Methods for simulation of dark matter dynamics in cosmology

While dark matter accounts for approximately 85% of the matter content of the observable universe, its fundamental nature is one of the most important mysteries of modern physics. Many different theories of dark matter have been proposed. We are studying ultra-light dark matter, a scenario in which the dark matter particle is far lighter than any particle currently known to have a non-zero mass. The behaviour of ultra-light dark matter is governed by the “Schroedinger-Poisson equations”. We will introduce PyUltraLight, the code we have developed at the University of Auckland to solve this system of coupled partial differential equations. PyUltraLight is written in Python and can run inside a Jupyter notebook; it is currently the only freely shared, open-source Schroedinger-Poisson solver available to astrophysicists. We are now using PyUltraLight to study galaxy formation and galaxy-galaxy interactions in a universe with ultra-light dark matter. One of the main challenges we are now facing is the need to simultaneously simulate large physical volumes while resolving dynamics on small scales, e.g. in the central regions of the galaxies or the detailed dynamics of galactic mergers. Increasing spatial resolution across the whole simulation is computationally expensive and we are developing a simulation tool that uses adaptive mesh refinement (AMR), a standard technique used to tackle problems where a significant proportion of the simulation volume is empty. AMR codes allow the resolution to be increased only in the locations of greatest interest, on the basis of specified refinement criteria. We will describe the numerical methods we are now developing to simulate dark matter dynamics and discuss some recent results and future research directions.