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Abstract The large-scale morphology of Milky Way (MW)–mass dark matter halos is shaped by two key processes: filamentary accretion from the cosmic web and interactions with massive satellites. Disentangling their contributions is essential for understanding galaxy evolution and constructing accurate mass models of the MW. We analyze the time-dependent structure of MW-mass halos from zoomed cosmological-hydrodynamical simulations by decomposing their mass distribution into spherical harmonic expansions. We find that the dipole and quadrupole moments dominate the gravitational power spectrum, encoding key information about the halo’s shape and its interaction with the cosmic environment. While the dipole reflects transient perturbations from infalling satellites and damps on dynamical timescales, the quadrupole—linked to the halo’s triaxiality—is a persistent feature. We show that the quadrupole’s orientation aligns with the largest filaments, imprinting a long-lived memory on the halo’s morphology even in its inner regions (∼30 kpc). At the virial radius, the quadrupole distortion can reach 1–2 times the spherical density, highlighting the importance of environment in shaping MW-mass halos. Using multichannel singular spectrum analysis, we successfully disentangle the effects of satellite mergers and filamentary accretion on quadrupole. We find that, compared to isolated MW–LMC simulations that typically use a spherical halo, the LMC-mass satellite induces a quadrupolar response that is an order of magnitude larger in our cosmological halo. This highlights the need for models that incorporate the MW’s asymmetry and time evolution, with direct consequences for observable structures such as disk warps, the LMC-induced wake, and stellar tracers—particularly in the era of precision astrometry. 

ABSTRACT Gaia Data Release 2 revealed that the Milky Way contains significant indications of departures from equilibrium in the form of asymmetric features in the phase space density of stars in the Solar neighbourhood. One such feature is the z–vz phase spiral, interpreted as the response of the disc to the influence of a perturbation perpendicular to the disc plane, which could be external (e.g. a satellite) or internal (e.g. the bar or spiral arms). In this work, we use Gaia Data Release 3 to dissect the phase spiral by dividing the local data set into groups with similar azimuthal actions, Jϕ, and conjugate angles, θϕ, which selects stars on similar orbits and at similar orbital phases, thus having experienced similar perturbations in the past. These divisions allow us to explore areas of the Galactic disc larger than the surveyed region. The separation improves the clarity of the z–vz phase spiral and exposes changes to its morphology across the different action-angle groups. In particular, we discover a transition to two armed ‘breathing spirals’ in the inner Milky Way. We conclude that the local data contain signatures of not one, but multiple perturbations with the prospect to use their distinct properties to infer the properties of the interactions that caused them. 

Abstract Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos (<10¹⁰M_⊙) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large data sets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST’s COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator of the subhalo mass function (SHMF) and place constraints on populations of lenses generated using a separate set of galaxy sources. We find that by combining our network with a hierarchical inference framework, we can both reliably infer the SHMF across a variety of configurations and scale efficiently to populations with hundreds of lenses. By conducting precise inference on large and complex simulated data sets, our method lays a foundation for extracting dark matter constraints from the next generation of wide-field optical imaging surveys.