Could Dark Matter Be a Wave That Gently Talks to Itself?

Imagine a galaxy as a vast, dim ocean. Its stars are the foam on the surface, bright enough for telescopes to see. Most of the mass, however, sits in the dark water underneath.

For decades, astronomers have inferred that hidden mass from the way galaxies rotate. Stars and gas move too fast to be held in place by visible matter alone. The usual explanation is dark matter, a form of matter that does not emit light and mostly reveals itself through gravity.

A thesis by Bihag Dave, accepted for a PhD degree at Ahmedabad University in September 2025, explores a specific and strange possibility: dark matter may be made of ultra-light spin-zero particles with mass around 10^-22 electron volts. At that mass, dark matter would behave less like a swarm of tiny bullets and more like a cosmic wave.

The dark matter particle that acts like a field

Ordinary particle dark matter models often picture dark matter as heavy particles moving through space. Ultra Light Dark Matter, or ULDM, changes that picture.

If the particle is light enough, many particles can occupy the same quantum state. The collection can then be described as a classical scalar field, meaning a smoothly varying quantity spread through space. In galaxy centers, this field can form stable, self-gravitating lumps called solitons.

A soliton here is not a star or a black hole. It is a dense dark matter core held together by gravity and shaped by the wave nature of the field.

The central question of the thesis is simple to state: if dark matter is an ultra-light wave, can galaxies tell us whether that wave interacts with itself?

Reading particle physics from galaxy centers

Dave takes a signature-driven approach. Instead of assuming a detailed particle model, the work asks what astronomical data can say about two quantities: the particle mass m and a self-coupling strength lambda.

The calculations use solutions of the Gross-Pitaevskii-Poisson equations. In plain terms, these equations describe how a wave-like dark matter field arranges itself under its own gravity, while also allowing the field to either attract or repel itself through a small self-interaction.

One test comes from galaxy centers that host supermassive black holes. Observations can place upper limits on how much mass is enclosed in the central region. If a dark matter soliton were too massive or too compact, it could exceed those limits.

The thesis finds that such central-mass limits can probe both attractive and repulsive self-interactions with strengths around lambda ~ ±10^-96 to 10^-95. These numbers are extremely small, but the point is physical: galaxy cores may be sensitive to particle properties far beyond direct laboratory reach.

Rotation curves become a test of the dark core

A second test uses galaxy rotation curves, which track how fast stars and gas orbit at different distances from the galactic center.

In the simplest ultra-light dark matter model with negligible self-interactions, earlier work had raised a problem. For particle mass near 10^-22 electron volts, the model could have difficulty matching observed rotation curves while also satisfying an empirical relation between the soliton mass and the larger halo mass.

Dave examines low surface brightness galaxies from the SPARC catalogue. These galaxies are useful because dark matter dominates much of their mass budget, making them cleaner laboratories for dark matter physics.

The thesis finds that including repulsive self-interactions can ease the tension. For m ~ 10^-22 electron volts and lambda greater than about 10^-90, ULDM can fit observed rotation curves while also satisfying a modified soliton-halo relation that includes self-interaction effects.

The message is not that this model is confirmed. It is that a version of wave dark matter that was under pressure may look different once the dark matter field is allowed to interact with itself.

A dwarf galaxy may survive because dark matter pulls inward

The thesis also studies satellite dwarf galaxies, small galaxies orbiting inside the gravitational field of a larger host halo.

Such satellites can lose dark matter through tidal effects. In wave dark matter, this loss can be treated as a slow leakage, or tunnelling, from the satellite over cosmic time.

Here the sign of the self-interaction matters. Attractive self-interactions help the satellite hold itself together. Repulsive self-interactions do the opposite and can shorten its lifetime.

Applied to the Fornax dwarf spheroidal galaxy, the analysis finds that attractive self-interactions can allow the satellite to survive over cosmological timescales for parameter choices that would otherwise be challenged in the non-interacting case. This means dwarf-galaxy survival may not rule out ULDM as directly as it might seem if self-interactions are ignored.

Letting neural networks read galaxy rotation

The final part of the thesis turns to machine learning.

Dave trains neural networks on simulated rotation curves of dwarf galaxies. The networks learn how the shape of a rotation curve depends on dark matter profile parameters, such as the ULDM particle mass and core structure, along with baryonic parameters such as the stellar mass-to-light ratio.

The trained networks are then applied to observed rotation curves to infer parameter values and uncertainties. The thesis reports that neural networks can recover parameters consistent with observations and with standard Bayesian approaches in the cases studied.

This part of the work is not a replacement for physical modeling. It is a test of whether fast, likelihood-free inference can help connect galaxy data to dark matter parameters.

The caveats are part of the story

The thesis rests on clear assumptions. It assumes dark matter is made of elementary spin-zero particles beyond the Standard Model. It does not consider modified gravity, primordial black holes, or other alternatives as the main explanation. It also assumes non-gravitational couplings between dark matter and ordinary particles are negligible.

The results are model-dependent. They depend on how galaxy cores are represented by solitonic configurations, how self-interactions enter the field equations, and how empirical relations between cores and halos are modified.

The machine-learning study also has limits. One stated limitation is that some trained networks use velocity lists without fully using the corresponding radius information, so two rotation curves with the same velocities but different radial sampling may not be distinguished. Future work could train networks that handle multiple galaxies with varied radius and velocity coverage while inferring one shared particle mass.

A small interaction with large astronomical footprints

The most striking idea in the thesis is scale.

A dark matter particle with mass near 10^-22 electron volts would be almost unimaginably light. Its self-coupling could be tiny. Yet the combined effect of many such particles could shape the cores of galaxies, the rotation of gas disks, and the survival of dwarf satellites.

That is why galaxies are not just scenery in this story. They are detectors, spread across cosmic distances, sensitive to physics that may be too faint to see in a laboratory.

If dark matter is a wave, then each galaxy may carry a trace of how that wave holds itself together.