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

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