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

TL;DR

This work tackles the problem of characterizing the Milky Way–Large Magellanic Cloud interaction by constraining the MW and LMC masses and the induced reflex motion using outer-halo kinematics. It introduces Simulation Based Inference with DELFI and normalizing-flow density estimation trained on 128,000 rigid MW–LMC simulations, forward-modeling observed velocity fields from DESI and all-sky H3+SEGUE+MagE data. The most precise results come from all-sky quadrant analyses of H3+SEGUE+MagE, yielding $M_{ m LMC}(<50\, m{kpc}) \approx 9.2^{+1.9}_{-2.3}\times10^{10} M_⊙$, $M_{ m MW}(<50\, m{kpc}) \approx 4.4^{+0.7}_{-0.7}\times10^{11} M_⊙$, and a reflex travel velocity $v_{travel} \approx 26.4^{+5.5}_{-4.4}$ km s$^{-1}$. The framework also finds the LMC’s total mass fraction to be about 10–15% of the MW, with dynamical-friction strength remaining weakly constrained. The SBI approach provides rapid, reliable constraints adaptable to future surveys, enabling refined mapping of the MW–LMC system as newer outer-halo velocity data become available.

Abstract

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.

Figures (11)

• Figure 1: Top panels: The distribution of all sources beyond a Galactocentric distance of $30 \, \rm kpc$ for the Dark Energy Spectroscopic Survey (DESI, left) and the all-sky H3+SEGUE+MagE outer halo surveys (right) in Galactic coordinates. The colour of individual sources reflects their solar corrected radial velocity, $v_{\rm GSR}$. The present-day position of the LMC is shown as the grey star along with an illustrative past orbit as the grey dashed line. The DESI northern (pink) and southern (blue) Galactic fields are shown as shaded regions. Bottom panel: The Galactocentric radial distribution of all sources between $30 - 100 \, \rm kpc$ for DESI (solid lines) and H3+SEGUE+MagE (dotted lines) contained within the DESI northern and southern Galactic fields.
• Figure 2: Panel (a): Mean radial velocity distributions, $\langle{v}_{\rm GSR} \rangle$, as a function of Galactocentric distance for the DESI sources in its northern (pink) and southern (blue) observing footprints. Panel (b): Same as the first panel for H3+SEGUE+MagE sources within the DESI survey footprints. Panel (c/d): The H3+SEGUE+MagE data divided into on-sky quadrant footprints. Panel (e): All-sky mean tangential velocity, $\langle v_{\rm t, b} \rangle$, distributions as a function of Galactocentric distance for DESI (orange), H3+SEGUE+MagE within $100\,\rm kpc$ (green) and the full H3+SEGUE+MagE datasets (purple). Points are offset in distance for improved readability. All $1\sigma$ uncertainties are determined via bootstrap resampling. There is a clear increase in $\langle v_{\rm t, b} \rangle$ with distance out to $160\,\rm kpc$ for the H3+SEGUE+MagE data.
• Figure 3: Posterior distributions - MW and LMC enclosed masses: The joint, and individual, posterior distributions for the MW and LMC masses enclosed within $50\,\rm kpc$. We show these distributions conditioned on the LMC centre present-day position & velocity, and radial and tangential velocities as data points. The open blue, green and red contours represent the posteriors conditioned using the DESI, H3+SEGUE+MagE (DESI footprint) and H3+SEGUE+MagE (Quadrants footprint) survey data, respectively. The prior distributions are shown as the filled grey contours. The contours delineate the $1\sigma$ and $2\sigma$ confidence intervals. For the 1D posterior panels we show the $16^{\rm th}-84^{\rm th}$ percentiles as shaded regions.
• Figure 4: Posterior distributions - Reflex motion velocity: The joint, and individual, posterior distributions of the Galactocentric Cartesian travel velocity components. We show these distributions conditioned on the LMC centre present-day position & velocity, and radial and tangential velocities as data points. The open blue, green and red contours represent the posteriors conditioned using the DESI, H3+SEGUE+MagE (DESI footprint) and H3+SEGUE+MagE (Quadrants footprint) survey data, respectively. The contours delineate the $1\sigma$ and $2\sigma$ confidence intervals. For the 1D posterior panels we show the $16^{\rm th}-84^{\rm th}$ percentiles as shaded regions. The measured mean and $1\sigma$ errors from Vasiliev2021, Yaaqib2024, Bystrom2025 and Chandra2025a are shown in each panel for comparison.
• Figure 5: Comparison of reflex motion constraints: The derived medians and $16^{\rm th}-84^{\rm th}$ percentiles of the magnitude of the travel velocity, $v_{\rm travel}$, for the posteriors shown in Fig. \ref{['fig4']}. The labels define the dataset used, the on-sky selection footprint used produce the constraint. The values from existing literature are shown as shaded bands Yaaqib2024Chandra2025aBystrom2025. The prior $1\sigma$ confidence interval is shown as the black dashed lines. The most precise constraint is produced by using the full depth of the H3+SEGUE+MagE dataset and dividing the binned velocity fields into four quadrants.