The Milky Way - Large Magellanic Cloud Interaction with Simulation Based Inference

The infall of the Large Magellanic Cloud (LMC) into the Milky Way (MW) has displaced the MW's centre of mass, manifesting as an observed reflex motion in the velocities of outer halo stars. We use a Simulation Based Inference framework to constrain properties of the MW, LMC and the induced reflex motion using the dynamics of outer MW halo stars. Specifically, we use the mean radial and tangential velocities of outer halo stars calculated in a set of distance and on-sky bins. We train neural networks to estimate parameter posterior distributions using a set of $128,000$ rigid MW--LMC simulations conditioned upon velocity data from the Dark Energy Spectroscopic Instrument (DESI) and the combined H3+SEGUE+MagE outer halo surveys. We constrain the reflex motion velocity and the enclosed MW and LMC masses within $50 \, \rm kpc$ using the DESI or H3+SEGUE+MagE dataset while varying the survey sky coverage and depth. We find the most precise constraints by using the radial and tangential velocity data from the H3+SEGUE+MagE survey and on-sky quadrant sky coverages. We report a reflex motion velocity, the speed at which the MW lurches towards the LMC, of $v_{\rm{travel}} = 26.4^{+5.5}_{-4.4} \, \rm km \, \rm s^{-1}$, while simultaneously finding an enclosed LMC mass of $M_{\rm LMC}(< 50 \, \rm kpc) = 9.2^{+1.9}_{-2.3} \times 10^{10}\, \rm M_{\odot}$ and enclosed MW mass of $M_{\rm MW}(< 50 \, \rm kpc) = 4.4^{+0.7}_{-0.7} \times 10^{11}\, \rm M_{\odot}$. Our results suggest that the LMC's total mass is at least $\approx 10-15 \%$ of that of the MW. This inference framework is flexible such that it can provide rapid and reliable constraints when applied to any future survey measuring the velocities of outer halo stars.