Machine Learning the Dark Matter Halo Mass of the Milky Way

TL;DR

This work tackles the longstanding challenge of constraining the Milky Way's dark matter halo mass by training deep neural networks to map observable satellite dynamics and environmental measures to host halo mass. The method avoids dynamical-equilibrium assumptions and the requirement that nearby galaxies be bound satellites, instead leveraging a flexible input set that includes neighboring halos' orbits and the largest satellite’s properties, with forward-modeled observational errors. The preferred result from ESMDPL with UM-SAGA and 25 neighboring halos yields $\log_{10}(M_\mathrm{vir}/M_\odot) = 12.20^{+0.163}_{-0.138}$ (and $\log_{10}(M_{200c}/M_\odot) = 12.14^{+0.163}_{-0.138}$), with RMSE around $0.16$ dex, illustrating reduced uncertainties relative to some prior approaches while accounting for selection effects. The study demonstrates a versatile framework for MW-mass inference and outlines clear paths to extend the technique to Andromeda and to predict additional halo properties such as concentration and assembly history.

Abstract

Although numerous dynamical techniques have been developed to estimate the total dark matter halo mass of the Milky Way, it remains poorly constrained, with typical systematic uncertainties of 0.3 dex. In this study, we apply a neural network-based approach that achieves high mass precision without several limitations that have affected past approaches; for example, we do not assume dynamical equilibrium, nor do we assume that neighboring galaxies are bound satellites. Additionally, this method works for a broad mass range, including for halos that differ significantly from the Milky Way. Our model relies solely on observable dynamical quantities, such as satellite orbits, distances to larger nearby halos, and the maximum circular velocity of the most massive satellite. In this paper, we measure the halo mass of the Milky Way to be log_10 M_vir / M_Sun = 12.20^{+0.163}_{-0.138}. Future studies in this series will extend this methodology to estimate the dark matter halo mass of M31, and develop new neural networks to infer additional halo properties including concentration, assembly history, and spin axis.

Figures (14)

• Figure 1: The neural network geometry we use to predict halo masses. Input features include neighboring halos' radial distance $R$, proper motion $\mu$, and radial velocity $V_\mathrm{los}$, as well as the maximum circular velocity of the most massive satellite ($v_\mathrm{max,sat}$), the distance to the nearest larger halo ($D_\mathrm{larger}$), and the distance to the nearest halo with $\log_{10}(M_\mathrm{vir}/M_\odot)>14$ ($D_\mathrm{14}$). For all networks (regardless of the number of inputs), there are 5 hidden layers, gradually decreasing from 10 nodes to 2 nodes, with one output layer corresponding to the predicted halo mass. (Figure graphic reproduced from 2024OJAp....7E..74H.)
• Figure 2: Distribution of satellite stellar masses as a function of distance. The detectability threshold (red dashed line) represents the mass cut applied to mimic observational limitations. The shaded region corresponds to the $\pm 1\sigma$ uncertainty in the selection function.
• Figure 3: Fractional distance errors for galaxies nearby the Milky Way as a function of their heliocentric distance and their luminosity. Satellite luminosity is represented by the color bar. The fractional distance error does not exhibit a significant trend with luminosity. However, there is a selection bias, as galaxies with lower luminosity become harder to detect at larger distances.
• Figure 4: Proper motion errors for galaxies nearby the Milky Way as a function of their heliocentric distance and luminosity. There is a trend indicating that greater brightness is associated with lower error rates. However, the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) likely represent exceptions, maintaining relatively high errors (see dark blue points in bottom plot) due to their more complex structures and dynamics compared to other galaxies.
• Figure 5: The plot shows the radial velocity error for Milky Way satellite halos as a function of their luminosity and the distance to their host halo. Also there isn't a strong trend with luminosity in terms of the typical errors.