Quantized Vortices in Superfluid Dark Matter

In 2015 Berezhiani & Khoury proposed a Superfluid Dark Matter (SFDM) model where dark matter condenses and forms a superfluid on galactic scales. In the superfluid state phonons interact with baryons, resulting in a behavior similar to that of Modified Newtonian Dynamics (MOND). If one assumes that the DM condensate rotates along with the galaxy, a grid of vortices should form throughout the superfluid component if the rotation is fast enough. We aim to investigate the size and impact of the vortices on surrounding baryons, and to further investigate the parameter space of the model. We also look for a possible vortex solution of the Lagrangian presented for the SFDM theory. We first take a simple approach and investigate vortex properties in a constant density DM halo, applying knowledge from condensed matter physics. We then use the zero-temperature condensate density profile as a template to vary the DM particle mass and the energy scale, $\Lambda$, of the SFDM model. Further, we attempt to find a vortex solution of the theory by extracting the Euler-Lagrange equation with respect to the modulus of the condensate wavefunction from the full relativistic SFDM Lagrangian. For the constant density approach we find that the vortices are on millimeter scale, and separated by distances $\sim0.002\,\rm{AU}$. The parameter space of the model is found to be substantial and a reduction in the DM particle mass leads to larger vortices with a higher energy. However, none of the parameter combinations explored here give both realistic values of $\Lambda$ and vortices energetic enough to have an observational impact on the galaxy as a whole. The vortex equation extracted from the Lagrangian of the model is unstable, and no solution exhibiting the standard properties of a vortex solution is found.