  We present measurements of the critical velocity for vortex shedding in a
highly oblate Bose-Einstein condensate with a moving repulsive Gaussian laser
beam. As a function of the barrier height $V_0$, the critical velocity $v_c$
shows a dip structure having a minimum at $V_0 \approx \mu $, where $\mu$ is
the chemical potential of the condensate. At fixed $V_0\approx 7\mu$, we
observe that the ratio of $v_c$ to the speed of sound $c_s$ monotonically
increases for decreasing $\sigma/\xi$, where $\sigma$ is the beam width and
$\xi$ is the condensate healing length. The measured upper bound for $v_c/c_s$
is about 0.4, which is in good agreement with theoretical predictions for a
two-dimensional superflow past a circular cylinder. We explain our results with
the density reduction effect of the soft boundary of the Gaussian obstacle,
based on the local Landau criterion for superfluidity.
