Unveiling Orbital Chaos: The Wild Heart of Fuzzy Dark Matter Structures

In this paper we study the behavior of test particles on top of a galactic-type of Fuzzy Dark Matter (FDM) structure, characterized by the core-halo density profile found in simulations. Our workhorse structure is an anisotropic, time-dependent, virialized core-tail FDM clump resulting from a multicore merger. For our analysis we allow this structure to keep evolving, which implies that the core oscillates and accretes matter from the halo, while the halo dynamics is dominated by its characteristic high kinetic energy. On top of this time-dependent structure that in turn has a time-dependent gravitational potential, we solve the motion equations of test particles with initial conditions associated to circular orbits at different radii. Our results indicate that: 1) no trajectory remains circular, 2) the trajectories are sensitive to initial conditions and 3) the departure of initially near trajectories has always a positive Lyapunov exponent. A qualitative result is that the motion of test particles is more erratic with a bigger Lyapunov exponent within and near the core than in the halo region, which can be understood in terms of the random motion of the core within the core-halo structure. We expect these results warn on the importance of the anisotropic and time-dependent nature of FDM clumps when studying the motion of test particles.