⚛️ general relativity

Comparison of MOND and Verlinde's emergent gravity in dwarf spheroidals

By analyzing radial accelerations in 23 dwarf spheroidal galaxies, this study demonstrates that Verlinde's emergent gravity aligns more closely with observed data than Modified Newtonian Dynamics (MOND), favoring the emergent gravity model with a statistical significance of 5.2σ.

Original authors: Youngsub Yoon, Sanghyeon Han, Ho Seong Hwang

Published 2026-02-02

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CC BY 4.0

Original authors: Youngsub Yoon, Sanghyeon Han, Ho Seong Hwang

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 universe is a giant, invisible dance floor. For a long time, scientists have been trying to figure out why the stars on the edges of galaxies are dancing so fast. According to the old rules of physics (Newton and Einstein), they should be flying off into space because there isn't enough visible "stuff" (stars and gas) to hold them in.

To solve this, most scientists have been looking for a "ghost partner"—invisible Dark Matter—that provides the extra gravity to keep the stars from flying away. But despite decades of searching, no one has ever found this ghost.

Two other scientists, MOND and Verlinde, decided to try a different approach. Instead of looking for a ghost, they suggested the rules of the dance floor itself might be wrong. They proposed that gravity behaves differently when things are moving very slowly or are very far apart.

This paper is a "taste test" to see which of these two new rulebooks works better. The authors tested them on 23 tiny, faint galaxies called "dwarf spheroidals." These are like the small, quiet side-dancers of the universe, and they are notoriously difficult to explain with the old rules.

The Two Contenders

MOND (The "Simple Rule"): Think of this as a simple, one-size-fits-all instruction manual. It says, "When gravity gets weak, just multiply the force by a specific number." It's a straightforward formula that has worked great for big, spinning galaxies.
Verlinde's Emergent Gravity (The "Complex Recipe"): This theory is more like a complex recipe that considers the "volume" of the universe, not just the surface. It suggests that gravity isn't a fundamental force but something that "emerges" from the way information and entropy (disorder) are arranged in space. It's a bit more complicated, but it has a special ingredient that changes how it behaves in different environments.

The Experiment: The "45-Degree Line" Test

The authors didn't just guess; they ran a math test. Imagine a graph where:

The X-axis is what the theory predicts the gravity should be.
The Y-axis is what we actually observe in the sky.

If a theory is perfect, all the data points should fall on a straight line at a 45-degree angle (like a perfect diagonal). If the line tilts too much to the left or right, the theory is wrong.

They ran this test for all 23 dwarf galaxies using both MOND and Verlinde's theory.

The Results: Who Won?

Here is what they found:

The Scoreboard: Out of the 23 galaxies tested, 21 of them followed Verlinde's complex recipe much more closely than MOND's simple rule. Only 2 galaxies preferred MOND.
The "Statistical Confidence": When they combined all the results together, the evidence for Verlinde's theory was incredibly strong. In the language of science, they reached a confidence level of 5.2 sigma. To put that in everyday terms: if you flipped a coin 100 times, getting 5.2 sigma means the result is so unlikely to be a fluke that you can be almost 100% sure it's real.
The "Secret Ingredient": The authors checked if Verlinde won just because they used a slightly different number in the formula. They realized that even if they adjusted the numbers to be fair, Verlinde still won. Why? Because Verlinde's formula includes a specific term (related to the density of stars) that acts like a "boost" in these tiny galaxies. MOND's simple rule doesn't have this boost, so it falls short.

The Bottom Line

Think of it like two mechanics trying to fix a car engine that is making a strange noise.

MOND says, "The engine needs a standard tune-up." It works great on big trucks (large galaxies) but struggles with this specific small car (dwarf galaxies).
Verlinde says, "The engine needs a special adjustment based on how the air moves inside the whole garage." This approach works perfectly for the big trucks and the small cars.

Conclusion: The paper claims that for these tiny, faint galaxies, Verlinde's Emergent Gravity is the better description of reality than MOND. It suggests that the universe might not need invisible "ghost" dark matter, but rather that our understanding of how gravity works needs a more sophisticated update—one that Verlinde seems to have provided.

