  The Milky Way's stellar disk can tilt in response to torques that result from
infalling satellite galaxies and their associated tidal debris. In this work,
we explore the dynamics of disk tilting by running N-body simulations of
mergers in an isolated, isotropic Milky Way-like host galaxy, varying over
satellite virial mass, initial position, and orbit. We develop and validate a
first-principles understanding of the dynamics that govern how the host
galaxy's stellar disk responds to the satellite's dark matter debris. We find
that the degree of disk tilting can be large for cosmologically-motivated
merger histories. In particular, our results suggest that the Galactic disk may
still be tilting in response to Gaia-Sausage-Enceladus, one of the most
significant recent mergers in the Milky Way's history. These findings have
implications for terrestrial direct detection experiments as disk tilting
changes the relative location of the Sun with respect to dark matter
substructure left behind by a merging galaxy.
