Revisiting galaxy rotation curves using a non-parametric regression method.

So far several density profiles have been proposed to explain the contribution of dark matter (DM) halos to rotation curves of galaxies. In this work, without any assumption about the dynamics of the system, we apply a non-parametric method to reproduce the rotation curves of SPARC galaxies for a set of models type Core, Cusp and Core+Cusp (Fuzzy) which are the Pseudo Isothermal (Piso), NFW, Burkert, Spano, Schive, the soliton+NFW profile in the Fuzzy DM (FDM) model with one continuity condition on the density profile (SNFWC) and with two continuity conditions on the density profile and on the first derivative of the density (SNFWDC). A comparison of the rotation curve obtained using the non-parametric reconstruction method with the one obtained using the standard model fitting method, is performed by computing the distance between central curves ($B_{DIST}$) and the distance between 1$sigma$ errors bands ($B_{D1sigma}$). Besides, with statistics tools such as $P$-value, BIC, AIC, $chi^2_{red}$ we do a model selection according with best values. Therefore, to do a model selection we stablish three conditions as a criterion to accept or reject models: the best BIC value; the lowest $B_{DIST}$ value and the lowest $B_{D1sigma}$ value. We work with two groups of models. The first one is a comparison between Core and Cusp models (Piso, NFW, Spano and Burkert) and we show that Spano is the most favored model satisfying the above three conditions with the $60.87 %$. For the second group we select Core, Cusp and Fuzzy models (Schive, NFW, SNFWDC, SNFWC), finding that Schive model is in agreement in $43.75%$ with the above established conditions. Moreover according with the statistical tools and non-parametric reconstruction we are able to classify some of the galaxies as Core or Cusp.