Equatorial section of the system. Left: Dark matter density (the vortex network corresponds to the network of underdense white dots in the core). Center: Phase of the underlying wave function, with stellar structure in the core associated with the vortex network. Right: Circular motion of the vortices inside the core.
The nature of dark matter remains one of the greatest mysteries in cosmology. Within the standard framework of non-collisional cold dark matter (CDM), various models are considered: WIMPs (Weakly Interacting Massive Particles, with masses of around 100 GeV/c2), primordial black holes, and ultralight axion-like particles (mass of 10-22 to 1 eV/c2). In the latter case, dark matter behaves like a wave, described by a Schrödinger equation, rather than as a collection of point particles. This generates specific behaviors at small scales, while following standard dynamics (CDM) at large scales.
Philippe Brax and Patrick Valageas, researchers at the Institute of Theoretical Â鶹ÒùÔºics, studied models of ultralight cold dark matter with repulsive self-interactions, whose dynamics are described by a non-linear variant of the Schrödinger equation, known as the Gross-Pitaevskii equation, also encountered in the physics of superfluids and Bose-Einstein condensates. In their work, the authors follow the formation and dynamics of particular structures, called "vortices" (whirlpools) and "solitons" (cores in hydrostatic equilibrium), within halos of rotating ultralight dark matter.
The papers are the journal Â鶹ÒùÔºical Review D.
As with a superfluid studied in the laboratory, in these models, dark matter cores are described by the equations of an "irrotational" fluid. The system can then only sustain overall rotation through the appearance of singularities, i.e., "vortices" (whirlpools).
Combining analytical and numerical approaches, the authors show that rotating dark matter halos indeed give rise to such vortices, which further organize into a stable rotating network in the halo's core. These vortices have a quantized angular momentum that depends on the mass of the dark matter particle. Due to centrifugal force, the "soliton" (dark matter core) acquires an axisymmetric, flattened shape.
If these vortices really exist, they could offer a new way to detect ultralight dark matter. For example, by analyzing the gravitational signatures they leave in galaxies. It would also be interesting to study the possible link between these "vortex lines" and the filaments of the cosmic web. Thus, vortices analogous to those observed in the laboratory in quantum superfluid physics could exist in dark matter halos on astrophysical or galactic scales.
More information: Philippe Brax et al, 3D vortices and rotating solitons in ultralight dark matter, Â鶹ÒùÔºical Review D (2025).
Philippe Brax et al, Vortices and rotating solitons in ultralight dark matter, Â鶹ÒùÔºical Review D (2025).
Journal information: Â鶹ÒùÔºical Review D
Provided by CEA Paris-Saclay
