A random walk model for halo triaxiality

We describe a semi-analytic model to predict the triaxial shapes of dark matter haloes utilizing the sequences of random merging events captured in merger trees to follow the evolution of each halo's energy tensor. When coupled with a simple model for relaxation toward a spherical shape, we find that this model predicts distributions of halo axis length ratios that approximately agree with those measured from cosmological N-body simulations once constrained to match the median axial ratio at a single halo mass. We demonstrate the predictive and explanatory power of this model by considering conditioned distributions of axis length ratios, and the mass dependence of halo shapes, finding these to be in good agreement with N-body results. This model provides both insight into the physics driving the evolution of halo triaxial shapes, and rapid quantitative predictions for the statistics of triaxiality connected directly to the formation history of the halo.