Gas-rich ultra-diffuse galaxies: alleviating the MOND tension with HMG

This study finds that while Hyperconical Modified Gravity (HMG) significantly alleviates the tension with Modified Newtonian Dynamics (MOND) regarding the rotation speeds of gas-rich ultra-diffuse galaxies, it still systematically overpredicts their velocities and fails to fully match the observed data.

The Gist

Imagine the universe as a giant, cosmic dance floor. For decades, physicists have been trying to figure out the rules of the dance.

The Problem: The "Ghost" Dancers
Most galaxies spin like merry-go-rounds. According to the standard rules of physics (Newton), if you know how much stuff (stars and gas) is on the merry-go-round, you can predict exactly how fast it should spin.

But then, astronomers found a weird group of galaxies called Ultra-Diffuse Galaxies (UDGs). They are like giant, fluffy clouds of stars and gas. When they measured how fast these clouds spin, they found something strange: they are spinning way too slowly.

It's like seeing a massive, heavy truck driving down a highway at the speed of a bicycle.

• Standard Physics (Newton): Says, "That truck should be going faster given its weight."
• The "Dark Matter" Solution: Says, "There must be invisible 'ghost' weight (Dark Matter) holding it together, but we can't see it."
• The "Modified Gravity" Solution (MOND): Says, "The rules of gravity change when things move very slowly. The truck should be going slow because gravity works differently out here."

The Contenders
This paper is a referee match between two theories trying to explain why these fluffy galaxies are spinning so slowly:

1. MOND (Modified Newtonian Dynamics): A popular theory that says gravity gets a "boost" at low speeds. It's like a magic spell that makes heavy things spin slower than expected.
2. HMG (Hyperconical Modified Gravity): A newer, more complex theory proposed by the author. It suggests that the shape of the universe itself (its geometry) creates an extra push or pull that affects how galaxies spin. Think of it as the dance floor itself tilting slightly, changing how the dancers move.

The Experiment: The "Speed Check"
The author took six of these "slow-spinning" galaxies and ran them through a computer simulation. He asked: Which theory predicts the actual speed we see in the telescope?

• The Newtonian Test (No Magic): Just using the visible weight of the stars and gas.
  • Result: It was actually pretty close! The predicted speed was only a little bit off from reality.
• The MOND Test:
  • Result: Total failure. The theory predicted these galaxies should be spinning much faster than they actually are. It was like predicting the truck would be doing 100 mph when it was doing 20. The math was off by a huge margin.
• The HMG Test:
  • Result: Better than MOND, but not perfect. The HMG theory got much closer to the real speed than MOND did. It fixed the "magic spell" problem. However, it still predicted the galaxies were spinning a little bit too fast. It's like the HMG theory said the truck should be doing 30 mph, while it was actually doing 20.

The Verdict
The paper concludes that HMG is a step in the right direction.

• It successfully "alleviates the tension" caused by MOND. It proves that MOND is likely wrong for these specific galaxies.
• However, HMG isn't the final answer yet. It's still a bit too optimistic about how fast these galaxies should spin.
• Interestingly, the simple "no-magic" Newtonian physics (just counting the visible stars) actually did the best job of all, though HMG is catching up.

The Big Picture Analogy
Imagine you are trying to tune a radio to a specific station.

• MOND is like turning the dial so far to the left that you are listening to static from a different country. It's completely off.
• Newtonian Physics is like being on the right station, but the signal is a little fuzzy.
• HMG is like turning the dial just a tiny bit to the right. It's much clearer than the static (MOND), but it's not quite as crisp as the Newtonian signal yet.

Why does this matter?
These "fluffy" galaxies are the ultimate stress test. They are the "tough customers" that break bad theories. This paper shows that the new HMG theory is a strong contender that fixes the biggest mistakes of the old MOND theory, but it still needs a little more work to be the perfect explanation for how the universe dances.

Technical Summary

1. Problem Statement

Gas-rich Ultra-Diffuse Galaxies (UDGs) present a significant challenge for gravitational theories. These systems possess large neutral hydrogen (H I) reservoirs and extended stellar discs but exhibit rotation speeds that are anomalously low relative to their baryonic masses.

• The Tension: Several isolated gas-rich UDGs (specifically a sample of six analyzed by Mancera Piña et al.) fall below the canonical Baryonic Tully–Fisher Relation (BTFR). Their observed outer circular velocities are too slow to be explained by Newtonian gravity acting on visible baryons alone, yet they are also too slow to be explained by standard Modified Newtonian Dynamics (MOND), which typically predicts higher velocities for such low-acceleration environments.
• The Goal: The study aims to test whether Hyperconical Modified Gravity (HMG), a relativistic MOND-like framework, can account for the observed kinematics of these six UDGs using its current "outer-radius prescription." Furthermore, it seeks to determine if gas-rich UDGs can serve as a discriminant between MOND, Newtonian gravity, and HMG.

2. Methodology

The author analyzed six isolated, gas-rich UDGs (AGC 114905, 122966, 219533, 248945, 334315, and 749290) using data from Leisman et al. (2017) and updated kinematics for AGC 114905 from Mancera Piña et al. (2022).

