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Discussion on the energy content of the galactic dark matter Bose-Einstein condensate halo in the Thomas-Fermi approximation

We show that the galactic dark matter halo, considered composed of an axionlike particles Bose-Einstein condensate \cite{pir12} trapped by a self-graviting potential \cite{boh07}, may be stable in the Thomas-Fermi approximation since appropriate choices for the dark matter particle mass and scattering length are made. The demonstration is performed by means of the calculation of the potential, kinetic and self-interaction energy terms of a galactic halo described by a Boehmer-Harko density profile. We discuss the validity of the Thomas-Fermi approximation for the halo system, and show that the kinetic energy contribution is indeed negligible.