WaveDM.jl: An Adaptable Simulation Framework for Dynamics of Baryonic and Wave Dark Matter on Galaxy Scales

arXiv:2606.25026 · astro-ph.GA · Submitted 2026-06-23 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "WaveDM.jl: An Adaptable Simulation Framework for Dynamics of Baryonic and Wave Dark Matter on Galaxy Scales".

Jocelyn: The gist: WaveDM.jl presents an open-source Julia package for high-performance simulations of wave dark matter dynamics on galaxy scales,

Vera: First, who's behind it and why it matters.

Paper summary: Vera: We talked about how this WaveDM.jl package aims to unify several different tools into one accessible framework for simulating wave dark matter on galaxy scales.

Jocelyn: Specifically, the paper introduces this framework which solves the time-dependent Schrödinger–Poisson equation using a pseudo-spectral Fourier method, and it connects that solver directly to N-body gravitational force solvers.

Subrahmanyan: The authors are showing how you can evolve wave dark matter dynamics alongside baryonic components in galaxy simulations simultaneously. This is key because it lets you see how the two interact dynamically on these scales.

Vera: They present a unified framework that supports multi-level parallelization, meaning it can scale from a single node up to multi-node computing environments without requiring huge code changes for the user.

Jocelyn: They also provide specialized tools for users, like initial condition generators and trajectory lookback capabilities, which makes setting up these simulations much easier.

Subrahmanyan: What's significant is that they address the gap where existing wave CDM simulation packages lack a unified framework that combines accessibility, performance, and those specialized tools needed specifically for galaxy-scale studies.

Conclusion: Vera: So, to wrap up this paper on "WaveDM.jl: An Adaptable Simulation Framework for Dynamics of Baryonic and Wave Dark Matter on Galaxy Scales", it’s a package that takes the complex physics of wave dark matter and makes it accessible with high performance.

Jocelyn: The title itself suggests adaptability, which is really what this framework delivers by unifying different parallelization strategies into one workflow.

Subrahmanyan: It means researchers can use this to study the interaction between dark matter waves and the visible matter in a way that scales across different computing setups, from local clusters to larger simulations.

Vera: For someone just listening, it means there’s now a more unified way to tackle these complex simulations that bridges the gap between pure theoretical physics and practical large-scale computational work.

Run-Yu Meng, Xiao-Bo Dong

Yunnan Astronomical Observatory · University of Chinese Academy of Sciences

astro-ph.GA

Submitted: 2026-06-23

Updated: 2026-10-13

Comments: Accepted. Comments welcome

DOI: 10.1088/1674-4527/ae9042

Code: https://github.com/JuliaAstroSim/WaveDM.jl

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: The gist: WaveDM.jl presents an open-source Julia package for high-performance simulations of wave dark matter dynamics on galaxy scales, integrating an SPE solver with N-body gravitational methods

Key concepts

Wave Dark Matter (Fuzzy CDM): This concept describes dark matter as ultralight bosons with very small masses, typically in the range of $10^{-23}$ to $10^{-20}$ eV. Because these particles are so light, their de Broglie wavelength can span astrophysical scales within galactic halos, leading to unique phenomena like solitonic cores and wave-like fluctuations.
Gross–Pitaevskii Equation (GPE): The GPE is the governing equation that describes the evolution of the macroscopic wavefunction $\psi(r, t)$, which acts as an order parameter for a Bose-degenerate bosonic system. It is coupled self-consistently with gravity, defining how the wave dark matter field evolves over time within a gravitational potential.
Split-Step Fourier Method: This is the numerical technique used to solve the time-dependent Schrödinger--Poisson equation. It works by breaking down the complex evolution operator into two simpler, exactly solvable parts—a potential step and a kinetic step—which are then applied sequentially in a 'kick-drift-kick' scheme for efficient simulation.

Terminology

Adaptability — 1× in this paper · explained in 1 episode
Generator — 1× in this paper · explained in 2 episodes
Modular Architecture — 1× in this paper · explained in 4 episodes

Summary

The gist: WaveDM.jl presents an open-source Julia package for high-performance simulations of wave dark matter dynamics on galaxy scales, integrating an SPE solver with N-body gravitational methods to simultaneously evolve wave dark matter and baryonic components<ref:2606.25026#pg2>.

