Measuring the Milky Way mass distribution in the presence of the LMC

The ongoing interaction between the Milky Way (MW) and its largest satellite - the Large Magellanic Cloud (LMC) - creates a significant perturbation in the distribution and kinematics of distant halo stars, globular clusters and satellite galaxies, and leads to biases in MW mass estimates from these tracer populations. We present a method for compensating these perturbations for any choice of MW potential by computing the past trajectory of LMC and MW and then integrating the orbits of tracer objects back in time until the influence of the LMC is negligible, at which point the equilibrium approximation can be used with any standard dynamical modelling approach. We add this orbit-rewinding step to the mass estimation approach based on simultaneous fitting of the potential and the distribution function of tracers, and apply it to two data sets with the latest Gaia EDR3 measurements of 6D phase-space coordinates: globular clusters and satellite galaxies. We find that models with LMC mass in the range $(1\!-\!2) \times 10^{11}\, \mathrm{M}_\odot$ better fit the observed distribution of tracers, and measure MW mass within 100 kpc to be $(0.75\pm 0.1)\times 10^{12}\, \mathrm{M}_\odot$, while neglecting the LMC perturbation increases it by ~15 per cent.