  Satellite galaxies are predicted to generate gravitational density wakes as
they orbit within the dark matter (DM) halos of their hosts, causing their
orbits to decay over time. The recent infall of the Milky Way's (MW) most
massive satellite galaxy, the Large Magellanic Cloud (LMC), affords us the
unique opportunity to study this process in action. In this work, we present
high-resolution ($m_{dm} = 4 \times 10^4 M_{\odot}$ ) N-body simulations of the
MW-LMC interaction over the past 2 Gyr. We quantify the impact of the LMC's
passage on the density and kinematics of the MW's DM halo and the observability
of these structures in the MW's stellar halo. The LMC is found to generate
pronounced Local and Global wakes in both the DM and stellar halos, leads to
both local overdensities and distinct kinematic patterns that should be
observable with ongoing and future surveys. Specifically, the Global Wake will
result in redshifted radial velocities of stars in the North and blueshifts in
the South, at distances larger than 45 kpc. The Local Wake traces the orbital
path of the LMC through the halo (50-200 kpc), resulting in a stellar
overdensity with a distinct, tangential kinematic pattern that persists to the
present day. The detection of the MW's halo response will constrain: the infall
mass of the LMC and its orbital trajectory, the mass of the MW, and it may
inform us about the nature of the dark matter particle itself.
