Constraining the Milky Way halo kinematics via its Linear Response to
  the Large Magellanic Cloud
  We model the response of spherical, non-rotating Milky Way (MW) dark matter
and stellar halos to the Large Magellanic Cloud (LMC) using the matrix method
of linear response theory. Our computations reproduce the main features of the
dark halo response from simulations. We show that these features can be well
separated by a harmonic decomposition: the large scale over/underdensity in the
halo (associated with its reflex motion) corresponds to the $\ell=1$ terms, and
the local overdensity to the $\ell\geq2$ multipoles. Moreover, the dark halo
response is largely dominated by the first order 'forcing' term, with little
influence from self-gravity. This makes it difficult to constrain the
underlying velocity distribution of the dark halo using the observed response
of the stellar halo, but it allows us to investigate the response of stellar
halo models with various velocity anisotropies: a tangential (respectively
radial) halo produces a shallower (respectively stronger) response. We also
show that only the local wake is responsible for these variations, the reflex
motion being solely dependent on the MW potential. Therefore, we identify the
structure (orientation and winding) of the in-plane quadrupolar ($m=2$)
response as a potentially good probe of the stellar halo anisotropy. Finally,
our method allows us to tentatively relate the wake strength and shape to
resonant effects: the strong radial response could be associated with the inner
Lindblad resonance, and the weak tangential one with corotation.
