Riding the waves: The formation and evolution of vertical bending waves in Milky Way-like disc galaxies
In this thesis we study the dynamics of vertical (bending) waves in Milky Way-like disc galaxies. The main goals of the thesis are to form a coherent picture for the formation and evolution of bending waves using three-dimensional $N$-body simulations, develop tools and machinery to aid in the study of vertical waves in both simulations and astrometric surveys, and to make predictions for what we might see in the analysis of Gaia data. The hallmark simulations presented in this thesis evolve a two-component disc embedded in smooth and `clumpy' haloes, where the latter contains multiple orbiting substructure. One of our main conclusions is that vertical (bending) waves should be generic, long-lived features of massive discs that can form with and without provocation from external agents, though the predominant type of vertical wave induced by the latter is dependent on the perturber's orbital parameters. Furthermore, we find that bending is a property almost exclusive to kinematically cooler (thin disc) stellar populations. In our simulations bending waves manifest as variations in mean vertical displacement and bulk vertical motions, that together behave largely as simple monochromatic plane waves. At intermediate radii they appear as tightly wound, short-wave corrugations that match smoothly onto the warp near the edge of the disc. By way of Fourier and spectral analyses, based on classical studies of in-plane density waves and further developed in this thesis for the study of vertical waves, we find that in general the waves are a superposition of modes that comprise two main branches on the radius-rotational frequency plane. The preeminent result of this thesis is a novel sequence of events describing the life-cycle of bending waves, which involves excitation, dispersion, phase-wrapping or shearing across the disc, self-gravitating wave-like action, and disc heating. This conclusion is largely borne out of the comparison between frequency power spectra of waves in our simulations with predictions from linear perturbation theory, and suggests that the wave-like features in astrometric surveys such as Gaia may indicate the existence of long-lived modes of a dynamically active disc in addition to perturbations from recent disc-satellite interactions.