Comparison between two scalar field models using rotation curves of
  spiral galaxies
  Scalar fields have been used as candidates for dark matter in the universe,
from axions with masses $\sim10^{-5}$eV until ultra-light scalar fields with
masses $\sim10^{-22}$eV. Axions behave as cold dark matter while the
ultra-light scalar fields galaxies are Bose-Einstein condensate drops. The
ultra-light scalar fields are also called scalar field dark matter model. In
this work we study rotation curves for low surface brightness spiral galaxies
using two scalar field models: the Gross-Pitaevskii Bose-Einstein condensate in
the Thomas-Fermi approximation and a scalar field solution of the Klein-Gordon
equation. We also used the zero disk approximation galaxy model where
photometric data is not considered, only the scalar field dark matter model
contribution to rotation curve is taken into account. From the best-fitting
analysis of the galaxy catalog we use, we found the range of values of the
fitting parameters: the length scale and the central density. The worst fitting
results (values of $\chi^2_{red}$ much greater than 1, on the average) were for
the Thomas-Fermi models, i.e., the scalar field dark matter is better than the
Thomas-Fermi approximation model to fit the rotation curves of the analysed
galaxies. To complete our analysis we compute from the fitting parameters the
mass of the scalar field models and two astrophysical quantities of interest,
the dynamical dark matter mass within 300 pc and the characteristic central
surface density of the dark matter models. We found that the value of the
central mass within 300 pc is in agreement with previous reported results, that
this mass is $\approx 10^{7}$ $M_\odot/$pc$^2$, independent of the dark matter
model. And, on the contrary, the value of the characteristic central surface
density do depend on the dark matter model.
