LMC-induced Perturbations in the Milky Way Halo II: Bridging Field-level Inference and Summary-level Simulation-Based Inference
The gravitational interaction between the Milky Way (MW) and the Large Magellanic Cloud (LMC) drives the outer halo into dynamical disequilibrium, imprinting the masses and structural parameters of both galaxies onto the 6D phase-space distribution of halo tracers. This signal has been characterised with summary statistics ranging from low-order velocity moments to basis function expansions, yet how much information these summaries discard, and whether they are complementary, remains unclear. We address these questions by comparing a likelihood of the halo phase-space distribution (field-level) with physically interpretable summaries for constraining $(M_{\mathrm{MW}}, M_{\mathrm{LMC}}, c, q)$, where $c$ and $q$ are the MW halo concentration and flattening. A Conditional Flow Matching (CFM) model trained on the HaloDance $N$-body suite provides an exact likelihood at a held-out fiducial point; for 5,000 tracers in $30$--$120$~kpc it tightens marginal constraints by factors of $2.5$--$9.9$ over an all-sky velocity-moment forecast. To narrow this gap, we construct four parameter-sensitive summaries via BFE+MOPED that capture the angular structure of the halo density and velocity and contain information complementary to the velocity moments. Combining the two sets of summaries tightens the marginal constraints by up to $15$ per cent relative to the angular summaries alone, and by $30$--$71$ per cent relative to the velocity moments alone, although the resulting constraints remain $1.3$--$2.9$ times broader than those from the full phase-space benchmark. We thus establish a physically interpretable summary-level route for applying this inference pipeline to future observations, while the field-level benchmark measures the information available for further improvement.