Background

We are working towards an understanding of the basic physical principles that determine the density and velocity structures of self-gravitating N-body systems. In particular, we aim to use a thermodynamic approach to describe the common end-states of simulated cosmological dark matter halos.

As a first step, we are creating a suite of simple N-body collapses that we can use to test our analytical predictions against.

Simulations

The simulations have been run using Sverre Aarseth's code NBODY2. This is a standard, straightforward code that can handle on the order of 10⁴ self-gravitating particles. The positions and velocities of all particles are output regularly along with quantities like energy, virial ratio, half-mass radius, etc.

The tables below list the various simulations we have run so far. The symbol key is: ε is the softening length, N is the particle number, Q is the initial virial fraction (Q=2T/|W|), T_f is the "temperature fraction" for clumpy initial conditions (see below).

The initial conditions come in two general flavors; particles are arranged in 1) single halos or 2) clumpy halos. For single halos, the particles are distibuted throughout a sphere of radius=1 and given velocities so that the desired Q-values are acheived. For clumpy halos, some number of clumps (typically 50) are created to hold all of the particles. Each clump contains different numbers of particles (which can be set). The velocities of the particles in the clumpy scenario are chosen so that there is a prescribed balance between the motion due to the center-of-mass of the clump and the motion about the center-of-mass of the clump. This balance is described with the "temperature fraction"; T_f =1.0 is a "cold" system (the velocities of all clump members equal the center-of-mass velocity), T_f =0.0 is a "hot" system (the center-of-mass velocities are all zero but clump member velocities are non-zero).

The initial density distributions of the halos vary between constant ρ=ρ₀, Gaussians ρ∝ exp(-r²), and power-law forms ρ∝ r^{- α}. So far, we have only run models with α=1.

ε=5x10^-2, N=10⁴, initial ρ=Gaussian

Q=0.1 Q=0.2 Q=0.3 Q=0.4 Q=0.5 Q=0.6 Q=0.7 Q=0.8 Q=0.9 Q=1.0

ε=5x10^-3, N=5x10³, initial ρ=ρ₀

Q=0.1 Q=0.2 Q=0.3 Q=0.4 Q=0.5 Q=0.6 Q=0.7 Q=0.8 Q=0.9 Q=1.0

ε=5x10^{- 4}, N=5x10³, initial ρ=ρ₀

Q=0.1 Q=0.2 Q=0.3 Q=0.4 Q=0.5 Q=0.6 Q=0.7 Q=0.8 Q=0.9 Q=1.0

ε=5x10^{- 4}, N=10⁴, initial ρ=ρ₀

Q=0.1 Q=0.2 Q=0.3 Q=0.4 Q=0.5 Q=0.6 Q=0.7 Q=0.8 Q=0.9 Q=1.0

ε=5x10^{- 4}, N=10⁴, initial ρ∝ r^-
1

Q=0.1 Q=0.2 Q=0.3 Q=0.4 Q=0.5 Q=0.6 Q=0.7 Q=0.8 Q=0.9 Q=1.0

ε=5x10^{- 4}, N=10⁴, initial ρ=Gaussian

Q=0.1 Q=0.2 Q=0.3 Q=0.4 Q=0.5 Q=0.6 Q=0.7 Q=0.8 Q=0.9 Q=1.0

ε=5x10^-2, N=10⁴, initial ρ=Gaussian
Q=0.1	Q=0.2	Q=0.3	Q=0.4	Q=0.5	Q=0.6	Q=0.7	Q=0.8	Q=0.9	Q=1.0

ε=5x10^-3, N=5x10³, initial ρ=ρ₀
Q=0.1	Q=0.2	Q=0.3	Q=0.4	Q=0.5	Q=0.6	Q=0.7	Q=0.8	Q=0.9	Q=1.0

ε=5x10^{- 4}, N=5x10³, initial ρ=ρ₀
Q=0.1	Q=0.2	Q=0.3	Q=0.4	Q=0.5	Q=0.6	Q=0.7	Q=0.8	Q=0.9	Q=1.0

ε=5x10^{- 4}, N=10⁴, initial ρ=ρ₀
Q=0.1	Q=0.2	Q=0.3	Q=0.4	Q=0.5	Q=0.6	Q=0.7	Q=0.8	Q=0.9	Q=1.0

ε=5x10^{- 4}, N=10⁴, initial ρ∝ r^- 1
Q=0.1	Q=0.2	Q=0.3	Q=0.4	Q=0.5	Q=0.6	Q=0.7	Q=0.8	Q=0.9	Q=1.0

ε=5x10^{- 4}, N=10⁴, initial ρ=Gaussian
Q=0.1	Q=0.2	Q=0.3	Q=0.4	Q=0.5	Q=0.6	Q=0.7	Q=0.8	Q=0.9	Q=1.0