Construction of Wave Dark Matter Halos: Numerical Algorithm and Analytical Constraints

TL;DR

This paper introduces a wave-based numerical method to construct and analyze self-consistent dark matter halos, demonstrating its effectiveness through stability tests and diverse density profile constructions.

Contribution

It develops a novel wave superposition approach for halo modeling, deriving analytical relations and verifying stability, advancing simulation techniques for wave dark matter.

Findings

The method accurately constructs halos with various density profiles.

Constructed halos exhibit stable evolution under Schrödinger-Poisson dynamics.

Core-halo relations can differ from standard models.

Abstract

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 Schr\"odinger-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.