AND YET IT MOVES: THE DANGERS OF ARTIFICIALLY FIXING THE MILKY WAY CENTER OF MASS IN THE PRESENCE OF A MASSIVE LARGE MAGELLANIC CLOUD

Motivated by recent studies suggesting that the Large Magellanic Cloud (LMC) could be significantly more massive than previously thought, we explore whether the approximation of an inertial Galactocentric reference frame is still valid in the presence of such a massive LMC. We find that previous estimates of the LMC's orbital period and apocentric distance derived assuming a fixed Milky Way (MW) are significantly shortened for models where the MW is allowed to move freely in response to the gravitational pull of the LMC. Holding other parameters fixed, the fraction of models favoring first infall is reduced. Due to this interaction, the MW center of mass within the inner 50 kpc can be significantly displaced in phase-space in a very short period of time that ranges from 0.3 to 0.5 Gyr by as much as 30 kpc and 75 km s(-1). Furthermore, we show that the gravitational pull of the LMC and response of the MW are likely to significantly affect the orbit and phase space distribution of tidal debris from the Sagittarius dwarf galaxy (Sgr). Such effects are larger than previous estimates based on the torque of the LMC alone. As a result, Sgr deposits debris in regions of the sky that are not aligned with the present-day Sgr orbital plane. In addition, we find that properly accounting for the movement of the MW around its common center of mass with the LMC significantly modifies the angular distance between apocenters and tilts its orbital pole, alleviating tensions between previous models and observations. While these models are preliminary in nature, they highlight the central importance of accounting for the mutual gravitational interaction between the MW and LMC when modeling the kinematics of objects in the MW and Local Group.