A Simulation Based Inference Approach to the Dynamics of the MW-LMC System -- Validation

TL;DR

This paper presents the first application of Simulation-Based Inference (SBI) to the Milky Way–Large Magellanic Cloud system, aiming to infer key parameters (MW mass $M_{200,\mathrm{MW}}$, LMC mass $M_{\mathrm{LMC}}$, and dynamical-friction strength $\lambda_{\mathrm{DF}}$) from the reflex motion of the Galactic halo. By generating a large library of 128,000 rigid MW–LMC simulations and using a Masked Autoregressive Flow, the authors obtain amortised posterior distributions that robustly recover true LMC masses across rigid, deforming, and cosmological analogues when reflex-motion observables ($v_{travel}$, $l_{apex}$, $b_{apex}$) are provided. Diagnostics including coverage tests, posterior predictive checks, and train–test splits demonstrate well-calibrated, unbiased posteriors and reasonable generalisation. The framework enables rapid inference that can scale to higher-fidelity simulations and observational data, with implications for constraining both MW and LMC properties and understanding the MW’s reflex motion dynamics.

Abstract

The infall of the LMC into the Milky Way (MW) has generated dynamical disequilibrium throughout the MW. The interaction has displaced the MW's centre of mass, manifesting as an apparent 'reflex motion' in velocities of outer halo stars. Often, expensive high fidelity MW--LMC simulations are required to model these effects, though the range of model parameter spaces can be large and complex. We investigate the ability of lower fidelity, rigid MW-LMC simulations to reliably infer the model parameters of higher fidelity N-body and hydrodynamical cosmological zoom-in MW--LMC simulations using a Simulation-Based Inference (SBI) approach. We produce and release a set of 128,000 MW--LMC rigid potentials, with stellar haloes evolved to present-day, each adopting a unique combination of model parameters including the MW mass, the LMC mass and the dynamical friction strength. For these simulation parameters, we use SBI to find their posterior distributions. We find that our SBI framework trained on rigid MW--LMC simulations is able to correctly infer the true simulation LMC mass within a $1σ$ confidence interval from both N-body and cosmological simulations when knowledge of the induced MW reflex motion is provided as data. This motivates future applications of the presented SBI framework to observational data, which will help constrain both MW and LMC properties, as well as the dynamics of the MW's reflex motion.

Figures (7)

• Figure 1: Validation on a rigid MW--LMC model: The joint, and individual, posterior distributions for MW mass, LMC mass and dynamical friction strength when there is knowledge of the LMC present-day position, velocity and the reflex motion parameters (purple). We also show the parameter prior distributions in grey. For the 1D posterior panels we show the $16^{\rm th}$ and $84^{\rm th}$ percentiles as shaded regions. The yellow square/lines represent the true values from the randomly selected rigid MW--LMC simulation from our larger simulation sample. The reflex motion parameters $v_\mathrm{travel}, l_\mathrm{apex}, b_\mathrm{apex}$ break model parameter degeneracies to add constraining power, particularly in the LMC mass and dynamical friction strength. The all-sky projection displays the average solar corrected radial velocity, $v_{\rm GSR}$, for all stellar halo particles beyond $50\,\rm kpc$. The net signal across the entire sky is subtracted. The pink cross denotes the reflex motion apex for this simulation. The past orbit of the LMC in this potential is shown as the black dashed line. Orbits computed using posterior samples for the masses and dynamical friction strength, for fixed LMC present-day conditions, are shown as the grey shaded region.
• Figure 2: Validation on a deforming MW--LMC models: The joint, and individual, posterior distributions for MW mass, LMC mass and dynamical friction strength when there is knowledge of the LMC present day position, velocity and the reflex motion parameters (purple). We also show the parameter prior distributions in grey. For the 1D posterior panels we show the $16^{\rm th}$ and $84^{\rm th}$ percentiles as shaded regions. The yellow squares/lines represent the true values from the fiducial deforming simulation of Garavito-Camargo2019. The reflex motion parameters $v_\mathrm{travel}, l_\mathrm{apex}, b_\mathrm{apex}$ break model parameter degeneracies to add constraining power, particularly in the LMC mass. The all-sky projection displays the average solar corrected radial velocity, $v_{\rm GSR}$, for all stellar halo particles beyond $50\,\rm kpc$. The net signal across the entire sky is subtracted. The pink cross denotes the reflex motion apex for this simulation. The past orbit of the LMC in this potential is shown as the black dashed line. Orbits computed using posterior samples for the masses and dynamical friction strength, for fixed LMC present-day conditions, are shown as the grey shaded region.
• Figure 3: Comparison of the true and inferred infall LMC masses: We compare the simulation truth and returned SBI posterior LMC mass for all of the MW--LMC deforming simulations in Garavito-Camargo2019. We show the $16^{\rm th} - 84^{\rm th}$ percentiles of the LMC mass posteriors as error bars. For all deforming MW--LMC simulations except the most massive LMC, the true and SBI returned LMC masses are consistent, i.e., they overlap on the 1:1 dashed grey line, within the $1\,\sigma$ confidence interval. Additionally, we show the re-weighted SBI masses, which account for any biases in the choice of the LMC mass prior, as the fainter points and errors. We colour each point by the measured simulation travel velocity to demonstrate its expected increase with increasing LMC mass.
• Figure 4: Validation on a cosmological MW--LMC analogue: The joint, and individual, posterior distributions for MW mass, LMC mass and dynamical friction strength when there is knowledge of the LMC present day position, velocity and the reflex motion parameters (purple). We also show the parameter prior distributions in grey. For the 1D posterior panels we show the $16^{\rm th}$ and $84^{\rm th}$ percentiles as shaded regions. The yellow squares/lines represent the true values of m12b's MW and LMC analogue from the FIRE latte project Wetzel2023. The all-sky projection displays the average solar corrected radial velocity, $v_{\rm GSR}$, for all stellar halo particles beyond $50\,\rm kpc$. The net signal across the entire sky is subtracted. The pink cross denotes the reflex motion apex for this simulation. The past orbit of the LMC in this potential is shown as the black dashed line. Orbits computed using posterior samples for the masses and dynamical friction strength, for fixed LMC present-day conditions, are shown as the grey shaded region.
• Figure 5: Tests of Accuracy with Random Points: This diagnostic check acts as a coverage probability test. The probability of true values in the appropriate credible intervals matches the expected coverage probability. A bootstrapped $2\sigma$ uncertainty is shown as the shaded region. This validates our SBI posterior estimation such that the posterior is representative of the probability that each of our model parameters has some true value.