An adaptively refined phase-space element method for cosmological simulations and collisionless dynamics

Abstract

N-body simulations are essential for understanding the formation and evolution of structure in the Universe. However, the discrete nature of these simulations affects their accuracy when modelling collisionless systems. We introduce a new approach to simulate the gravitational evolution of cold collisionless fluids by solving the Vlasov-Poisson equations in terms of adaptively refineable "Lagrangian phase space elements". These geometrical elements are piecewise smooth maps between Lagrangian space and Eulerian phase space and approximate the continuum structure of the distribution function. They allow for dynamical adaptive splitting to accurately follow the evolution even in regions of very strong mixing. We discuss in detail various one-, two- and three-dimensional test problems to demonstrate the performance of our method. Its advantages compared to N-body algorithms are: i) explicit tracking of the fine-grained distribution function, ii) natural representation of caustics, iii) intrinsically smooth gravitational potential fields, thus iv) eliminating the need for any type of ad-hoc force softening. We show the potential of our method by simulating structure formation in a warm dark matter scenario. We discuss how spurious collisionality and large-scale discreteness noise of N-body methods are both strongly suppressed, which eliminates the artificial fragmentation of filaments. Therefore, we argue that our new approach improves on the N-body method when simulating self-gravitating cold and collisionless fluids, and is the first method that allows to explicitly follow the fine-grained evolution in six-dimensional phase space.

19 pages, 20 figures; minor changes; matches version accepted by MNRAS

References in corpus (10)

• The Effective Field Theory of Cosmological Large Scale Structures
• Dark matter and cosmic structure
• N-body simulations of gravitational dynamics
• Environmental Dependence of Cold Dark Matter Halo Formation
• The fine-grained phase-space structure of Cold Dark Matter halos
• The ${\nu }^2$GC Simulations : Quantifying the Dark Side of the Universe in the Planck Cosmology
• An exact general remeshing scheme applied to physically conservative voxelization
• Dark Matter Caustics
• Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory
• Vlasov limit and discreteness effects in cosmological N-body simulations

Cited by in corpus (70)

• Disruption of Dark Matter Substructure: Fact or Fiction?
• The BACCO Simulation Project: Exploiting the full power of large-scale structure for cosmology
• Large-scale dark matter simulations
• Zooming in on accretion - I. The structure of halo gas
• Accurate initial conditions for cosmological N-body simulations: Minimizing truncation and discreteness errors
• Splashback Shells of Cold Dark Matter Halos
• A Deep Learning Approach to Galaxy Cluster X-ray Masses
• The outer profile of dark matter halos: an analytical approach
• Earth-mass haloes and the emergence of NFW density profiles
• An exact general remeshing scheme applied to physically conservative voxelization
• Hints against the cold and collisionless nature of dark matter from the galaxy velocity function
• ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
• Reducing Noise in Cosmological N-body Simulations with Neutrinos
• Solving the Vlasov equation in two spatial dimensions with the Schrödinger method
• What sets the central structure of dark matter haloes?
• Relativistic Interpretation of Newtonian Simulations for Cosmic Structure Formation
• General relativistic weak-field limit and Newtonian N-body simulations
• Post-collapse perturbation theory in 1D cosmology -- beyond shell-crossing
• Relativistic initial conditions for N-body simulations
• The effect of early radiation in N-body simulations of cosmic structure formation
• Phase-space structure of protohalos: Vlasov versus Particle-Mesh
• Voids in cosmological simulations over cosmic time
• The Limited Accuracy of Linearized Gravity
• Measuring the Tidal Response of Structure Formation: Anisotropic Separate Universe Simulations using TreePM
• Shell-crossing in quasi-one-dimensional flow
• Simulating the Complexity of the Dark Matter Sheet I: Numerical Algorithms
• Spurious Small-Scale Structure & Discreteness-Driven Relaxation in Cosmological Simulations
• Cosmological Newtonian limits on large spacetime scales
• A new approach to cosmological structure formation with massive neutrinos
• The median density of the Universe
• Phase-space structure of cold dark matter halos inside splashback: multi-stream flows and self-similar solution
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• The Effect of Thermal Velocities on Structure Formation in N-body Simulations of Warm Dark Matter
• Novel Adaptive softening for collisionless N-body simulations: Eliminating spurious halos
• Perturbation theory with dispersion and higher cumulants: framework and linear theory
• Finding closure: approximating Vlasov-Poisson using finitely generated cumulants
• The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos
• The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation
• Topology and geometry of the dark matter web: a multistream view
• Noise-Induced Magnetic Field Saturation in Kinetic Simulations
• Quasi-spherical collapse of matter in $\Lambda$CDM
• Einstein-Vlasov Calculations of Structure Formation
• The features of the Cosmic Web unveiled by the flip-flop field
• Gravitational-wave event rates as a new probe for dark matter microphysics
• A "metric" semi-Lagrangian Vlasov-Poisson solver
• Non-Halo Structures and their Effects on Gravitational Lensing
• Universal subhalo accretion in cold and warm dark matter cosmologies
• BullFrog: Multi-step perturbation theory as a time integrator for cosmological simulations
• Identifying Dark Matter Haloes by the Caustic Boundary
• Numerical Discreteness Errors in Multi-Species Cosmological N-body Simulations
• Suitable Initial Conditions for Newtonian Simulations with Massive Neutrinos
• Structure formation in warm dark matter cosmologies: Top-Bottom Upside-Down
• Integer Lattice Dynamics for Vlasov-Poisson
• On the probabilistic approach to the N-body problem
• N-body simulations of dark matter-baryon interactions
• Dark matter haloes: a multistream view
• Starting Cosmological Simulations from the Big Bang
• Massively Parallel Computation of Accurate Densities for N-body Dark Matter Simulations using the Phase-Space-Element Method
• Universal multi-stream radial structures of cold dark matter halos
• Statistical exploration of halo anisotropic clustering and intrinsic alignments with the mass-Peak Patch algorithm
• Stochastic Super-resolution of Cosmological Simulations with Denoising Diffusion Models
• The Boosted Potential
• Axion Structure Formation II: The Wrath of Collapse
• Discreteness effects in $N$-body simulations of warm dark matter
• Excursion Sets with a "Perfect" Collapse Model
• Non-halo structures and their effects on gravitationally lensed galaxies
• Tidal adaptive softening and artificial fragmentation in cosmological simulations
• Simulating the complexity of the dark matter sheet II: halo and subhalo mass functions for non-cold dark matter models
• Modeling supernova feedback in galaxy formation simulations with energy-conserving momentum injection
• Comparison of simulations and semi-analytical model for WDM subhalo mass functions