Mapping the Distorted Dark Matter Distribution of the LMC-SMC System Prior to Milky Way Infall with Basis Function Expansions

Abstract

The SMC orbits within the LMC's dark matter (DM) halo in a $\sim$1:10 mass-ratio encounter. The LMC:Milky Way (MW) interaction is also $\sim$1:10, and is expected to perturb the MW's DM distribution. However, no framework exists to quantify the severity of these perturbations over multiple pericenters and longer periods of time, such as the LMC-SMC interaction history. We construct basis function expansions of a high-resolution \textit{N}-body simulation of the Clouds interacting in isolation and analyze their DM distributions at an epoch approximating the time of their infall to the MW. Our goal is to quantify how the Clouds distort each other's DM distributions \textit{without} the MW. The LMC halo's response to the SMC includes a $\sim 20$ kpc long dynamical friction wake and the displacement of the LMC's density center during each SMC pericenter, which produces two overdensities in the LMC halo (at $\sim$60 and $\sim$100 kpc) at MW infall. The SMC's tidal radius at infall is just $\sim4$ kpc, at which point the SMC has lost two-thirds of its initial DM mass to the LMC. The distortions to the Clouds' halos produce a highly asymmetric acceleration field. Accurate orbit integration in the LMC-SMC system must account for the time-dependent shapes of both halos. The SMC-induced perturbations in the LMC DM halo resemble the MW-LMC system, and persist over multiple SMC pericenters. We conclude that 1:10 satellite-host encounters induce characteristic deformations in both DM halos across host-mass scales, with implications for merger rates and tests of DM models.