Phase wrapping of epicyclic perturbations in the Wobbly Galaxy

We use test-particle integrations to show that epicyclic motions excited by a pericentre passage of a dwarf galaxy could account for bulk vertical velocity streaming motions recently observed in the Galactic stellar disc near the Sun. We use fixed potential test-particle integrations to isolate the role of phase wrapping of epicyclic perturbations from bending and breathing waves or modes, which require self-gravity to oscillate. Perturbations from a fairly massive Sagittarius dwarf galaxy, $M_d \sim 2.5 \times 10^{10} M_\odot$, are required to account for the size of the observed streaming motions from its orbital pericentre approximately a Gyr ago. A previous passage of the dwarf through the Galactic disc approximately 2.2 Gyr ago (with a then more massive dwarf galaxy) is less effective. If phase wrapping of epicyclic perturbations is responsible for stellar streaming motions in the Galactic disc, then there should be variations in velocity gradients on scales of a few kpc in the vicinity of the Sun.