A Semi-Analytic model for Effects of Fuzzy Dark Matter Granule Perturbations on Orbital Motion

TL;DR

This paper introduces a semi-analytic Fourier-based model to analyze how quantum-induced density fluctuations in fuzzy dark matter affect the orbital dynamics of subhalos, extending previous methods to individual objects and finite sizes.

Contribution

It presents a novel Fourier series framework for modeling granule perturbations on individual orbits, including finite-size effects, advancing beyond prior simulation and statistical approaches.

Findings

The model accurately captures granule-induced accelerations on subhalos.

Finite-size subhalos experience suppressed perturbations compared to point-mass approximations.

Validation confirms the model's effectiveness in representing stochastic orbital effects.

Abstract

In fuzzy dark matter scenarios, the quantum wave nature of ultralight axion-like particles generates stochastic density fluctuations inside dark matter halos. These fluctuations, known as granules, perturb the orbits of subhalos and other orbiting bodies. While previous studies have simulated these effects using N-body techniques or modeled them statistically using diffusion approximations, we propose an alternative framework based on representing the perturbations as a Fourier series with random coefficients, which can be applied to individual orbits, not just populations. We extend the model to finite-size subhalos, identifying a critical length scale below which subhalos behave as point-mass particles. In contrast, larger subhalos exhibit suppressed perturbations from granules due to their extended mass profiles. Using FDM-Simulator, we validate our finite-size model by isolating granule accelerations and confirming their statistical effects on subhalo dynamics.