2025MNRAS.544.2434S

The gravitational interaction between the Milky Way (MW) and Large Magellanic Cloud (LMC) perturbs the MW halo's density and kinematics, encoding information about both galaxies' masses and structures. We present a suite of 2848 high-resolution ($10^{7}$ particles) N-body simulations that systematically vary the mass and shape of both galaxies' haloes. We model how the mean velocities and velocity dispersions of halo stars (30-120 kpc) depend on system parameters, and forecast constraints achievable with current and future observations. With fiducial values of $M_{\mathrm{MW}} = 0.7\times 10^{12}\,\mathrm{ M}_\odot$, $M_{\mathrm{LMC}} = 1.5\times 10^{11}\,\mathrm{ M}_\odot$, $c=9.415$ (MW halo concentration), $q=1.0$ (halo flattening), and assuming Gaia DR3-level astrometry, 20 km s^–1 radial velocity precision, 10 per cent distance precision, and a sample of 4000 RR Lyrae stars, we achieve $1\sigma$ uncertainties of $0.11\times 10^{12}\,\mathrm{ M}_\odot$ in $M_{\mathrm{MW}}$, $2.33\times 10^{10}\,\mathrm{ M}_\odot$ in $M_{\mathrm{LMC}}$, 2.38 in c, and 0.06 in q. These correspond to fractional uncertainties of 11 per cent, 16 per cent, 25 per cent, and 6 per cent, respectively, relative to fiducial values. Improved Gaia proper motions (DR5) yield modest gains (up to 14 per cent), while adding radial velocities improves constraints by up to 60 per cent relative to using Gaia astrometry alone. Doubling the sample size to $\sim$8000 stars provides additional 30 per cent improvements, whereas reducing distance uncertainties has minimal impact ($\lesssim$10 per cent). Mean velocities trace LMC-induced perturbations, while velocity dispersions constrain the MW halo properties, jointly breaking degeneracies. Our results demonstrate that combining Gaia astrometry with large spectroscopic surveys will enable precise characterization of the MW-LMC system. This methodology paper establishes the framework for interpreting observations; future work will apply these tools to existing spectroscopic data sets. The full simulation suite, HaloDance, will be made publicly available at github.com/Yanjun-Sheng/HaloDance.