Technical Summary: Comparison of MOND and Verlinde's Emergent Gravity in Dwarf Spheroidals

Problem Statement
The "missing mass" problem remains a central unresolved issue in astrophysics. While the mainstream dark matter paradigm posits an invisible, non-baryonic substance to explain gravitational anomalies, direct detection efforts have thus far been fruitless. Alternatively, Modified Newtonian Dynamics (MOND), proposed by Milgrom, suggests modifying the laws of gravity rather than postulating dark matter. MOND successfully explains the flatness of galactic rotation curves and the baryonic Tully–Fisher relation in rotation-supported galaxies. However, previous studies have identified a significant discrepancy: MOND underpredicts the gravitational accelerations observed in dwarf spheroidal galaxies. Furthermore, MOND relies on an "interpolating function" that must be fitted to observations rather than derived from first principles. Verlinde's emergent gravity, a theory grounded in thermodynamic and entropic principles, offers an alternative explanation for these phenomena without dark matter. This study aims to rigorously compare the predictive capabilities of MOND and Verlinde's emergent gravity specifically within the context of dwarf spheroidal galaxies.

Methodology
The authors analyzed 23 dwarf spheroidal galaxies, comprising 8 classical Milky Way satellites and 15 additional systems. The study excluded specific samples with unreliable data (e.g., those with significant rotational velocity components or insufficient data points).

The methodology involved the following steps:

Theoretical Calculation: The galaxies were approximated as spheres. The Newtonian gravitational acceleration ( $g_{bar}$ $g_{ba r}$ ) was calculated based on the baryonic mass distribution $M(r)$ $M (r)$ .
- MOND Prediction: The acceleration ( $g_{MOND}$ ) was derived using the standard interpolating function (Eq. 2) with Milgrom's constant $a_M = 1.2 \times 10^{-10} \, \text{m/s}^2$ .
- Verlinde Prediction: The acceleration ( $g_{Ver}$ ) was calculated using Verlinde's emergent gravity formula (Eq. 3), which incorporates an "apparent dark matter" component ( $g_d$ ) derived from the volume contribution to entropy. The study utilized the "quasi-de Sitter" value for the fundamental acceleration scale, $a_0 = 5.41 \times 10^{-10} \, \text{m/s}^2$ , resulting in a scale parameter $a_0/6$ that is approximately 25% smaller than the standard MOND $a_M$ .
Statistical Comparison: For each galaxy, the authors plotted the theoretical acceleration ( $g_{th}$ ) against the observed radial acceleration ( $g_{obs}$ ). They performed error-weighted linear regressions to determine the slope of the best-fit line.
Evaluation Metric: A perfect theoretical match would yield a slope of 1 (an angle of $45^\circ$ ). The theory producing a slope angle closer to $45^\circ$ was deemed superior for that specific sample.
Significance Aggregation: The statistical significance of the preference for one theory over the other was calculated for each sample. These were combined using Stouffer's method and Fisher's method to determine the overall significance across the entire dataset.

Key Contributions and Results

Superiority of Verlinde's Emergent Gravity: Out of the 23 dwarf spheroidal samples analyzed, 21 showed a better fit to the observed data under Verlinde's emergent gravity compared to MOND. Only 2 samples favored MOND.
Statistical Significance: The combined statistical significance of Verlinde's superiority over MOND across all 23 samples was found to be 5.2 $\sigma$ (using Stouffer's method) and 4.5 $\sigma$ (using Fisher's method). Even using a conservative binomial distribution approach (ignoring individual significance magnitudes and counting only the 21/23 favor), the result remains at 4.0 $\sigma$ .
Robustness Against Parameter Choice: The authors addressed a potential confounding factor: the use of the quasi-de Sitter value for $a_0$ , which is smaller than the standard MOND $a_M$ . They demonstrated that simply adjusting the MOND constant to match the smaller $a_0/6$ value did not significantly alter the trend or improve the MOND fit. The superior performance of Verlinde's gravity was attributed to the specific functional form of the theory, particularly the term $4\pi G \rho_{bar} r$ (Eq. 6), which cannot be expressed solely as a function of $g_{bar}$ . This term allows Verlinde's gravity to predict higher accelerations in dwarf spheroidals than MOND does, even with a smaller fundamental scale.
Internal Consistency: Unlike the authors' previous work which compared aggregate datasets, this study confirmed that Verlinde's gravity follows the trend of observed values within each individual dwarf spheroidal more closely than MOND.

Significance
The paper concludes that while both MOND and Verlinde's emergent gravity successfully account for accelerations in rotation-supported galaxies (a feat where dark matter theories have struggled), Verlinde's emergent gravity is the superior model for dwarf spheroidal systems. The study suggests that the specific functional form of Verlinde's gravity, which naturally arises from entropic principles and volume contributions, provides a more accurate description of gravitational dynamics in these low-acceleration environments than the phenomenological interpolating function of MOND. This result supports the viability of emergent gravity as a framework for addressing the missing mass problem without invoking dark matter.

The Two Contenders

The Experiment: The "45-Degree Line" Test

The Results: Who Won?

The Bottom Line

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