Theoretical Frameworks Tested:

1. Newtonian Gravity: Calculated circular velocity ($v_N$) based solely on the enclosed baryonic mass ($M_{bar}$) at the outer radius ($r_{sys}$): $v_N^2 = G M_{bar} / r_{sys}$.
2. MOND: Used the standard McGaugh–Lelli–Schombert (MLS) inverse interpolation function ($\hat{\nu}$) with $a_0 = 1.2 \times 10^{-10} \, \text{m s}^{-2}$. The acceleration is $g_{MOND} = \hat{\nu}(g_N/a_0) g_N$.
3. HMG (Hyperconical Modified Gravity):
   • Utilized a relativistic framework where apparent acceleration arises from the relative geometry between the system and the cosmological background.
   • Applied the outer-radius prescription (Monjo & Banik 2025; Monjo 2025a,b).
   • The total centripetal acceleration is given by:
     $$g_{HMG}(s) \approx \sqrt{g_N^2 + g_N a_{\gamma_0}(s)}$$
     where $a_{\gamma_0}$ depends on a system angle $\gamma_s$ and the Hubble expansion speed.
   • Parameter Scan: The model was tested by scanning the global neighbourhood-scale factor $s$. The study focused on the asymptotic branch ($s \gg 1$), where the relative neighbourhood density parameter $\epsilon_s^2$ approaches the asymptotic constant $1/6$.

Statistical Analysis:

• Chi-Square ($\chi^2$): Calculated using observed central values and asymmetric observational errors.
• Tension Metric ($z$): Defined as the difference between model prediction and observation divided by a combined uncertainty ($\sigma_{comb}$), which includes both observational and model-side (Monte Carlo sampled baryonic mass) errors.
• Comparison: The $\chi^2$ and $z$-scores for HMG were compared against Newtonian baryons and standard MOND.

3. Key Contributions

• Application of HMG to UDGs: This is the first application of the specific outer-radius HMG prescription to the challenging sample of gas-rich UDGs that are known to fail standard MOND tests.
• Quantitative Discrimination: The study provides a rigorous statistical comparison ($\chi^2$ and $\sigma$-tension) between Newtonian, MOND, and HMG predictions for a specific, difficult dataset.
• Identification of Model Limits: It demonstrates that while HMG improves upon MOND, the current implementation still struggles to match the low velocities of specific UDGs without further theoretical refinement (e.g., resolved disk calculations vs. point-mass approximations).

4. Results

The analysis yielded the following hierarchy of model performance:

• MOND Performance:

  • Extremely Poor: MOND predictions were grossly inconsistent with the data.
  • Statistics: $\chi^2 \approx 615.7$.
  • Tension: Per-galaxy tensions ranged from 3.7$\sigma$ to 5.9$\sigma$. MOND significantly overpredicts the rotation speeds.

• Newtonian Performance:

  • Best Fit (among the three): Surprisingly, Newtonian gravity using only baryons provided the best fit to the central values.
  • Statistics: $\chi^2 \approx 9.7$.
  • Tension: Per-galaxy tensions ranged from 0.1$\sigma$ to 1.7$\sigma$.

• HMG Performance:

  • Intermediate: The HMG model alleviated the severe tension seen in MOND but did not fully match the Newtonian fit.
  • Asymptotic Limit: The $\chi^2$ scan showed no interior minimum; the best fit occurred at the asymptotic limit ($s \gg 1$, $\epsilon_s^2 \approx 1/6$).
  • Statistics: $\chi^2 \approx 18.1$ (for the asymptotic branch).
  • Tension: Per-galaxy tensions ranged from 0.2$\sigma$ to 2.1$\sigma$.
  • Specific Failures: HMG still overpredicted velocities by $\sim 8–12 \, \text{km s}^{-1}$ for three galaxies (AGC 114905, 334315, 749290), while fitting two others (AGC 122966, 219533) well.

Relative Likelihood:
When comparing the combined tensions ($\chi^2_{comb}$), Newtonian gravity was favored over HMG, but HMG retained a relative Gaussian weight of approximately 7% compared to Newton. This is a stark contrast to MOND, which was effectively ruled out by this dataset.

5. Significance and Conclusions

• Alleviation of MOND Tension: The primary conclusion is that the current HMG implementation successfully alleviates the severe tension between MOND and gas-rich UDGs. It brings predicted velocities much closer to the observed values, reducing the discrepancy from ~5$\sigma$ (MOND) to ~1$\sigma$ (HMG).
• Not a Definitive Solution: Despite the improvement, the current HMG prescription is not yet sufficient to fully account for the published central values of the sample, as it still systematically overshoots the velocities for several galaxies.
• Discriminant Power: Gas-rich UDGs serve as a powerful discriminant:
  • They strongly disfavor standard MOND.
  • They moderately distinguish between Newtonian gravity and HMG (favoring Newton slightly, but keeping HMG viable).
• Future Directions: The author suggests that to fully accommodate these galaxies, HMG may require:
  1. Moving from a point-mass outer-radius estimate to a resolved disk calculation.
  2. Revising the relationship between the system angle $\gamma_{sys}$ and the effective centripetal term.
  3. A full hierarchical treatment of observational systematics (distance and inclination uncertainties).

In summary, the paper positions gas-rich UDGs as a critical "stress test" for modified gravity theories, demonstrating that while HMG is a promising alternative to MOND, it requires further development to match the precision of Newtonian dynamics in these specific low-surface-brightness environments.