  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.
