Coherent and incoherent structures in fuzzy dark matter halos

We show that fuzzy dark matter halos exhibit spatial differentiation in the degree of coherence of the field configuration, ranging from completely coherent in the central solitonic core to incoherent outside it, with a crossover region in between the two phases. The solitonic core is indeed a pure condensate which overlaps almost perfectly with the Penrose-Onsager mode corresponding to the largest eigenvalue of the one-particle density matrix. The virialized outer halo surrounding the core exhibits no clear coherence as a whole upon radial and temporal averaging. However, when viewed locally and for short times, it can be described as a collection of quasi-condensate lumps exhibiting locally suppressed fluctuations which can be identified with the structures commonly referred to as granules. Phase coherence across the entire halo is inhibited by a dynamically evolving tangled web of vortices separating the localized quasi-condensate regions. Moreover, the dimensionless phase-space density in the outer halo drops significantly below its value at the core. We further examine the dynamics of this spatial structure and find that the oscillations of the core can be accurately described by two time-dependent parameters respectively characterizing the size of the core, $r_c(t)$, and the crossover region, $r_t(t)$. For the halos produced in our merger simulations this feature is reflected in the (anti-)correlated oscillation of the peak value of the field configuration's power-spectrum. The turbulent vortex tangle of the virialized halo appears to reach a quasi-equilibrium state over probed timescales, with the incompressible component of the kinetic energy exhibiting a characteristic $k^{-3}$ tail in its spectrum, indicative of a $\rho\sim r^2$ density profile around the quantum vortex cores. Comparison of the peak wavenumbers in the corresponding power-spectra shows that the inter-vortex...