Analysis of Bose-Einstein condensation times for self-interacting scalar dark matter

TL;DR

This paper analyzes the timescales for Bose-Einstein condensation of self-interacting scalar dark matter, emphasizing the importance of gravity and validating the Wigner formalism as an effective analytical tool.

Contribution

It extends previous work by applying the Wigner formalism to include self-interactions and virial velocity effects, clarifying their impact on condensation timescales.

Findings

Self-interactions delay condensation compared to gravity-driven processes.

Condensation timescale scales as the square of the self-interaction strength.

Wigner formalism effectively corroborates numerical estimates and aids in identifying artifacts.

Abstract

We investigate the condensation time of self-interacting axion-like particles in a gravitational well, extending the prior work [arXiv:2007.07438] which showed that the Wigner formalism is a good analytic approach to describe a condensing scalar field. In the present work, we use this formalism to affirm that $\phi^4$ self-interactions will take longer than necessary to support the time scales associated with structure formation, making gravity a necessary part of the process to bring axion dark matter into a solitonic form. Here we show that when the axions' virial velocity is taken into account, the time scale associated with self-interactions will scale as $\lambda^2$. This is consistent with recent numerical estimates, and it confirms that the Wigner formalism described in prior work~\cite{Relax} is a helpful analytic framework to check computational work for potential numerical artifacts.