Constraining condensate dark matter in galaxy clusters

Abstract: We constrain scattering length parameters in a Bose-Einstein condensate dark matter model by using galaxy clusters radii, with the implementation of a method previously applied to galaxies. At the present work, we use a sample of 114 clusters radii in order to obtain the scattering lengths associated with a dark matter particle mass in the range $10^{-6}-10^{-4}\, {\rm eV}$. We obtain scattering lengths that are five orders of magnitude larger than the ones found in the galactic case, even when taking into account the cosmological expansion in the cluster scale by means of the introduction of a small cosmological constant. We also construct and compare curves for the orbital velocity of a test particle in the vicinity of a dark matter cluster in both the expanding and the non-expanding cases.