Orbits and Vorticity in Quantum Wave Dark Matter

The nature of the dark matter (DM) in the Universe remains one of the greatest open problems in contemporary science. While cosmological observations have determined the cosmic energy density in DM with high precision, its particle nature is still unknown. Standard DM candidates are weakly-interacting, massive particles from extensions to the standard model of particle physics, which give rise to what has become the standard collisionless cold dark matter (CDM) model. This model has been successful so far to explain observations on large cosmic scales. However, its predictions have failed on the smaller spatial scales of dwarf galaxies, despite the fact that the latter are dominated by DM. Moreover, CDM predicts a lot of small-scale substructure within large galaxies which should have been indirectly confirmed by now, using observations. These discrepancies constitute one main reason why the scientific community has embarked on studying alternative DM models. In this project, we will analyse the properties of a certain class of DM candidates, namely quantum wave dark matter (QDM). Here, the behavior of DM is akin to quantum- mechanical systems, albeit on galactic scales. We will investigate the dynamics of QDM within galaxies, at the level of individual orbis ("quantum orbits"), but also collective phenomena such as the formation of "vortices", and modelling of quantum turbulence. The dynamics of QDM - and for that matter any DM - affects via gravity the motions of visible matter, such as stars and gas, within galaxies. Therefore, we can make predictions concerning the different effects upon that visible matter that arise due to the different dynamics between CDM and QDM models. This information can eventually be used by astronomers to compare our theoretical predictions with galaxy observations, in hopes to clarify whether QDM might be a possible resolution of the DM problem in the Universe. The insights that we gain will also help to deepen our understanding of quantum systems under self-gravity, and touch upon fundamental questions in physics. We will pursue several methodological approaches in our dynamical modelling, though they can be formulated within a unified mathematical framework. We will be mostly concerned with analytical calculations, but numerical simulations of involved system configurations will be also performed.