Oscillations and Random Walk of the Soliton Core in a Fuzzy Dark Matter
  Halo
  A Fuzzy Dark Matter (FDM) halo consists of a soliton core close to the center
and an NFW-like density profile in the outer region. Previous investigations
found that the soliton core exhibits temporal oscillations and random walk
excursions around the halo center. Analyzing a set of numerical simulations, we
show that both phenomena can be understood as the results of wave interference
-- a suitable superposition of the ground (solitonic) state and excited states
in a fixed potential suffices to account for the main features of these
phenomena. Such an eigenmode analysis can shed light on the evolution of a
satellite halo undergoing tidal disruption. As the outer halo is stripped away,
reducing the amplitudes of the excited states, the ground state evolves
adiabatically. This suggests diminished soliton oscillations and random walk
excursions, an effect to consider in deducing constraints from stellar heating.
