In the last two decades, some arguments have accumulated for a more important mass ratio of the Large Magellanic Cloud (LMC) to the Milky Way (MW) than was previously thought, of about 10% or more. This implies that the LMC has a measurable influence on the dynamics in the MW stellar halo, including both stellar densities and kinematics, as observed by Conroy et al. (2021) and Petersen et al. (2021). While this merger has been previously reproduced using N-body simulations (see, e.g., Garavito-Camargo et al., 2019), I will present the results of a recent study (Rozier et al., 2022) which aimed at modelling the merger via linear response theory. More specifically, we integrated the linearized collisionless Boltzmann-Poisson system of partial differential equations using a methodology known as the matrix method. Our results display the same large scale behaviour as state-of-the-art simulations, with a dipolar over/underdense pattern related to the reflex motion of the MW, as well as an overdense wake trailing behind the LMC. These results represent an efficient way of constraining the LMC to MW mass ratio, since this ratio is directly proportional (given the linear nature of the theory) to the amplitude of the relative density variations of the MW stellar halo, both in physical and in phase space. However, the amplitude of these variations may also depend on some model parameters, such as the structure of the MW potential (including a possible dark matter component), the initial density distribution of the stellar halo, as well as its initial internal kinematics. I will focus on the latter source of degeneracy, showing how the initial velocity anisotropy of the stellar halo impacts its response to the LMC. Interestingly enough, it appears that the physical space density of the (dipolar) reflex motion is insensitive to the stellar halo’s initial velocity anisotropy, and can therefore represent an efficient probe of the LMC to MW mass ratio.
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