Formation and relaxation of halos in the context of wave DM particles evolving on a background of a neutrino condensate

We investigate the formation and relaxation of dark matter halos in the context of wave dark matter particles evolving on a background of a neutrino condensate. To this aim, we solved numerically the Schrödinger-Poisson system to model the dynamical evolution of ultralight bosonic dark matter particles in the presence of neutrino condensate. The latter appears as an additional source of the gravitational field in the Poisson equation, while its dynamical evolution and interaction with the environment are neglected. We found that, depending on the value of the cutoff parameter, the presence of the background neutrino condensate can affect the formation and relaxation of wave dark matter halos. Nevertheless, for value of the cutoff of the order of a few eV, the two species can coexist showing only marginal differences with the only-wave dark matter case. These results open the possibility of investigating more complex cosmological scenarios involving the formation of dark matter halos.