  We characterize the mechanisms of vortex pinning in a superfluid thin film
described by the two-dimensional Gross-Pitaevskii equation. We consider a
vortex "scattering experiment" whereby a single vortex in a superfluid flow
interacts with a circular, uniform pinning potential. By an analogy with linear
dielectrics, we develop an analytical hydrodynamic approximation that predicts
vortex trajectories, the vortex fixed point and the unpinning velocity. We then
solve the Gross-Pitaevskii equation to validate this model, and build a phase
portrait of vortex pinning. We identify two different dynamical pinning
mechanisms marked by distinctive phonon emission signatures: one enabled by
acoustic radiation and another mediated by vortex dipoles nucleated within the
pin. Relative to obstacle size, we find that pinning potentials on the order of
the healing length are more effective for vortex capture. Our results could be
useful in mitigating the negative effects of drag due to vortices in superfluid
channels, in analogy to maximising supercurrents in type-II superconductors.
