Occam's Razor and a Three-Family Ultralight Fermionic Dark Matter Model
Inspired by the three generations in the Standard Model, we propose that dark matter particles are simply three non-interacting ultralight fermions. This model is tested at galactic scales with the SPARC catalog of rotational velocity curves. This is done by modeling the dark matter halo as the self-gravitating configuration of three gravitationally coupled fermion species. This configuration is capable of forming more complex rotational curves which gives it flexibility to describe more complex and diverse morphologies of galaxy rotation curves. The core of the halos will be described by degenerate fermions and the transitions from a degenerate core to a non-degenerate halo will be described by either a perfect-fluid-like halo or a NFW density profile. In order to construct the priors of the three-fermion model, first we performed a single-fermion analysis and obtained three characteristic mass regions around 20, 40, and 65-70 eV, for both halo types. It is found that the three-component fermion model improves the goodness of fit for 94.9\% of the galaxies considered. To estimate if the additional parameters are favored despite the added complexity by the corresponding improvement in the fit, the information criteria of AICc and BIC were computed and we found that more than $50\%$ of the galaxies analyzed prefer the three-component fermion model over a single fermion model. The three-fermion model is particularly favored for galaxies with larger radial extent and more complex rotation curves. The multicomponent fermionic dark sector is able to describe a large diversity of rotation curves while maintaining characteristic fermion mass scales across the galaxy sample.