Quantifying the Milky Way, LMC and their interaction using all-sky kinematics of outer halo stars

Abstract

The recent pericentric passage of the Large Magellanic Cloud (LMC) through the Milky Way (MW) has dislodged its centre of mass, inducing a state of dynamical disequilibrium, the reflex motion, in the kinematics of outer stellar halo stars. Using data out to distances of $160 \, \rm kpc$ from the combined H3+SEGUE+MagE outer halo survey, we constrain the mass of the MW and LMC, as well as the resulting reflex motion and the velocity anisotropy of the stellar halo. Using a suite of 32,000 rigid MW--LMC simulations, each with a MW stellar halo evolved to the present day in the combined MW--LMC potential, we perform Simulation Based Inference by training a neural posterior estimator on the means and dispersions of the radial and tangential velocities of stars from the combined H3+SEGUE+MagE outer halo sample. Relative to halo stars at $100 \, \rm kpc$, we find the magnitude of the reflex velocity to be $v_{\rm travel} = 39.4^{+7.6}_{-7.2}\,\rm km \, s^{-1}$. Simultaneously, we determine the enclosed MW mass to be $M_{\rm MW}(< 50 \, \rm kpc) = 3.63 \pm 0.16 \times 10^{11}\, \rm M_{\odot}$ and the enclosed LMC mass to be $M_{\rm LMC}(< 50 \, \rm kpc) = 9.74^{+2.07}_{-1.81} \times 10^{10}\, \rm M_{\odot}$. Our results suggest that the total LMC mass must be at least $\sim20\%$ that of the MW. The velocity anisotropy prior to the LMC's infall is constrained to be $β_0 = 0.61 \pm 0.03$. Finally, we demonstrate that failing to account for the LMC in models biases the MW mass estimate to prefer slightly more massive values.

Figures (13)

• Figure 1: Mean velocity distributions in the radial and tangential components, $\langle{v}_{\rm GSR} \rangle$ and $\langle v_{\rm t, b} \rangle$, as a function of Galactocentric distance for the H3+SEGUE+MagE data divided into on-sky quadrant footprints. Q1/2 are in the Galactic North, Q3/4 are in the Galactic South. Vertical error bars represent the $1\sigma$ uncertainties are determined via bootstrap resampling. Horizontal error bars display the bin width. Data points with increased transparency, and distinct markers, are poorly represented by simulated data counterparts.
• Figure 2: Velocity dispersions distributions in the radial and tangential components, $\langle \sigma_{{v}_{\rm GSR}} \rangle$ and $\langle \sigma_{v_{ t, b}} \rangle$, as a function of Galactocentric distance for the H3+SEGUE+MagE data divided into on-sky quadrant footprints. Q1/2 are in the Galactic North, Q3/4 are in the Galactic South. Vertical error bars represent the $1\sigma$ uncertainties are determined via bootstrap resampling. Horizontal error bars display the bin width. Data points with increased transparency, and distinct markers, are poorly represented by simulated data counterparts.
• Figure 3: The MW and LMC enclosed masses: The joint, and individual, posterior distributions for the MW and LMC masses enclosed within $50\,\rm kpc$ using data from the H3+SEGUE+MagE survey. The yellow and blue contours represent the posteriors conditioned using the means, or means and dispersions, of the stellar velocities, respectively. The red contours use the mean and dispersion data, but removing spurious data points. 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: The reflex motion velocity: The joint, and individual, posterior distributions of the Galactocentric Cartesian travel velocity components using data from the H3+SEGUE+MagE survey. The yellow and blue contours represent the posteriors conditioned using the means, or means and dispersions, of the stellar velocities, respectively. The red contours use the mean and dispersion data, but removing spurious data points. 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: Apex direction and magnitude of the reflex motion -- Top panel: A stereographic projection centred on the south galactic pole showing the apex direction of the travel velocity, $(l_{\rm apex}, b_{\rm apex})$. The red posterior contours are placed at the $40^{\rm th}$, $70^{\rm th}$, and $90^{\rm th}$ quantiles, corresponding to Gaussian-equivalent levels of $0.5 \sigma$, $1 \sigma$, and $1.5 \sigma$. The posterior distribution is conditioned on the mean and dispersion velocity data after removing spurious data points. The values from existing literature are shown as markers Vasiliev2021Yaaqib2024Chandra2025aBystrom2025. Additionally, we show the apex direction of the fiducial $N$-body simulation in Garavito-Camargo2019 as the light blue pentagon. The past LMC orbit is calculated using the best-fit values from the inference with the present-day location denoted by the black star. Lower panel: A comparison of the magnitude of the travel velocity, $v_{\rm travel}$, from the same literature values and our posterior median and $1 \sigma$ percentiles as the red line and shaded region. The prior $1\sigma$ confidence interval is shown as the grey dashed lines.