Q-balls, neural networks, and galaxy rotation curves

Can a dynamically robust (also known as stable) 𝑄-ball reproduce the rotation curve of a disk galaxy? In an astrophysical environment, 𝑄-balls are nontopological solitons that are transparent and only perceived by their gravitational effects. Traditionally, scalar 𝑄-balls are modeled with a polynomial potential, but axionlike periodic potentials are also expected to support such solitonic configurations. In the presence of angular momentum, 𝑄-balls acquire a toroidal structure with a central density void, qualitatively resembling the axially symmetric structure of disk galaxies. Motivated by this similarity, we explore whether rotating scalar 𝑄-balls can reproduce the observed rotation curves of disk galaxies. In this work, we use a recently developed hybrid numerical framework that combines a high-accuracy pseudospectral method with a physics-informed neural network approach to construct both static and rotating 𝑄-ball solutions. We assess the ability of this simplified 𝑄-ball model to mimic the dark matter halos in galaxies by fitting the observed rotation curves of a sample of disk galaxies from the SPARC catalog. While 𝑄-ball configurations are built considering a negligible self-gravity, we show their use as dark matter halos to be valid for the field parameters and halo masses relevant to disk galaxies. Our simplified model provides an overall good agreement with observational data when imposing physically motivated priors on the halo total mass, and a reasonable fit when compared to standard dark matter profiles such as the Navarro-Frenk-White; we have further found an average preferred range of the scalar field particle’s mass 𝑚𝜙 ∼10−27  eV, in agreement with similar galactic-scale soliton solutions.