In our simulations, the orbits of bodies are perturbed by halo fluctuations and by the numerical approximations made in force calculation and orbital integration. The fluctuations are the effect we wish to study, while the numerical errors are artifacts which tend to mask the signal from the halo. Here, short calculations are used to determine the time-step and force-calculation parameters.

These calculations adopted the initial conditions with *κ
* = 1.35 used in the initial data tests. Below, results are
shown for four runs with different time-steps and force-calculation
parameters; the `quick scan' runs use a fast version of the tree code
which constructs minimal interaction lists, while the run with
*θ* = 0.8 imposes a further
opening-angle criterion which improves the force accuracy. All runs
included quadrupole moments.

Δt = 1/16quick scan |
Δt = 1/32quick scan |
Δt = 1/32κ = 0.8 |
Δt = 1/64quick scan |

These images are linked to animations showing how the binding
energy of each body changes over 8 time units. On the whole, all four
runs yield similar results. But in the run with the longest time-step
a small number of bodies suffer relatively large changes in binding
energy; this does not happen in the other runs. Thus a time-step
*Δt* = 1/32 seems necessary for
accurate integration, but further refinements may not be needed.

Joshua E. Barnes (barnes@ifa.hawaii.edu)

Last modified: May 8, 2002

`http://www.ifa.hawaii.edu/~barnes/research/halo_noise/test_runs.html`