Effect of boundary conditions on structure formation in fuzzy dark matter

Abstract

We illustrate the effect of boundary conditions on the evolution of structure in fuzzy dark matter. Scenarios explored include the evolution of single, ground-state equilibrium solutions of the Schr\"odinger-Poisson system, relaxation of a Gaussian density fluctuation, mergers of two equilibrium configurations, and the random merger of many solitons. For comparison, each scenario is evolved twice, with isolation vs periodic boundary conditions, the two commonly used to simulate isolated systems and structure formation, respectively. Replacing isolation boundary conditions (implemented by an absorbing sponge at large radius) by periodic boundary conditions changes the domain topology and dynamics of each scenario by affecting the outcome of gravitational cooling. With periodic boundary conditions, the initial ground-state equilibrium solution and Gaussian fluctuation each evolve toward the single equilibrium solitonic core of the isolated case, but surrounded by an envelope, or tail, in which additional mass is distributed nearly uniformly, unlike the isolated versions. The case of head-on, binary merger introduces additional effects caused by the pull on the system due to the infinite network of periodic images along each axis of the domain. Adding angular momentum to this binary merger results in a tail with polynomial profile when using a periodic domain. Finally, the 3D merger of many, randomly placed solitonic cores of different mass makes a solitonic core surrounded by a tail with power-law-like profile, for periodic boundary conditions, while producing a core with a much sharper falloff in the isolated case. This suggests the conclusion of earlier work, that the ground-state equilibrium solution is an attractor for the asymptotic state, is true even in 3D and for more general circumstances than previously considered, but only if gravitational cooling is able to carry mass and energy off to infinity, which isolation boundary conditions allow, but periodic ones do not.