  We measure the momentum density in a Bose-Einstein condensate (BEC) with
dilute spin impurities after an expansion in the presence of interactions. We
observe tails decaying as $1/k^4$ at large momentum $k$ in the condensate and
in the impurity cloud. These algebraic tails originate from the impurity-BEC
interaction, but their amplitudes greatly exceed those expected from two-body
contact interactions at equilibrium in the trap. Furthermore, in the absence of
impurities, such algebraic tails are not found in the BEC density measured
after the interaction-driven expansion. These results highlight the key role
played by impurities when present, a possibility that had not been considered
in our previous work [Phys. Rev. Lett. 117, 235303 (2016)]. Our measurements
suggest that these unexpected algebraic tails originate from the non-trivial
dynamics of the expansion in the presence of impurity-bath interactions.
