On the stability of soliton cores of ultra-light axion-like dark matter halos

Abstract

In this thesis, I numerically investigate interactions involving dark matter halos surrounding dwarf galaxies in the case where dark matter is primarily comprised of ultra-light particles. Due to the extremely light masses of these particles (on the order of 10−22 eV), their typical de Broglie wavelengths will be on the order of kiloparsecs. As a result it becomes necessary to calculate the dynamics of these dark matter halos using the Schrodinger-Poisson equation, in which case wave-like effects such as interference and an effective ‘quantum pressure’ can arise. The simplest form of a stable dark matter halo in this model is the soliton solution of the Schrodinger-Poisson equation, for which interference effects have been previously explored. I have designed Python code to numerically solve the Schrodinger-Poisson equation using the Split-Step Fourier method, and I use this to study the evolution of these solitons. I focus on the stability of dwarf galaxy-sized dark matter solitons interacting with the potentials of much larger galaxies. These solitons represent a ‘best-case’ scenario for stability. That is, configurations that are not stable for a soliton will not be stable for a more complex object. Studies of the stability of these objects could potentially be compared to observations, placing constraints on the mass of potential ultra-light dark matter candidates, such as axions. Moreover, they serve as simple objects with which to test the code I have developed.