  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 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 superfluid
velocity beyond which the vortex cannot be trapped. 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: firstly a "fall-on" regime enabled
by acoustic radiation, and secondly a "pair-creation" regime, mediated by
vortex dipoles nucleated within the pin. Pinning potentials with a size on the
order of the healing length are found to be optimal for vortex capture. Our
results will be useful in mitigating the deleterious effects of drag due to
vortices in superfluid channels, in analogy to maximising supercurrents in
type-II superconductors.
