Comparison between two scalar field models using rotation curves of spiral galaxies

Scalar fields have been used as candidates for dark matter in the universe, from axions with masses $\sim10^{-5}$eV until ultra-light scalar fields with masses $\sim10^{-22}$eV. Axions behave as cold dark matter while the ultra-light scalar fields galaxies are Bose-Einstein condensate drops. The ultra-light scalar fields are also called scalar field dark matter model. In this work we study rotation curves for low surface brightness spiral galaxies using two scalar field models: the Gross-Pitaevskii Bose-Einstein condensate in the Thomas-Fermi approximation and a scalar field solution of the Klein-Gordon equation. We also used the zero disk approximation galaxy model where photometric data is not considered, only the scalar field dark matter model contribution to rotation curve is taken into account. From the best-fitting analysis of the galaxy catalog we use, we found the range of values of the fitting parameters: the length scale and the central density. The worst fitting results (values of $\chi^2_{red}$ much greater than 1, on the average) were for the Thomas-Fermi models, i.e., the scalar field dark matter is better than the Thomas-Fermi approximation model to fit the rotation curves of the analysed galaxies. To complete our analysis we compute from the fitting parameters the mass of the scalar field models and two astrophysical quantities of interest, the dynamical dark matter mass within 300 pc and the characteristic central surface density of the dark matter models. We found that the value of the central mass within 300 pc is in agreement with previous reported results, that this mass is $\approx 10^{7}$ $M_\odot/$pc$^2$, independent of the dark matter model. And, on the contrary, the value of the characteristic central surface density do depend on the dark matter model.