Construction of wave dark matter halos: Numerical algorithm and analytical constraints

We present a wave generalization of the classic Schwarzschild method for constructing self-consistent halos-such a halo consists of a suitable superposition of waves instead of particle orbits, chosen to yield a desired mean density profile. As an illustration, the method is applied to spherically symmetric halos. We derive an analytic relation between the particle distribution function and the wave superposition amplitudes and show how it simplifies in the high-energy (WKB) limit. We verify the stability of such constructed halos by numerically evolving the Schrodinger-Poisson system. The algorithm provides an efficient and accurate way to simulate the time-dependent halo substructures from wave interference. We use this method to construct halos with a variety of density profiles, all of which have a core from the ground-state wave function, though the core-halo relation need not be the standard one.

Automated summary

We present a wave-based method for constructing self-consistent halos, which uses wave superposition instead of particle orbits to achieve the desired density profile. The stability of the constructed halos is verified through numerical evolution, and an efficient and accurate way to simulate the time-dependent substructures of dark matter halos is provided.