Dynamics of One-dimensional Self-gravitating Systems Using Hermite-Legendre Polynomials

Abstract

The current paradigm for understanding galaxy formation in the universe depends on the existence of self-gravitating collisionless dark matter. Modeling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective nonlinear dynamics of many-particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyze the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase space distribution functions f(x,v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N-body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.

12 pages, accepted for publication in MNRAS

References in corpus (21)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• A Universal Density Profile from Hierarchical Clustering
• The Structure of Cold Dark Matter Halos
• Simulating the joint evolution of quasars, galaxies and their large-scale distribution
• A direct empirical proof of the existence of dark matter
• The Inner Structure of LambdaCDM Halos III: Universality and Asymptotic Slopes
• The Phase-Space Density Profiles of Cold Dark Matter Halos
• A universal density slope - velocity anisotropy relation for relaxed structures
• COSMOLOGICAL CONSTRAINTS FROM CLUSTER X-RAY MORPHOLOGIES
• Self-Similar Solutions of Triaxial Dark Matter Halos
• Quasi-stationary states in the self-gravitating sheet model
• Evolution of the Power Spectrum and the Self-Similarity in the Expanding One-Dimensional Universe
• Light/Mass Offsets in the Lensing Cluster Abell 3827: Evidence for Collisional Dark Matter?
• Thermodynamics and dynamics of a 1-D gravitational system
• Block-Structured Adaptive Mesh Refinement Algorithms for Vlasov Simulation
• Algebraic damping in the one-dimensional Vlasov equation
• A cloudy Vlasov solution
• Emergence of power-law correlation in 1-dimensional self-gravitating system
• Gravitational Collapse in One Dimension
• Exponents of non-linear clustering in scale-free one dimensional cosmological simulations
• Solving the Vlasov equation for one-dimensional models with long range interactions on a GPU

Cited by in corpus (3)

• Predicting Steady States of One-dimensional Collisionless Gravitating Systems
• Relaxation of One-dimensional Collisionless Gravitating Systems
• Violent relaxation in one-dimensional self-gravitating system: deviation from the Vlasov limit due to finite-$N$ effect