Bending and breathing modes of the Galactic disc

We explore the hypothesis that a passing satellite or dark matter subhalo has excited coherent oscillations of the Milky Way's stellar disc in the direction perpendicular to the Galactic mid-plane. This work is motivated by recent observations of spatially dependent bulk vertical motions within similar to 2 kpc of the Sun. A satellite can transfer a fraction of its orbital energy to the disc stars as it plunges through the Galactic mid-plane, thereby heating and thickening the disc. Bulk motions arise during the early stages of such an event when the disc is still in an unrelaxed state. We present simple toy-model calculations and simulations of disc-satellite interactions, which show that the response of the disc depends on the relative velocity of the satellite. When the component of the satellite's velocity perpendicular to the disc is small compared with that of the stars, the perturbation is pre-dominantly a bending mode. Conversely, breathing and higher order modes are excited when the vertical velocity of the satellite is larger than that of the stars. We argue that the compression and rarefaction motions seen in three different surveys are in fact breathing-mode perturbations of the Galactic disc.