  Cold dark matter (CDM) has shown to be an excellent candidate for the dark
matter (DM) of the Universe at large scales, however it presents some
challenges at the galactic level. The scalar field dark matter (SFDM), also
called fuzzy, wave, Bose-Einstein condensate or ultra-light axion DM, is
identical to CDM at cosmological scales but different at the galactic ones.
SFDM forms core halos, it has a natural cut-off in its matter power spectrum
and it predicts well-formed galaxies at high redshifts. In this work we
reproduce the rotation curves of high-resolution low surface brightness (LSB)
and SPARC galaxies with two SFDM profiles: (1)~The soliton+NFW profile in the
fuzzy DM (FDM) model, arising empirically from cosmological simulations of
real, non-interacting scalar field (SF) at zero temperature, and (2)~the
multistate SFDM (mSFDM) profile, an exact solution to the Einstein-Klein-Gordon
equations for a real, self-interacting SF, with finite temperature into the SF
potential, introducing several quantum states as a realistic model for a SFDM
halo. From the fits with the soliton+NFW profile, we obtained for the boson
mass $0.212< m_\psi/(10^{-23} \mathrm{eV}/c^2)<27.0$ and for the core radius
$0.326< r_c/\mathrm{kpc}<8.96$. From the combined analysis with the LSB
galaxies, we obtained $m_\psi = 0.554 \times10^{-23}\mathrm{eV}$, a result in
tension with the severe cosmological constraints. Also, we show the analytical
mSFDM model fits the observations as well as or better than the empirical
soliton+NFW profile, and it reproduces naturally the wiggles present in some
galaxies, being a theoretically motivated framework additional or alternative
to the FDM profile.
