Two-dimensional superflow past an obstacle of arbitrary penetrability: Exact results for the critical velocity

We report analytical and numerical results for the critical velocity for dissipationless motion of a two-dimensional scalar superfluid past a localized and static repulsive obstacle. In contrast to most of the state of the art, our study is not restricted to an impenetrable obstacle, nor to a quartic interaction. This makes it possible to get closer to recent experiments with atomic Bose-Einstein condensates and paraxial superfluids of light.