The recent LMC-SMC collision: Timing and impact parameter constraints
  from comparison of Gaia LMC disk kinematics and N-body simulations
  We present analysis of the proper-motion (PM) field of the red clump stars in
the Large Magellanic Cloud (LMC) disk using the Gaia Early Data Release 3
catalog. Using a kinematic model based on old stars with 3D velocity
measurements, we construct the residual PM field by subtracting the
center-of-mass motion and internal rotation motion components. The residual PM
field reveals asymmetric patterns, including larger residual PMs in the
southern disk. Comparisons between the observed residual PM field with those of
five numerical simulations of an LMC analog that is subject to the tidal fields
of the Milky Way and the Small Magellanic Cloud (SMC) show that the present-day
LMC is not in dynamical equilibrium. We find that both the observed level of
disk heating (PM residual root-mean-square of 0.057$\pm$0.002 mas yr$^{-1}$)
and kinematic asymmetry are not reproduced by Milky Way tides or if the SMC
impact parameter is larger than the size of the LMC disk. This measured level
of disk heating provides a novel and important method to validate numerical
simulations of the LMC-SMC interaction history. Our results alone put
constraints on an impact parameter $\lesssim$10 kpc and impact timing $<$250
Myr. When adopting the impact timing constraint of $\sim$140--160 Myr ago from
previous studies, our results suggest that the most recent SMC encounter must
have occurred with an impact parameter of $\sim$5 kpc. We also find consistent
radial trends in the kinematically- and geometrically-derived disk inclination
and line-of-node position angles, indicating a common origin.
