Core-Halo Mass Relation in Cosmological Vector Dark Matter

We study the cosmological core-halo relation in vector dark matter using three-component Schr\"odinger-Poisson simulations. Starting from cosmological vector-field initial conditions, which due to the evolution of the vector field during inflation are enhanced on small scales, we find that nonlinear evolution begins almost immediately following matter-radiation equality and produces compact self-gravitating Proca-star condensates at the centers of halos. After confirming the central condensates through their radial density profiles, we find the empirical relation $\widetilde M_\star\propto \widetilde M_{\rm h}^{0.6403}$ between the Proca star mass and halo mass, although interestingly we find that we are only able to confirm Proca stars in $\mathcal{O}(10\%)$ of halos. This serves as important input for future studies of the abundance and merger rates of Proca stars in models of vector dark matter. We also examine the vector-field structure of the objects through global longitudinal and transverse polarization fractions and local spin density inside halos, which increases over cosmic time.