Uncovering the first-infall history of the LMC through its dynamical impact in the Milky Way halo

The gravitational interactions between the LMC and the Milky Way cause dynamical perturbations in the MW halo, leading to biased distributions of stellar density and kinematics. We run 50 high-resolution N-body simulations exploring varying masses and halo shapes of the MW and LMC to study the evolution of LMC-induced perturbations. By measuring mean velocities of simulated halo stars, we identify a discontinuity between the first-infall and second-passage scenarios of the LMC's orbital history. In the first infall, the Galactocentric latitudinal velocity hovers around 16 km/s for stars at 50-100 kpc, while it subsides to about 8 km/s in the second-passage scenario. We demonstrate that this reduced perturbation magnitude in the second-passage scenario is mainly due to the short dynamical times of the Galactic inner halo and the lower velocity of the LMC during its second infall into the MW. Using a subset of $\sim 1100$ RR Lyrae stars located in the outer halo ($50 \leq R_{\mathrm{GC}} < 100$ kpc) with precise distance estimates from Gaia, we find the mean latitudinal velocity ($v_{b}$) in the Galactocentric frame to be $\langle v_{b} \rangle = 18.1 \pm 4.1$ km/s. The observation supports the first-infall scenario with a massive LMC ($\sim 2.1 \times 10^{11} \mathrm{M}_{\odot}$) at infall, an oblate MW halo with a virial mass $M_{200} < 1.4 \times 10^{12} \mathrm{M}_{\odot}$ and a flattening parameter $q > 0.7$. Our study indicates that LMC-induced kinematic disturbances can reveal its orbital history and key characteristics, as well as those of the MW. This approach shows promise in helping determine fundamental parameters of both galaxies.