Galaxy rotation curves using a non-parametric regression method: core, cusp and fuzzy scalar field dark matter models

Abstract: We present a non-parametric reconstruction of the rotation curves (RC) for 88 spiral galaxies under the LOESS+SIMEX technique. In order to compare methods we also perform the parametric approach assuming core and cuspy dark matter (DM) profiles: PISO, NFW, Burkert, Spano, the soliton and two fuzzy soliton$+$NFW. As result of this two approaches, a comparison of the RC obtained is carried out by computing the distance between central curves and the distance between 1$\sigma$ error bands. Furthermore, we perform a model selection according to two statistical criteria, the BIC and the value of $\chi^2_{red}$. We work with two groups. The first one is a comparison between PISO, NFW, Spano and Burkert showing that Spano is the most favored model satisfying our selection criteria. For the second group we select soliton, NFW and Fuzzy models, resulting the soliton as the best model. Moreover according to the statistical tools and non-parametric reconstruction we are able to classify galaxies as core or cusp. Finally, using an MCMC method, we compute for each of the DM models the characteristic surface density, $\mu_{DM}=\rho_s r_s$, and the mass within 300 pc. We found that there is a common mass for spiral galaxies of the order of $10^7$ M$\odot$, which is in agreement with results for dSph Milky Way satellites, independent of the model. This result is also consistent with our finding that there is a constant characteristic volume density of haloes. Finally, we also find that $\mu{DM}$ is not constant, which is in tension with previous literature.