Disc distortion revisited

ABSTRACT We revisit the dynamics of razor-thin, stone-cold, and self-gravitating discs. By recasting the equations into standard cylindrical coordinates, the linearized vertical dynamics of an exponential disc can be followed for several giga years on a laptop in a few minutes. An initially warped disc rapidly evolves into a flat inner region and an outward-propagating spiral corrugation wave that rapidly winds up and would quickly thicken a disc with non-zero radial-velocity dispersion. The Sgr dwarf galaxy generates a similar warp in the Galactic disc as it passes through pericentre, and the warp generated by the dwarf’s last pericentre $\sim 35\, \mathrm{Myr}$ ago is remarkably similar to the warp traced by the Galaxy’s H i disc. The resemblance to the observed warp is fleeting but its timing is perfect. For the adopted parameters, the amplitude of the model warp is a factor 3 too small, but there are several reasons for this being so. The marked flaring of our Galaxy’s low-$\alpha$ disc just outside the solar circle can be explained as a legacy of earlier pericentres.