Bayesian analysis for rotational curves with ℓ-boson stars as a dark matter component

Abstract

Abstract Using Low Brightness Surface Galaxies (LBSG) rotational curves we inferred the free parameters of ℓ-boson stars as a dark matter component. The ℓ-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 ℓ = (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 ℓ = 0, ℓ = 1 and multi-states of ℓ-boson stars. We used the Akaike information criterion (AIC), Bayesian information criterion and the Bayes factor to compare the excited state (ℓ=1) and the multi-state case with the ground state (ℓ=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.