  Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we
observe for the first time Abelian dominance in the confining part of the
static potential in local unitary gauges such as the F12 gauge. We also study
the flux-tube profile between the quark and antiquark in these local unitary
gauges and find a clear signal of the dual Meissner effect. The Abelian
electric field is found to be squeezed into a flux tube by the monopole
supercurrent. This feature is the same as that observed in the non-local
maximally Abelian gauge. These results suggest that the Abelian confinement
scenario is gauge independent. Observing the important role of space-like
monopoles in the Polyakov gauge also indicates that the monopoles defined on
the lattice do not necessarily correspond to those proposed by 't Hooft in the
context of Abelian projection.
