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The vertical distribution of stars in the solar neighbourhood is not inequilibrium but contains a wave signature in both density and velocity spaceoriginating from a perturbation. With the discovery of the phase-space spiralin Gaia data release 2, determining the origin of this perturbation has becomeeven more urgent. We develop and test a fast method for calculating theperturbation from a passing satellite on the vertical component of a part of adisc galaxy. This fast method allows us to test a large variety of possibleperturbations to the vertical disc very quickly. We apply our method to therange of possible perturbations to the solar neighbourhood stemming from therecent passage of the Sagittarius dwarf galaxy (Sgr), varying its mass, massprofile, and present-day position within their observational uncertainties, andits orbit within different realistic models for the Milky Way's gravitationalpotential. We find that we are unable to reproduce the observed asymmetry inthe vertical number counts and its concomitant breathing mode in velocity spacefor any plausible combination of Sgr and Milky-Way properties. In all cases,either the amplitude or the perturbation wavelength of the number-countasymmetry and of the oscillations in the mean vertical velocity produced by thepassage of Sgr is in large disagreement with the observations from Gaia DR2. Weconclude that Sgr cannot have caused the observed oscillations in the verticaldisc or the Gaia phase-space spiral.

Did Sgr cause the vertical waves in the solar neighbourhood?