Consequences for the Scalar Field Dark Matter model from The McGaugh
  Observed-Baryon Acceleration Correlation
  Although the standard cosmological model, the so-called $\Lambda$ Cold Dark
Matter ("$\Lambda$CDM"), appears to fit well observations at the cosmological
level, it is well known that it possesses several inconsistencies at the
galactic scales. In order to address the problems of the $\Lambda$CDM at small
scales, alternative models have been proposed, among the most popular ones the
proposal of dark matter in the Universe being made of ultra-light bosons is a
strong candidate nowadays. At this work, we study through an analytical
approach the consequences arising from confronting the SPARC catalogue
observed-baryon acceleration correlation with the scalar field dark matter
model. We carry out such analysis either considering the features of galactic
haloes extracted from structure formation simulations either from considering
the existence of other non-dark-matter elements in the whole system (such as
baryons or a supermassive black hole). Specifically, we address a recent claim
that the model is not capable of reproducing a constant surface density in the
core in contrast to what observations suggest for a host of galaxies with
different sizes and morphologies. In this direction, we show that this
discrepancy can be alleviated once the contributions of no-dark-matter
constituents in the whole galactic system are taken into account. Additionally,
we find that a mass of $m \simeq 1.41 \times 10^{-22}\ eV/c^2$ is capable of
reproducing all our findings and correctly adjusting the rotation curves coming
from the Milky Way galaxy.
