Formation of solitons and their transitions in scalar-field dark matter models with a non-polynomial self-interaction potential

TL;DR

This paper investigates how scalar-field dark matter can form different types of solitons depending on self-interaction strength, revealing transitions between soliton states and highlighting the importance of wave effects over hydrodynamical intuition.

Contribution

It introduces a non-polynomial self-interaction potential model for scalar dark matter and analyzes soliton formation and transitions, emphasizing the role of subdominant self-interactions.

Findings

Solitons can be of Thomas-Fermi or Fuzzy Dark Matter type depending on parameters.

Transitions between soliton types occur as stability conditions change.

Subdominant self-interactions can seed Fuzzy Dark Matter solitons at later times.

Abstract

We study the formation of solitons inside scalar-field dark matter halos with a non-polynomial self-interaction potential. We consider a self-interaction potential that is quartic in the scalar field in the low-density regime but saturates at large densities. This mimics the behaviour of axion monodromy potentials. We concentrate on the semi-classical regime, where the de Broglie wavelength is much smaller than the size of the system. We find that depending on the strength and scale of the self-interactions, the system can form solitons of the Thomas-Fermi type (dominated by self-interactions) or of the Fuzzy Dark Matter type (dominated by the quantum pressure). The system can also display transitions from a Thomas-Fermi soliton to a Fuzzy Dark Matter soliton as the former becomes unstable. We show that these behaviours can be understood from a simple Gaussian ansatz. We find that even in cases where the self-interactions are always subdominant they can play a critical role, by providing a small density boost that is enough to generate the seed for the formation of a Fuzzy Dark Matter soliton at much later times. We also point out that the intuition derived from a hydrodynamical picture can be misleading in regimes where wave effects are important.