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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 Measurements of the accelerations of stars enabled by time-series extreme-precision spectroscopic observations, pulsar timing, and eclipsing binary stars in the solar neighborhood offer insights into the mass distribution of the Milky Way that do not rely on traditional equilibrium modeling. Given the measured accelerations, we can determine a total mass density and infer the amount of dark matter (DM) by accounting for the mass in stars, gas, and dust. Leveraging FIRE-2 simulations of Milky Way–mass galaxies we compare vertical acceleration profiles between cold DM (CDM) and self-interacting DM (SIDM) with a constant cross section of 1 cm²g⁻¹across three halos with diverse assembly histories. Notably, significant asymmetries in vertical acceleration profiles near the midplane at fixed radii are observed in both CDM and SIDM, particularly in halos recently affected by mergers with satellites of Sagittarius/SMC-like masses or greater. These asymmetries offer a unique window into exploring the merger history of a galaxy. We show that SIDM halos manifest a more oblate shape and consistently exhibit higher local stellar and DM densities and steeper vertical acceleration gradients, up to 10%–30% steeper near the solar neighborhood. However, similar magnitude changes can arise from azimuthal variations in the baryonic components at a fixed radius and external influences like mergers, making it difficult to distinguish between CDM and SIDM using acceleration measurements in a single galaxy.