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

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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.