How Big Are Ultralight Dark Matter Cores?

Hypothetical particles of "Cold dark matter" usually has a natural tendency to form a cusp at the center of a galaxy. But this isn't how inferred dark matter distributions look in real life. Instead, they are inferred from galaxy dynamics and lensing observations to form a more homogeneous "core" with fairly constant density a.k.a. (in some models) a soliton, in the inner region of a dark matter halo.

But hypothetical ultralight dark matter has wave-like behavior of the appropriate scale that in theory cause it to form cores in galaxies, rather than forming cuspy central regions of these dark matter halos as more massive cold dark matter particle candidates, such as WIMPs (weakly interacting massive particles) with masses in the GeV range, suggested as dark matter candidates in supersymmetry theories would.

A new paper explains how this happens and how big the cores are predicted to be at a technical level in ultralight dark matter scenarios. By making predictions about the size of ultralight dark matter cores, this, in turn, provides a way to test the ultralight dark matter particle theory in new observations or new analyses of old data. 

The paper and its abstract are as follows:

In theories of ultralight dark matter, solitons form in the inner regions of galactic halos. The observational implications of these depend on the soliton mass. Various relations between the mass of the soliton and properties of the halo have been proposed. We analyze the implications of these relations, and test them with a suite of numerical simulations. 

The relation of Schive et al. 2014 is equivalent to (E/M)(sol)=(E/M)(halo) where E(sol)(halo) and M(sol)(halo) are the energy and mass of the soliton (halo). If the halo is approximately virialized, this relation is parametrically similar to the evaporation/growth threshold of Chan et al. 2022, and it thus gives a rough lower bound on the soliton mass. A different relation has been proposed by Mocz et al. 2017, which is equivalent to E(sol)=E(halo), so is an upper bound on the soliton mass provided the halo energy can be estimated reliably. 

Our simulations provide evidence for this picture, and are in broad consistency with the literature, in particular after accounting for ambiguities in the definition of E(halo) at finite volume.

Kfir Blum, Marco Gorghetto, Edward Hardy, Luca Teodori, "Bracketing the soliton-halo relation of ultralight dark matter" arXiv:2504.16202 (April 22, 2025).

The introduction to the paper frames the question in the context of ultralight dark matter theories and the astronomy observations relevant to them.

Ultra-Light Dark Matter (ULDM) is a well-motivated Dark Matter (DM) candidate, potentially arising in high energy completions of the Standard Model of Particle Physics. It is generically produced in the early Universe via the vacuum misalignment mechanism, and is stable on cosmological timescales. Compared to collision-less Cold Dark Matter, ULDM leads to novel behavior on distances comparable to or smaller than its de-Broglie wavelength λdB = 2π/(mv), where v is the characteristic velocity of a system. On such scales ULDM’s wave-like nature is manifest. This results in a suppression of power in cosmological perturbations, leaving observable imprints on the Cosmic Microwave Background (CMB) anisotropy power spectrum, galaxy clustering, and the Lyman-alpha forest. ULDM wave-like density fluctuations can also lead to astrophysical effects inside galaxies, such as dynamical heating and dynamical friction, leading to constraints using systems like dwarf and ultra-faint dwarf galaxies. Observational constraints on the magnitude of such effects bounds the particle mass of an ULDM candidate m that comprises all of Dark Matter to satisfy m ≳ 10^−21eV.

Another key feature of ULDM, on which we focus in this work, is the formation of cored density profiles at the centers of galaxy halos. These cores consist of ‘solitons’, which are a ground state of the system in the sense that the soliton solution to the ULDM equations of motion minimizes the energy for a fixed mass. Solitons have been seen in ULDM halos in many numerical simulations. Solitons can affect the observed rotation curves of low-surface-brightness galaxies and irregular dwarf galaxies, stellar kinematics and dynamics of dwarf galaxies, and even strong gravitational lensing time delays, and involve interesting physics such as stochastic motion and quasi-normal mode fluctuations. It has been suggested that soliton cores may play a role in resolving the core-cusp problem, namely, the mismatch between simulations of cold dark matter and observations.

A natural question is whether a soliton forms within the lifetime of a galaxy and, if so, what is its expected mass for a given host galaxy halo. Dynamical relaxation estimates of the timescale for soliton formation are consistent with the results of simulations that use “noise” initial conditions, which are designed to be in the kinetic regime. Meanwhile, simulations with cosmological initial conditions suggest that solitons in cosmological halos may form more rapidly than predicted by kinetic theory estimates. Regarding the expected soliton mass, the cosmological simulations . . . provided numerical evidence for a simple relation between the soliton mass and the host halo mass and energy. Those authors also suggested that the relation may represent an attractor of the equations of motion, supporting this point via simulations with different initial conditions. Many other investigations of the soliton-halo relation have subsequently appeared in the literature, reporting varying levels of agreement. In this work, we present a new perspective on the problem.