Theoretical Framework

Fuzzy cold dark matter (also called wave CDM) describes dark matter as ultralight bosons with masses typically in the range ma ∼ 10−23 –10−20 eV<ref:2606.25026#pg2>. For such small particle masses, the de Broglie wavelength, λdB ≡ h/(mav), can reach astrophysical scales in galactic halos<ref:2606.25026#pg2>. This leads to phenomena absent in conventional particle CDM, including solitonic cores presumably supported by quantum pressure, granules mainly due to wave interference, and wave-like halo fluctuations<ref:2606.25026#pg2>. The dynamics of a highly Bose-degenerate bosonic system can be well described by a single complexvalued macroscopic wavefunction ψ(r, t), which plays the role of the order parameter<ref:2606.25026#pg2>. The evolution of the order parameter is governed by the well-known Gross–Pitaevskii equation (GPE)<ref:2606.25026#pg2>.

Governing Equations and Potentials

The governing equation of ψ(r, t), namely GPE, is coupled self-consistently with the Poisson equation of gravity in the DM halos<ref:2606.25026#pg2>. The Madelung transformation provides a hydrodynamic representation of the SPE by expressing ψ in polar form as ψ(r, t) = r−1ρ(r, t)e(iS(r,t)/ħ)<ref:2606.25026#pg2>. This yields the velocity field u(r, t) = 1/m∇S(r, t), which is irrotational<ref:2606.25026#pg2>. The quantum version of the generalized Bernoulli equation for unsteady flows is ∂S/∂t + m2u2 + mΦtotal + Q = 0<ref:2606.25026#pg2>. The Bohm potential Q accounts for quantum effects, given by Q = −ħ2/4m∇2ρ/ρ − 1/2(∇ρ)2/ρ2<ref:2606.25026#pg2>. The generalized form of the nonlinear Schrödinger equation supported by WaveDM.jl is i∂ψ/∂t = −1/2∇2ψ + V(r, t, ψ)ψ<ref:2606.25026#pg2>. The potential V can be local, such as the Kerr-type nonlinearity V = κψ2, or nonlocal, written as V(r, t) = ∫U(r − r′)ψ(r', t)2d3r'<ref:2606.25026#pg2>.

Numerical Methods and Architecture

WaveDM.jl employs a pseudo-spectral split-step Fourier method to simulate wave dark matter dynamics, decomposing the evolution operator into two exactly solvable components<ref:2606.25026#pg2>. The computational sequence at each timestep involves a kick-drift-kick scheme where the wavefunction evolves according to ψ(r, t + ϵ) ≈ e(ϵ/2 Nˆe(iϵDˆe(iϵNˆψ(r, t))<ref:2606.25026#pg2>. The Fourier transforms F and F−1 are implemented using the fast Fourier transform (FFT) algorithm, which provides O(N log N) complexity for grids of size N<ref:2606.25026#pg2>. The simulation uses a uniform Cartesian grid with Nx × Ny × Nz points<ref:2606.25026#pg2>.

Baryonic Physics and Parallelization

WaveDM.jl supports the optional baryonic physics module (AstroNbodySim.jl) which supports both particle-based (N-body) and mesh-based treatments<ref:2606.25026#pg2>. Users can choose between modes such as:mesh,:particles static, and:particles dynamic<ref:2606.25026#pg2>. The N-body force calculations utilize algorithms like::DirectSum with O(N2) complexity or::Tree with O(N log N) complexity<ref:2606.25026#pg2>. The framework utilizes a multi-level parallel framework that combines multi-threading, distributed-memory, and GPU acceleration<ref:2606.25026#pg2>.

Galaxy Simulation Toolbox and Diagnostics

The galaxy simulation toolbox provides trajectory lookback, tidal force calculations, logging, real-time visualization (AstroPlot.jl), and post-processing tools<ref:2606.25026#pg2>. Initial conditions are generated by AstroIC.jl, which supports sampling arbitrary density distributions from user-defined functions<ref:2606.25026#pg2>. Criteria for three stationary states include overall energy terms (K, V, Q), mass-fraction radii to diagnose radial stationarity, and velocity-dispersion profiles to diagnose Quasi-Stationary States (QSS)<ref:2606.25026#pg2>. The virial theorem at virial equilibrium states that 2K + 2Q + V = 0<ref:2606.25026#pg2>.

Convergence and Applications

Systematic convergence tests assess sensitivity to spatial resolution ∆x, domain size L, timestep ∆t, and initial condition parameters<ref:2606.25026#pg2>. For instance, finer grids (0.75∆x) resolve interference patterns more accurately while leaving the overall halo structure unchanged<ref:2606.25026#pg2>. The generalized nonlinear Schrödinger equation framework enables applications to nonlinear optical propagation and dynamical processes of ultracold atoms<ref:2606.25026#pg2>. WaveDM.jl is open source and available on https://github.com/JuliaAstroSim/WaveDM.jl<ref:2606.25026#pg2>.

