  In recent years, the scalar field dark matter (SFDM), also called ultralight
bosonic dark matter, has received considerable attention due to the number of
problems it might help to solve. Among these are the cusp-core problem and the
abundance of small structures of the standard cold dark matter (CDM) model. In
this paper we show that multi-state solutions of the low energy and weak
gravitational field limit of field equations, interpreted as galactic halo
density profiles, can provide a possible explanation to the anisotropic
distribution of satellite galaxies observed in the Milky Way, M31 and Centaurus
A, where satellites trajectories seem to concentrate on planes close to the
poles of the galaxies instead of following homogeneously distributed
trajectories. The core hypothesis is that multi-state solutions of the
equations describing the dynamics of this dark matter candidate, namely, the
Gross-Pitaevskii-Poisson equations, with monopolar and dipolar contributions,
can possibly explain the anisotropy of satellite trajectories. In order to
construct a proof of concept, we study the trajectories of a number of test
particles traveling on top of the gravitational potential due to a multi-state
halo with modes (1,0,0)+(2,1,0). The result is that particles accumulate
asymptotically in time on planes passing close to the poles. Satellite galaxies
are not test particles but interpreted as such, our results indicate that in
the asymptotic time their trajectories do not distribute isotropically, instead
they prefer to have orbital poles accumulating near the equatorial plane of the
multistate halo. The concentration of orbital poles depends on whether the
potential is monopolar or dipolar dominated.
