invisible truck. The MOND models couldn't match the data; they predicted the stars would keep spinning at a constant speed forever, but the data showed the stars actually start to slow down at the very edges.

3. The Visible Weight (Baryons) Was a Tie
When they compared the three different ways of weighing the visible stars, no single method won decisively.

The Metaphor: It's like three different chefs weighing a bag of flour using different scales. They all got slightly different numbers, but none of them was so clearly "wrong" that the others could be thrown out. The data wasn't precise enough to pick a single winner for the visible matter.

The Conclusion

The paper concludes that if you want to describe the Milky Way's rotation curve using the latest Gaia data, the Einasto profile is the best description of the dark matter we have. It suggests the dark matter is "cored" (flat in the middle) rather than "cuspy" (spiky).

However, the authors are careful to note that all the data they used comes from the same satellite (Gaia), so they share the same potential measurement errors. They also emphasize that while they found the best shape for the dark matter, they still can't be 100% sure about the exact amount of visible matter (stars/gas) because the data isn't quite precise enough to separate the two perfectly.

In short: The invisible hand holding our galaxy together looks more like a smooth, gentle hill than a sharp spike, and the idea that we don't need dark matter at all doesn't hold up against the new data.

Technical Summary: Determination of the Best Dark Matter Profile for the Milky Way with Gaia DR3 using Bayesian Model Comparison

Problem Statement
The rotation curves (RCs) of spiral galaxies, including the Milky Way, exhibit velocities that cannot be accounted for by visible baryonic matter alone, a discrepancy historically attributed to "missing mass" or dark matter (DM). While the Cold Dark Matter (CDM) paradigm is the standard cosmological model, it faces persistent challenges at galactic scales, such as the core-cusp problem and the missing satellite problem. Conversely, Modified Newtonian Dynamics (MOND) offers an alternative by modifying gravity in low-acceleration regimes but has faced difficulties in explaining certain galactic dynamics without dark matter.

Recent high-precision data from the Gaia satellite (specifically Data Release 3, DR3) has enabled the reconstruction of the Milky Way's rotation curve with unprecedented accuracy, revealing a decline in rotational velocity at radii beyond approximately 20 kpc. However, uncertainties remain regarding the optimal parametric form of the dark matter halo density profile that best fits these new observations. This study aims to rigorously determine which dark matter model, when combined with various baryonic mass distributions, provides the most statistically robust description of the Milky Way's rotation curve.

Methodology
The authors employ a Bayesian model comparison framework to evaluate the relative evidence of competing dynamical models against four distinct compilations of Milky Way rotation curve data derived from Gaia DR3:

Datasets: Four datasets (D1–D4) ranging from $r \approx 5$ kpc to $r \approx 30$ kpc, utilizing different tracers (OB stars, Red Giant Branch stars) and methodologies for distance and velocity estimation (e.g., APOGEE, LAMOST, 2MASS).
Baryonic Models: Three distinct models for the visible matter distribution (bulge and disk):
- B0: Hernquist potential for the bulge; a multi-component exponential thin disk (stellar, dust, gas).
- B1: Plummer potential for the bulge; Miyamoto-Nagai potentials for thin and thick disks.
- B2: Hernquist potential for the bulge; a double-exponential density profile for the disk components.
Dark Matter & Alternative Models: Seven dark matter density profiles and three MOND interpolating functions:
- DM Profiles: NFW (cuspy), Isothermal, Burkert, gNFW (generalized NFW), $\beta$ -profile, Hernquist, and Einasto.
- MOND: Standard, Simple, and Radial Acceleration Relation (RAR) interpolating functions, tested both with $a_0$ as a free parameter and fixed at the standard value ( $1.2 \times 10^{-10} \, \text{m/s}^2$ ).
Statistical Analysis: The study calculates the Bayesian evidence ( $Z$ ) for each model combination using dynamic nested sampling (via the dynesty package). The Bayes factor ( $B_{21}$ ) is computed relative to a null hypothesis consisting of the NFW profile combined with a specific baryonic model. Jeffreys' scale is used to interpret the significance of the evidence.

Key Contributions and Results

Preference for the Einasto Profile: Across the majority of dataset and baryonic model combinations, the Einasto profile emerges as the preferred phenomenological fit. It yields decisive Bayes factors ( $>100$ ) over the standard NFW profile for datasets D3 and D4 across all baryonic models, and for D1 and D2 in most cases. The best-fit Einasto index ( $\alpha$ ) is consistently positive, suggesting a profile closer to a cored distribution than a cuspy one.
Cored vs. Cuspy Halos: The analysis finds that cored dark matter profiles (Burkert, $\beta$ , and Einasto) are generally preferred over the cuspy NFW profile. Specifically, the Burkert and $\beta$ profiles show strong evidence ( $B > 100$ ) for datasets D2 and D3.
Performance of gNFW and Hernquist: The generalized NFW (gNFW) profile is decisively favored over NFW for D2 and D3 but performs worse for D1 and D4. The Hernquist profile also shows a preference over NFW across all datasets.
MOND Disfavored: Within the implementations considered, MOND models provide significantly poorer fits than the preferred dark matter profiles. The standard MOND paradigm (fixed $a_0$ ) is strongly disfavored, particularly because the interpolating functions predict constant velocities at large radii, contradicting the observed declining trend in the Gaia-based rotation curves. Even when $a_0$ is treated as a free parameter, the Bayes factors remain insignificant compared to dark matter models.
Baryonic Model Indeterminacy: No single baryonic model (B0, B1, or B2) is decisively favored over the others. The Bayes factors comparing baryonic models (using the B0 + Einasto combination as the reference) are generally low ( $<10$ ), indicating that the current rotation curve data does not strongly constrain the specific choice of baryonic potential.

Significance and Claims
The paper claims that, within the adopted modeling framework and using the latest Gaia DR3-based rotation curve datasets, the Einasto profile provides the most robust phenomenological description of the Milky Way's dark matter halo. This conclusion holds across most combinations of datasets and baryonic models.

The authors emphasize that their results align with recent cosmological simulations (e.g., FIRE-2) and other observational studies that suggest the presence of dark matter cores or Einasto-like profiles in Milky Way halos. They note that while the Einasto profile is preferred, the data does not decisively rule out other cored profiles like Burkert or $\beta$ . Furthermore, the study highlights that the four datasets used are not fully independent, as they share common systematic uncertainties inherent to Gaia DR3 (e.g., parallax zero-point offsets).

The authors modestly conclude that while their analysis favors specific dark matter profiles over the standard NFW and MOND alternatives, the sensitivity of the results to prior choices for disk mass and halo parameters was tested and found to be robust. They suggest that future insights into the nature of dark matter will likely require data from upcoming facilities such as the Vera Rubin LSST, Square Kilometer Array, and next-generation telescopes.

The Setup: The Contestants

The Method: The Bayesian Scorecard

The Results: Who Won?

The Conclusion

More like this