How gravitational turbulence may help galaxies settle down

When a galaxy forms or two galaxies merge, their changing gravitational pull reshapes particle orbits. Stars or dark-matter particles can collectively approach a relatively steady arrangement long before repeated encounters between individual particles would accomplish the same task. Astrophysicists call this rapid process violent relaxation: the violence lies in the changing gravitational field, not necessarily in physical collisions.

In the preprint Violent relaxation redux, submitted to arXiv on 6 November 2026, Michael L. Nastac and colleagues propose a revised explanation of this process. They combine a turbulence theory with one-dimensional particle simulations. Their results support the proposed mechanism in that simplified setting, rather than establish how real galaxies reach equilibrium.

An old theory with changing constraints

In 1967, Donald Lynden-Bell proposed that violent relaxation produces a state of maximum mixing entropy: roughly, the most thoroughly mixed arrangement compatible with the system’s constraints.

Those constraints include more than total mass and energy. In an ideal collisionless description, particles move through a combined space of positions and velocities, called phase space. The distribution stretches into fine filaments, but the phase-space volume occupied by each density level remains fixed. These restrictions are encoded in quantities called Casimir invariants.

Lynden-Bell’s theory has had limited success in predicting the final distributions. The new paper argues that its constraints should not be treated as permanently fixed in systems made of finite numbers of particles. Instead, the system may pass through a succession of approximately maximum-entropy states while those constraints slowly change.

Mixing down to the particle-noise limit

The proposed mechanism is gravitational turbulence. Irregular, changing gravitational fields stretch and rearrange the particle distribution, producing structure on progressively finer scales in both position and velocity.

Eventually, that structure reaches scales where fluctuations caused by the finite number of particles dominate. The authors treat structure below this noise threshold as dissipated from the smooth distribution. Their argument therefore concerns finite-particle effects and a physically motivated smoothing scale; it does not overturn phase-space conservation in the ideal collisionless equations.

Their scaling theory focuses on distances below the Jeans scale, where particle motion can resist gravitational collapse. It assumes that two mixing processes—particles streaming at different velocities and acceleration by gravity—operate on comparable timescales. From this, the authors predict how fluctuation power varies with scale and how quickly fine structure reaches the noise threshold.

The resulting dissipation time grows approximately as the dynamical time multiplied by the logarithm of the particle number. During strong fluctuations, this is longer than the rapid orbital rearrangement but much shorter than the paper’s estimate for relaxation through repeated two-particle encounters.

What the simulations found

Using the open-source code wendy, the researchers simulated one-dimensional systems initially arranged in ten separated rectangular patches of phase space. The systems began far from equilibrium, collapsed into small concentrations and subsequently merged into a central concentration.

They ran 100 realizations at each of five particle counts, ranging from 100,000 to 10 million. Changing the random patch positions tested variation within this family of starting conditions; changing particle number tested the predicted noise cutoff and timescale.

The simulations agreed with the predicted small-scale density spectrum: fluctuation power fell approximately as the inverse square of spatial wavenumber. They also supported the predicted phase-space spectral structure and logarithmic dependence of dissipation time on particle number. For that timing comparison, the researchers used a specific diagnostic: the first 5% decline in a measure of distribution structure above the noise floor, not the time to complete equilibrium.

Distributions calculated using the evolving, measured density-level constraints matched the simulated distributions reasonably well. Crucially, this is not yet a prediction of the outcome from initial conditions alone: the changing constraints were supplied by the simulations.

Close to equilibrium, not all the way

The simulations approached a calculated minimum-energy arrangement compatible with their evolving constraints. This did not involve losing total energy. Instead, the minimum allowed energy rose toward the system’s conserved energy as the constraints changed.

In one reported late-time state, that minimum reached about 95% of the total energy. Persistent bumps and a maximum particle energy nevertheless showed that relaxation remained incomplete. Averaging 100 realizations reduced many irregularities, but the energy cutoff survived.

The broader limitations matter. Numerical tests were one-dimensional, gas dynamics were omitted, and the theory is not expected to describe highly symmetric collapses without chaotic mixing. Three-dimensional applications also require additional treatment to avoid infinite-mass equilibrium models. The authors lack a general proof that the gravitational ground state is unique and have not derived the evolution of the constraints themselves.

The work offers a testable account of how turbulent mixing could modify an influential theory. Explaining the common structures of galaxies and dark-matter halos remains a hypothesis, not a demonstrated result.