Tango for three: Sagittarius, LMC, and the Milky Way
  We assemble a catalogue of candidate Sagittarius stream members with 5d and
6d phase-space information, using astrometric data from Gaia DR2, distances
estimated from RR Lyrae stars, and line-of-sight velocities from various
spectroscopic surveys. We find a clear misalignment between the stream track
and the direction of the reflex-corrected proper motions in the leading arm of
the stream, which we interpret as a signature of a time-dependent perturbation
of the gravitational potential. A likely cause of this perturbation is the
recent passage of the most massive Milky Way satellite - the Large Magellanic
Cloud (LMC). We develop novel methods for simulating the Sagittarius stream in
the presence of the LMC, using specially tailored N-body simulations and a
flexible parametrization of the Milky Way halo density profile. We find that
while models without the LMC can fit most stream features rather well, they
fail to reproduce the misalignment and overestimate the distance to the leading
arm apocentre. On the other hand, models with an LMC mass in the range
(1.3+-0.3)x10^11 Msun rectify these deficiencies. We demonstrate that the
stream can not be modelled adequately in a static Milky Way. Instead, our
Galaxy is required to lurch toward the massive in-falling Cloud, giving the Sgr
stream its peculiar shape and kinematics. By exploring the parameter space of
Milky Way potentials, we determine the enclosed mass within 100 kpc to be
(5.6+-0.4)x10^11 Msun, and the virial mass to be (9.0+-1.3)x10^11 Msun, and
find tentative evidence for a radially-varying shape and orientation of the
Galactic halo.
