Two body relaxation in CDM simulations

Abstract

N-body simulations of the hierarchical formation of cosmic structures suffer from the problem that the first objects to form always contain just a few particles. Although relaxation is not an issue for virialised objects containing millions of particles, collisional processes will always dominate within the first structures that collapse. First we quantify how the relaxation varies with resolution, softening, and radius within isolated equilibrium and non-equilibrium cuspy haloes. We then attempt to determine how this numerical effect propagates through a merging hierarchy by measuring the local relaxation rates of each particle throughout the hierarchical formation of a dark matter halo. The central few percent of the final structures - a region which one might naively think is well resolved at the final time since the haloes contains about 10^6 particles - suffer from high degrees of relaxation. It is not clear how to interpret the effects of the accumulated relaxation rate, but we argue that it describes a region within which one should be careful about trusting the numerical results. Substructure haloes are most affected by relaxation since they contain few particles at a constant energy for the entire simulation. We show that relaxation will flatten a cusp in just a few mean relaxation times of a halo. We explore the effect of resolution on the degree of relaxation and we find that increasing N slowly reduces the degree of relaxation proportional to N^{-0.25} rather than proportional to N. Simulated with the same relative mass resolution (i.e. equal numbers of particles) cluster mass objects suffer significantly more relaxation than galaxy mass objects since they form relatively late and therefore more of the particles spend more time in small N haloes.

11 pages, 14 figures. Accepted for publication in MNRAS. Movies available at http://www-theorie.physik.unizh.ch/~diemand/tbr

References in corpus (1)

• Generating Equilibrium Dark Matter Halos: Inadequacies of the Local Maxwellian Approximation

Cited by in corpus (87)

