  Formation of vortex rings around moving spherical objects in superfluid He-4
at 0 K is modeled by time-dependent density functional theory. The simulations
provide detailed information of the microscopic events that lead to vortex ring
emission through characteristic observables such as liquid current circulation,
drag force, and hydrodynamic mass. A series of simulations were performed to
determine velocity thresholds for the onset of dissipation as a function of the
sphere radius up to 1.8 nm and at external pressures of zero and 1 bar. The
threshold was observed to decrease with the sphere radius and increase with
pressure thus showing that the onset of dissipation does not involve roton
emission events (Landau critical velocity), but rather vortex emission (Feynman
critical velocity), which is also confirmed by the observed periodic response
of the hydrodynamic observables as well as visualization of the liquid current
circulation. An empirical model, which considers the ratio between the boundary
layer kinetic and vortex ring formation energies, is presented for
extrapolating the current results to larger length scales. The calculated
critical velocity value at zero pressure for a sphere that mimics an electron
bubble is in good agreement with the previous experimental observations at low
temperatures. The stability of the system against symmetry breaking was linked
to its ability to excite quantized Kelvin waves around the vortex rings during
the vortex shedding process. At high vortex ring emission rates, the downstream
dynamics showed complex vortex ring fission and reconnection events that appear
similar to those seen in previous Gross-Pitaevskii theory-based calculations,
and which mark the onset of turbulent behavior.
