  Multi-scale interaction between the LMC, Galactic halo, and the disk is
examined with N-body simulations, and precise amplitudes of the Galactic warp
excitation are obtained. The Galactic models are constructed most realistically
to satisfy available observational constraints on the local circular velocity,
the mass, surface density and thickness of the disk, the mass and size of the
bulge, the local density of the halo matter at the solar radius, and the mass
and orbit of the LMC. By using hybrid algorithm (SCF-TREE) I have succeeded to
follow the evolution with millions of particles. The orbiting satellite excites
density enhancement as a wake, and the wake exerts a tidal force on the disk.
Because of the additional torque from the wakes in the halo, the amplitudes of
the induced warps are much larger than the classical estimate by [hunt1969],
who considered only the direct torque from the LMC. The obtained amplitudes of
m=0, 1, 2 warps in the larger halo model show very good agreement with the
observed amplitude in the Milky Way. This result revives the LMC as a possible
candidate of the origin of the Galactic warp. Our smaller halo model, however,
yield only weak warps in all the harmonic modes. Therefore the halo still has
significant influence on excitation of warp even in the interaction scenario
for excitation of warps.