• Forming Disk Galaxies in Lambda CDM Simulations
• Velocity and spatial biases in CDM subhalo distributions
• Disruption of Dark Matter Substructure: Fact or Fiction?
• Dark Matter Substructure in Numerical Simulations: A Tale of Discreteness Noise, Runaway Instabilities, and Artificial Disruption
• Density Profiles of Cold Dark Matter Substructure: Implications for the Missing Satellites Problem
• The Formation of a Realistic Disk Galaxy in Lambda Dominated Cosmologies
• An accurate physical model for halo concentrations
• Convergence and scatter of cluster density profiles
• Cusps in CDM halos
• Flat-Cored Dark Matter in Cuspy Clusters of Galaxies
• The distribution and kinematics of early high-sigma peaks in present-day haloes: implications for rare objects and old stellar populations
• Large-scale dark matter simulations
• The Dark Matter Annihilation Signal from Galactic Substructure: Predictions for GLAST
• Forming Early-Type Galaxies in LambdaCDM Simulations -I. Assembly histories
• Density profiles of LCDM clusters
• The Origin and Properties of Intracluster Stars in a Rich Cluster
• The Cusp/Core problem and the Secondary Infall Model
• Constraints on dark matter and the shape of the Milky Way dark halo from the 511 keV line
• The Abacus Cosmos: A Suite of Cosmological N-body Simulations
• Dark Matter Subhaloes in Numerical Simulations
• A new approach to simulating collisionless dark matter fluids
• Diurnal and Annual Modulation of Cold Dark Matter Signals
• The splashback radius of halos from particle dynamics. I. The SPARTA algorithm
• Numerical convergence of simulations of galaxy formation: the abundance and internal structure of cold dark matter haloes
• The Caustic Ring Model of the Milky Way Halo
• Dwarf galaxy populations in present-day galaxy clusters: I. Abundances and red fractions
• Post-Newtonian dynamical modeling of supermassive black holes in galactic-scale simulations
• Conserved actions, maximum entropy and dark matter halos
• Discreteness Effects in Lambda Cold Dark Matter Simulations: A Wavelet-Statistical View
• Numerical estimation of densities
• Major Mergers of Galaxy Haloes: Cuspy or Cored Inner Density Profile?
• The surprising accuracy of isothermal Jeans modelling of self-interacting dark matter density profiles
• Discreteness effects in cosmological N-body simulations
• The Impact of Box Size on the Properties of Dark Matter Haloes in Cosmological Simulations
• Multi-Dimensional Density Estimation and Phase Space Structure Of Dark Matter Halos
• The Evolution of Substructure in Galaxy, Group and Cluster Haloes II: Global Properties
• Characterization of Dark-Matter-induced anisotropies in the diffuse gamma-ray background
• EDGE: Two routes to dark matter core formation in ultra-faint dwarfs
• ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
• Linear perturbative theory of the discrete cosmological N-body problem
• Extragalactic gamma-ray background radiation from dark matter annihilation
• Dark matter density profiles from the Jeans equation
• The Inner Caustics of Cold Dark Matter Halos
• Quasi-stationary states and the range of pair interactions
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Infall caustics in dark matter halos?
• Towards quantitative control on discreteness error in the non-linear regime of cosmological N body simulations
• Multimass spherical structure models for N-body simulations
• Quantification of discreteness effects in cosmological N-body simulations: I. Initial Conditions
• The Evolution of Substructure in Galaxy, Group and Cluster Haloes III: Comparison with Simulations
• Quantification of discreteness effects in cosmological N-body simulations: II. Evolution up to shell crossing
• Evolution of Characteristic Quantities for Dark Matter Halo Density Profiles
• Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
• A numerical comparison of theories of violent relaxation
• Phase-space structure of protohalos: Vlasov versus Particle-Mesh
• Adaptive gravitational softening in GADGET
• Robustness of Discrete Flows and Caustics in Cold Dark Matter Cosmology
• Spurious Small-Scale Structure & Discreteness-Driven Relaxation in Cosmological Simulations
• The Next Generation Virgo Cluster Survey. IX. Estimating the Efficiency of Galaxy Formation on the Lowest-Mass Scales
• A wavelet add-on code for new-generation N-body simulations and data de-noising (JOFILUREN)
• Novel Adaptive softening for collisionless N-body simulations: Eliminating spurious halos
• The real and apparent convergence of N-body simulations of the dark matter structures: is the Navarro-Frenk-White profile real?
• The Adaptive TreePM: An Adaptive Resolution Code for Cosmological N-body Simulations
• Formation and relaxation of quasi-stationary states in particle systems with power law interactions
• Good and Proper: Self-similarity of N-body Simulations with Proper Force Softening
• Two Body Relaxation in Simulated Cosmological Haloes
• Collisional relaxation of two-dimensional self-gravitating systems
• Growth of correlations in gravitational N-body simulations
• Particle linear theory on a self-gravitating perturbed cubic Bravais lattice
• Gravitational collapse in an expanding background and the role of substructure II: Excess power at small scales and its effect of collapse of structures at larger scales
• Missing Dwarf Problem in Galaxy Clusters
• Particle number dependence in the non-linear evolution of N-body self-gravitating systems
• Resolving infall caustics in dark matter halos
• Diffusion and mixing in globular clusters
• A toy model to test the accuracy of cosmological N-body simulations
• Numerical Discreteness Errors in Multi-Species Cosmological N-body Simulations
• Properties of self-gravitating quasi-stationary states
• Nuclear star clusters as probes of dark matter halos: the case of the Sagittarius Dwarf Spheroidal Galaxy
• Cosmological simulations of structure formation and the Vlasov equation
• The Assembly of the Virgo Cluster, Traced by its Galaxy Halos
• BASILISK II. Improved Constraints on the Galaxy-Halo Connection from Satellite Kinematics in SDSS
• Vlasov limit and discreteness effects in cosmological N-body simulations
• Numerical Simulations of the Dark Universe: State of the Art and the Next Decade
• A Physical Bias in Cosmological Simulations
• On the origin of transient features in cosmological N-Body Simulations
• Introducing a new multi-particle collision method for the evolution of dense stellar systems II. Core collapse
• Detecting a physical difference between the CDM halos in simulation and in nature