Bayesian analysis for rotational curves with $\mathrm{\ell }$-boson stars as a dark matter component

Using Low Brightness Surface Galaxies (LBSG) rotational curves we inferred the free parameters of $\mathrm{\ell }$-boson stars as a dark matter component. The $\mathrm{\ell }$-boson stars are numerical solutions to the non-relativistic limit of the Einstein-Klein-Gordon system, the Schrödinger-Poisson (SP) system. These solutions are parametrized by an angular momentum number $\mathrm{\ell }=(N-1)\mathrm{/}2$ and an excitation number $n$. We perform a bayesian analysis by modifying the SimpleMC code to perform the parameter inference, for the cases with $\mathrm{\ell }=0$, $\mathrm{\ell }=1$ and multi-states of $\mathrm{\ell }$-boson stars. We used the Akaike information criterion (AIC), Bayesian information criterion and the Bayes factor to compare the excited state ($\mathrm{\ell }$=1) and the multi-state case with the ground state ($\mathrm{\ell }$=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.