Relaxation times for Bose-Einstein condensation by self-interaction and gravity

TL;DR

This paper investigates the timescales of Bose-Einstein condensation for scalar fields with self-interaction and gravity, revealing inverse proportionality to density and coupling, and proposing an additive model for combined effects.

Contribution

It provides a comprehensive analysis of condensation timescales considering both self-interaction and gravity, supported by dynamical simulations and solving coupled equations.

Findings

Condensation timescale ∝ n^{-2} g^{-2} for self-interacting scalar fields.

Combined effects of self-interaction and gravity follow an additive model for the cross section.

Results are relevant for understanding boson star formation via condensation.

Abstract

In this paper, we study the Bose-Einstein condensation of a scalar field with an attractive self-interaction, with or without gravitational interactions. We confirm through full dynamical simulation that the condensation timescale due to self-interaction is inversely proportional to the square of the number density $n$ and the self-coupling constant $g$ : $\tau \propto n^{-2} g^{-2}$. We also investigate the condensation timescale when self-interaction and gravity are both important by solving the Gross-Pitaevskii-Poisson equations, and find that the condensation time scales according to an additive model for the cross section. We discuss the relevance of our results to theoretical models of boson star formation by condensation.