  Using Low Brightness Surface Galaxies (LBSG) rotational curves we inferred
the free parameters of $\ell$-boson stars as a dark matter component. The
$\ell$-boson stars are numerical solutions to the non-relativistic limit of the
Einstein-Klein-Gordon system, the Schr\"odinger-Poisson (SP) system. These
solutions are parametrized by an angular momentum number $\ell = (N-1)/2$ and
an excitation number $n$. We perform a bayesian analysis by modifying the
SimpleMC code to perform the parameter inference, for the cases with $\ell =
0$, $\ell = 1$ and multi-states of $\ell$-boson stars. We used the Akaike
information criterion (AIC), Bayesian information criterion and the Bayes
factor to compare the excited state ($\ell$=1) and the multi-state case with
the ground state ($\ell$=0) as the base model due to its simplicity. We found
that the data in most galaxies in the sample favours the multi-states case and
that the scalar field mass tends to be slightly bigger than the ground state
case.
