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Using N-body simulations of the Milky Way interacting with a satellitesimilar to the Sagittarius dwarf galaxy, we quantitatively analyse the verticalresponse of the Galactic disc to the satellite's repeated impacts. Weapproximate the vertical distortion of the Galactic disc as the sum of thefirst three Fourier azimuthal terms m = 0, 1 and 2, and observe their evolutionin different dynamical regimes of interaction. After the first interaction, them=0 term manifests itself as outgoing ring-like vertical distortions. The m=1term (S-shape warp) is prograde when the impacts of the satellite are morefrequent, or in general close to an interaction, whereas it is slowlyretrograde 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 thatthe vertical response of the disc can be recovered in an unbiased way using theinstantaneous positions and velocities of stars in a limited volume of theGalactic disc, analogous to real data, and that the measured vertical patternspeeds have a constraining power in the context of a Milky Way-satelliteinteraction.

Measuring the vertical response of the Galactic disc to an infalling satellite