  Gravitational interactions between the Large Magellanic Cloud (LMC) and the
stellar and dark matter halo of the Milky Way are expected to give rise to
disequilibrium phenomena in the outer Milky Way. A local wake is predicted to
trail the orbit of the LMC, while a large-scale over-density is predicted to
exist across a large area of the northern Galactic hemisphere. Here we present
the detection of both the local wake and Northern over-density (hereafter the
"collective response") in an all-sky star map of the Galaxy based on 1301 stars
at 60<R_gal<100 kpc. The location of the wake is in good agreement with an
N-body simulation that includes the dynamical effect of the LMC on the Milky
Way halo. The density contrast of the wake and collective response are both
stronger in the data than in the simulation. The detection of a strong local
wake is independent evidence that the Magellanic Clouds are on their first
orbit around the Milky Way. The wake traces the path of the LMC, which will
provide insight into the orbit of the LMC, which in turn is a sensitive probe
of the mass of the LMC and the Milky Way. These data demonstrate that the outer
halo is not in dynamical equilibrium, as is often assumed. The morphology and
strength of the wake could be used to test the nature of dark matter and
gravity.
