Minimum critical velocity of a Gaussian obstacle in a Bose-Einstein condensate

When a superfluid flows past an obstacle, quantized vortices can be created in the wake above certain critical velocity. In experiment by Kwon et al. [Phys. Rev. A 91, 053615 (2015)], velocity ${v}_{c}$ was measured for atomic Bose-Einstein condensates (BECs) using moving repulsive Gaussian potential, and minimized when potential height ${V}_{0}$ of obstacle close to condensate chemical $\ensuremath{\mu}$. Here we numerically investigate evolution vortex shedding two-dimensional BEC with increasing show that minimum at strength ${V}_{0c}\ensuremath{\approx}\ensuremath{\mu}$ results from local density reduction vortex-pinning effect obstacle. The spatial distribution superflow around just below is examined. particle tip decreases as increases ${V}_{c0}$, strength, dipole suddenly formed dragged indicating onset pinning. exhibits power-law scaling size $\ensuremath{\sigma}$ ${v}_{c}\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}\ensuremath{\gamma}}$ $\ensuremath{\gamma}\ensuremath{\approx}1/2$.