  Observations with the Gaia satellite have confirmed that the satellite
galaxies of the Milky Way (MW) are not distributed as homogeneously as
expected. The same occurs in galaxies such as Andromeda and Centaurus A, where
satellite galaxies around their host galaxies have been observed to have orbits
aligned perpendicular to the galactic plane of the host galaxy. This problem is
known as Vast Polar Structure (VPOS) for the MW. The Scalar Field Dark Matter
Field (SFDM), also known as Ultralight-, Fuzzy-, BEC-, Axion-dark matter,
proposes that DM is a scalar field (SF), which in the non-relativistic limit
follows the Schr\"odinger equation coupled to the Poisson equation. Although
the SF here is classical, the Schr\"odinger equation contains a ground and
excited states as part of its nature. In this work, we show that such quantum
character of the SFDM can naturally explain the VPOS observed in galaxies. By
taking into account the finite temperature corrections for a complex,
self-interacting SF at very early epochs of the Universe, we show that the
resulting ground and first excited states only, we can fit the rotation curves
of the galaxies in a very simple way, and with the best-fit parameters
obtained, we can explain the VPOS. We do this with particular galaxies, such as
the MW, M31, Centaurus A, and other six galaxies whose satellites have been
observed. From this result, it follows that the multistate SFDM is not
distributed homogeneously around the galaxy, and therefore might explain the
anisotropic distribution of the satellite galaxies. According to this result,
this could be a general characteristic of the galaxies in the Universe.
Finally, we also show how the scale of each galaxy depends on a parameter that
is determined by the final temperature of the SF of the galaxy halo under
study. This explains why different galaxies with SFDM give different values of
the mass of the SF.
