Vlasov versus N-body: the Hénon sphere

Abstract

We perform a detailed comparison of the phase-space density traced by the particle distribution in Gadget simulations to the result obtained with a spherical Vlasov solver using the splitting algorithm. The systems considered are apodized Hénon spheres with two values of the virial ratio, R ~ 0.1 and 0.5. After checking that spherical symmetry is well preserved by the N-body simulations, visual and quantitative comparisons are performed. In particular we introduce new statistics, correlators and entropic estimators, based on the likelihood of whether N-body simulations actually trace randomly the Vlasov phase-space density. When taking into account the limits of both the N-body and the Vlasov codes, namely collective effects due to the particle shot noise in the first case and diffusion and possible nonlinear instabilities due to finite resolution of the phase-space grid in the second case, we find a spectacular agreement between both methods, even in regions of phase-space where nontrivial physical instabilities develop. However, in the colder case, R=0.1, it was not possible to prove actual numerical convergence of the N-body results after a number of dynamical times, even with N=10${}^8$ particles.

arXiv comment19 pages, 11 figures, MNRAS, in press

References in corpus (28)

• The cosmological simulation code GADGET-2
• The Aquarius Project: the subhalos of galactic halos
• GADGET: A code for collisionless and gasdynamical cosmological simulations
• The Inner Structure of LambdaCDM Halos I: A Numerical Convergence Study
• Resolving the Structure of Cold Dark Matter Halos
• Triaxial Modeling of Halo Density Profiles with High-resolution N-body Simulations
• Density Profiles of Dark Matter Halo are not Universal
• Quantifying the heart of darkness with GHALO - a multi-billion particle simulation of our galactic halo
• A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
• How universal are the density profiles of dark halos?
• N-body simulations of gravitational dynamics
• The Cosmic Web, Multi-Stream Flows, and Tessellations
• Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations
• A new approach to simulating collisionless dark matter fluids
• Simulation techniques for cosmological simulations
• Discreteness effects in cosmological N-body simulations
• Demonstrating Discreteness and Collision Error in Cosmological N-body Simulations of Dark Matter Gravitational Clustering
• Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
• Energy ejection in the collapse of a cold spherical self-gravitating cloud
• A cloudy Vlasov solution
• Dissipationless collapse of a set of N massive particles
• The Radial Orbit Instability in Collisionless N-Body Simulations
• Scaling up Tides in Numerical Models of Galaxy- and Halo-Formation
• Arbitrarily high order Convected Scheme solution of the Vlasov-Poisson system
• The origin and formation of cuspy density profiles through violent relaxation of stellar systems
• Violent and mild relaxation of an isolated self-gravitating uniform and spherical cloud of particles
• Growth of Velocity Dispersions for Collapsing Spherical Stellar Systems
• Smooth particle methods without smoothing

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• The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation
• The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos
• Description of the evolution of inhomogeneities on a Dark Matter halo with the Vlasov equation
• Confrontation of Top-Hat Spherical Collapse against Dark Halos from Cosmological N-Body Simulations
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• Phase-space structure analysis of self-gravitating collisionless spherical systems
• Cosmology in One Dimension: Vlasov Dynamics
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• Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies
• How gravitational softening affects galaxy stability I. Linear mode analysis of disc galaxies
• Spherical accretion of a collisionless kinetic gas into a generic static black hole