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ABSTRACT Our situation as occupants of the Milky Way (MW) Galaxy, bombarded by the Sagittarius dwarf galaxy, provides an intimate view of physical processes that can lead to the dynamical heating of a galactic disc. While this evolution is instigated by Sagittarius, it is also driven by the intertwined influences of the dark matter halo and the disc itself. We analyse an N-body simulation following a Sagittarius-like galaxy interacting with a MW-like host to disentangle these different influences during the stages of a minor merger. The accelerations in the disc plane from each component are calculated for each snapshot in the simulation, and then decomposed into Fourier series on annuli. The analysis maps quantify and compare the scales of the individual contributions over space and through time: (i) accelerations due to the satellite are only important around disc passages; (ii) the influence around these passages is enhanced and extended by the distortion of the dark matter halo; (iii) the interaction drives disc asymmetries within and perpendicular to the plane and the self-gravity of these distortions increase in importance with time eventually leading to the formation of a bar. These results have interesting implications for identifying different influences within our own Galaxy. Currently, Sagittarius is close enough to a plane crossing to search for localized signatures of its effect at intermediate radii, the distortion of the MW’s dark matter halo should leave its imprint in the outer disc and the disc’s own self-consistent response is sculpting the intermediate and inner disc. 

Abstract Using N-body simulations of the Milky Way interacting with a satellite similar to the Sagittarius dwarf galaxy, we quantitatively analyse the vertical response of the Galactic disc to the satellite’s repeated impacts. We approximate the vertical distortion of the Galactic disc as the sum of the first three Fourier azimuthal terms m = 0, 1 and 2, and observe their evolution in different dynamical regimes of interaction. After the first interaction, the m = 0 term manifests itself as outgoing ring-like vertical distortions. The m = 1 term (S-shape warp) is prograde when the impacts of the satellite are more frequent, or in general close to an interaction, whereas it is slowly retrograde in the most quiescent phases. The m = 2 term is typically prograde, and close to an interaction it couples with the m = 1 term. Finally, we find that the vertical response of the disc can be recovered in an unbiased way using the instantaneous positions and velocities of stars in a limited volume of the Galactic disc, analogous to real data, and that the measured vertical pattern speeds have a constraining power in the context of a Milky Way-satellite interaction.