to these Galactic waves may have been observed in external galaxies. For example, corrugations in the line-of-sight velocity field have been detected in the H$\alpha$ emission of nearly face-on spiral galaxies by @alfaro2001 and @sanchez-gil2015. These wave-like variations in the vertical velocity field appear to coincide with large amplitude spiral arms. One explanation is that they arise from the interaction between spiral density waves and the galaxy’s gaseous disc via the hydraulic bore mechanism [@martos1998; @martos1999]. On the other hand, simulations show that corrugated velocity patterns in the vertical velocity field arise in both stellar and gaseous discs [@gomez2016; @gomez2017], a result that suggests a gravitational rather than hydrodynamic origin.

Departures from planarity in the disc of the Milky Way often appear as asymmetries in the phase space distribution of stars North and South of the Galactic midplane. For example, the discovery of bending waves by @xu2015 involved mapping the North-South number count asymmetry as a function of position in the disc plane. Evidence for a North-South asymmetry in the vertical profile of number counts for a $1\,{\rm kpc}$ cylinder centered on the Sun had already been found by @widrow2012 and @yanny2013 (see @ferguson2017 for a more recent confirmation using 