Jeans mass-radius relation of self-gravitating Bose-Einstein condensates and typical parameters of the dark matter particle

TL;DR

This paper analyzes the mass-radius relation of Bose-Einstein condensate dark matter, exploring how different self-interactions affect cosmic structures and constraining dark matter particle properties using observational data.

Contribution

It provides a comprehensive study of the Jeans mass-radius relation for BEC dark matter with various self-interactions and constrains particle parameters based on halo observations.

Findings

Jeans radius remains constant in the Thomas-Fermi regime with repulsive interactions.

Transition occurs at a maximum Jeans mass similar to halo maximum mass.

Observational data constrains dark matter particle mass and scattering length.

Abstract

We study the Jeans mass-radius relation of Bose-Einstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the mass-radius relation of Bose-Einstein condensate dark matter halos [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)]. Bosons with a repulsive self-interaction generically evolve from the Thomas-Fermi regime to the noninteracting regime as the Universe expands. In the Thomas-Fermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. Bosons with an attractive self-interaction generically evolve from the nongravitational regime to the noninteracting regime as the Universe expands. In the nongravitational regime, the Jeans radius and the Jeans mass increase. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. The transition occurs at a maximum Jeans mass which is similar to the maximum mass of Bose-Einstein condensate dark matter halos with an attractive self-interaction. We use the mass-radius relation of dark matter halos and the observational evidence of a ``minimum halo'' (with typical radius $R\sim 1\, {\rm kpc}$ and typical mass $M\sim 10^8\, M_{\odot}$) to constrain the mass $m$ and the scattering length $a_s$ of the dark matter particle.