Modified gravity still leaves galaxy clusters with missing mass

Could cold gas or stellar remnants supply the extra gravity needed to hold a galaxy cluster’s hot gas in place? A study by Francoise Combes examines that question within Modified Newtonian Dynamics, or MOND. Its conclusion is conditional: changing the gravity law substantially reduces the inferred mass requirement, but additional, unseen matter is still needed.

The work is available as arXiv preprint version 2611.08702v1, submitted on November 5, 2026. Its arXiv record states that it has been accepted in PNAS.

Why changing gravity is not enough

MOND modifies the relationship between matter and gravitational acceleration when accelerations become extremely small. It has been used successfully to describe many galaxies’ rotation curves—the way orbital speeds change with distance from their centers—without invoking exotic dark matter particles.

Galaxy clusters present a harder problem. Much of their visible mass is not in stars but in the hot, X-ray-emitting gas between galaxies, called the intracluster medium. Even under MOND, the observed matter generally cannot provide the gravity inferred from that gas.

Combes investigates whether the shortfall could consist of “dark baryons”: ordinary matter, such as faint stellar remnants or cold molecular gas, that is difficult to observe. Here, “dark” describes its lack of detectable light, not an established identity as an exotic particle.

Using hot gas to reconstruct mass

The analysis uses the extended HIFLUGCS sample of 106 nearby galaxy clusters and groups selected through their X-ray emission. It divides them into 56 systems without cool cores, 25 with weak cool cores and 25 with stronger cool cores. Cool-core systems have central gas that is cooler than the surrounding hot atmosphere.

The calculation first assumes spherical symmetry and hydrostatic equilibrium: outward gas-pressure support balances inward gravity. Gas temperatures and density profiles then provide an estimate of the mass required under Newtonian gravity. The modeling includes central temperature gradients and, where appropriate, two gas-density components.

Next, Combes calculates how much matter MOND would require to produce the same inferred acceleration. The adopted transition between Newtonian and low-acceleration behavior follows the radial acceleration relation, an empirical relationship used in galaxy studies.

An important distinction follows: agreement with that relation is built into this reconstruction. It is not an independent demonstration that clusters obey it using their observed matter alone.

Finally, the estimated mass of hot gas, cluster galaxies, the brightest central galaxy and diffuse intracluster starlight is subtracted. The remainder is the inferred missing mass, not a direct detection of hidden material.

A concentrated residual, especially in cool cores

The paper’s summary reports that MOND reduces the required dynamical mass by a factor of roughly four to ten relative to Newtonian estimates, with larger reductions in less massive systems. A substantial residual remains, tracking the hot-gas mass and averaging about half its value.

Cool-core clusters show the highest central densities of inferred missing matter. The reconstructed density falls steeply around the gas core radius—typically a few tens of kiloparsecs in these systems, with the abstract highlighting 20–30 kiloparsecs. Non-cool-core systems have much broader gas cores, typically hundreds of kiloparsecs.

These are model-dependent distributions: they describe where additional matter would need to reside if the assumptions hold.

Where the reconstruction becomes inconsistent

Every non-cool-core system shows a central inconsistency: estimated visible matter exceeds the dynamically inferred mass there. Combes points to uncertainty in the scaling relations used to estimate the central galaxy and diffuse starlight. Their small contribution to the overall cluster mass does not make the local inconsistency disappear.

Some systems also develop problems in their outskirts, where the reconstructed missing-mass profile ceases to be physically usable. Faint gas, ongoing accretion, turbulence and departures from equilibrium complicate these regions. The paper cites previous comparisons finding mass differences of up to 50–80% between galaxy-motion and hydrostatic methods for some clusters.

MOND’s external field effect—the influence of surrounding gravitational fields on internal dynamics—might help explain outer-region anomalies. This study does not calculate that effect in detail; doing so requires simulations beyond its scope.

Candidates, not discoveries

The paper discusses stellar remnants, ultra-diffuse galaxies and tiny, dense molecular clouds as possible reservoirs. Observed molecular gas in Perseus provides an example of cold material in a cluster core, but not proof of the much larger hidden reservoir proposed here.

For illustration, the cold-cloud hypothesis would require roughly 100 trillion solar masses within a 500-kiloparsec radius. Whether such a population can exist and reproduce cluster dynamics remains unresolved.

This account uses the supplied full-paper PDF text extraction. Figures were omitted, and equations, tables and layout may be damaged by extraction. The result is therefore a constrained mass reconstruction and a set of hypotheses—not a detection of the missing matter or a resolution of the competition between MOND and dark matter.