One-Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics

TL;DR

This paper develops simplified one-dimensional models of Fuzzy Dark Matter to study structure growth and dynamics, aiming to facilitate more efficient simulations that retain key phenomenological features of the full three-dimensional models.

Contribution

It introduces two novel 1D models derived from the 3D Schrödinger-Poisson system, capturing essential FDM behaviors with reduced computational complexity.

Findings

Different transversal matter distributions affect relaxation processes.

Asymptotic states depend on initial conditions and model specifics.

Models are relevant for interpreting low-dimensional FDM simulations and experiments.

Abstract

This paper investigates the feasibility of simulating Fuzzy Dark Matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in $(1+1)$-dimensional space time, that - under well controlled system conditions - is capable of realizing important aspects of the full-fledged $(3+1)$-FDM phenomenology by means of one-dimensional analogues. Based on the coupled, nonlinear and nonlocal $(3+1)$-Schr\"odinger-Poisson equation under periodic boundary conditions, we derive two distinct one-dimensional models that differ in their transversal matter distribution and consequently in their nonlocal interaction along the single dimension of interest. We show that these discrepancies change the relaxation process of initial states as well as the asymptotic, i.e., thermalized and virialized, equilibrium state. Our investigation includes the dynamical evolution of artificial initial conditions for non-expanding space, as well as cosmological initial conditions in expanding space. The findings of this work are relevant for the interpretation of numerical simulation data modelling nonrelativistic fuzzy cold dark matter in reduced dimensions, in the quest for testing such models and for possible laboratory implementations of them.