Summary

WaveDM.jl is an open-source package for simulations of wave dark matter dynamics on galactic scales, integrating an SPE solver with N-body gravitational methods to simultaneously evolve wave dark matter and baryonic components<ref:2606.25026#pg2>. Its design philosophy centers on extensibility and adaptability, providing a unified framework that unifies shared-memory, distributed-memory, and GPU execution<ref:2606.25026#pg2>. The package offers three key capabilities: simultaneous evolution of wave dark matter and baryonic components, multi-level parallel execution across diverse computing environments, and a dedicated galaxy-simulation toolbox<ref:2606.25026#pg2>.

How it works

The core simulation involves solving the time-dependent Schrödinger–Poisson equation (SPE) using a second-order split-step Fourier method<ref:2606.25026#pg2>. This method decomposes the evolution operator into two exactly solvable components, and implements a second-order symmetric “kick-driftkick” time-integration scheme<ref:2606.25026#pg2>. The computational sequence at each timestep involves a first half potential kick, a full kinetic drift in Fourier space, an gravitational potential update from the density field, and a second half potential kick<ref:2606.25026#pg2>.

Key Features

The package integrates an SPE solver with N-body gravitational methods within a multi-level parallel framework<ref:2606.25026#pg2>. It supports simultaneous evolution of wave dark matter and baryonic components, with support for time-dependent tidal forces from host galaxies and perturbers<ref:2606.25026#pg2>. The framework allows users to choose parallelization strategies in terms of their scientific purposes and available computing resources<ref:2606.25026#pg2>.

Future Development

Planned improvements include incorporating a smoothed-particle hydrodynamics (SPH) solver for more realistic modeling of gaseous components, implementing adaptive timestepping based on the minimum de Broglie wavelength across the simulation domain, and supporting MPI as an alternative communication backend<ref:2606.25026#pg2>. The framework is also designed to be extensible by allowing users to add new physical models through well-defined interfaces<ref:2606.25026#pg2>.

Cross-Disciplinary Potential

The generalized nonlinear Schrödinger equation framework enables applications to other fields, specifically modeling nonlinear optical propagation and dynamical processes of ultracold atoms<ref:2606.25026#pg2>. This makes WaveDM.jl a general-purpose framework for various nonlinear Schrödinger systems, enabling inter-disciplinary studies among astrophysics, nonlinear optics, and condensed-matter physics<ref:2606.25026#pg2>.

Summary

WaveDM.

Improvements for AI systems

Bold header: Unified High-Performance Simulation Framework for Wave Dark Matter Dynamics

This framework can simultaneously evolve wave dark matter and baryonic components using a unified workflow that scales from single-node to multi-node computing environments without requiring major code changes.

Bold header: Multi-Level Parallel Execution for Scalability

The system can leverage shared-memory, distributed-memory, and GPU execution within a multi-level parallelization framework, enabling efficient scaling for tasks like the FFT solver and Nbody force calculations.

Bold header: Specialized Galaxy Simulation Toolbox

The improved AI system can perform complex astrophysical analyses using a dedicated toolbox that includes features like trajectory lookback, tidal force calculations, logging, real-time visualization, allowing users to study phenomena such as the effect of the LMC perturbations on satellite orbits.

Bold header: Resolution-Aware Initial Condition Generation

The AI can generate initial conditions by sampling arbitrary density distributions from user-defined functions, including models like the generalized Navarro-Frenk-White (gNFW) profile, ensuring that spatial resolution respects constraints such as ∆x ≤ λdB/3 for resolving quantum oscillations.

Bold header: Quasi-Stationary State Diagnostics

The system can diagnose the dynamical state of simulated halos by applying criteria derived from the paper, including checking if the kinetic and potential energies satisfy the virial relation or monitoring mass-fraction radii to diagnose radial stationarity.

Abstract

We present WaveDM. jl, an open-source Julia package for high-performance simulations of wave dark matter dynamics on galaxy scales, with a design philosophy centered on extensibility and adaptability. The code solves the time-dependent Schrödinger--Poisson equation (SPE) using a pseudo-spectral Fourier method. The spectral solver is tightly integrated with N-body gravitational force solvers, enabling simultaneous evolution of wave dark matter and baryonic components in galaxy-scale simulations. WaveDM. jl unifies shared-memory, distributed-memory, and GPU execution within a multi-level parallelization framework, enabling the same computational workflow to scale from single-node to multi-node computing environments without requiring major code changes. To further facilitate user-friendly galaxy-scale simulations, the package provides a dedicated toolbox that integrates flexible initial condition generators, trajectory lookback, tidal force calculations, and real-time visualization. Beyond astrophysical applications, the code's modular architecture and general nonlinear Schrodinger framework enable cross-disciplinary studies such as nonlinear optics and cold-atom physics. The code is open source and available on https://github. com/JuliaAstroSim/WaveDM. jl.