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.
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