Reference Run

April 2001

Before running calculations with halo substructure, we measure the level of noise due to discreteness in the N-body representation.

This calculation used Nb + Ns + Nh = 20480 + 65536 + 229376 massive bodies. In addition, 2048 test particles were distributed like the mass, and another 2048 were placed in a thin, rotating disk. We used Plummer smoothing with ε = 0.05, and a leap-frog time-step of Δt = 1/32.

t = 0:32 t = 32:64 t = 0:64

These images and animations show the change in binding energy of each body over various time intervals.

The vertical stripes evident in the above images were unexpected. It seems that the diffusion rate is a sensitive function of binding energy E; within the stripes, the diffusion rate appears several times what it is between the stripes. The reason for this effect is unclear. Since E and the orbital period to are tightly correlated, it may arise through a resonance with some characteristic frequency in this simulation.

Binding energy change with respect to time t = 0. Red represents bulge bodies, blue represents disk bodies. Successive curves are first through seventh octiles; heavy curves are medians.

Binding energy change with respect to time t = 32.

Another way to show the drift of energies is to plot changes in binding energy ΔE / E as functions of time. In the results shown above the red curves represent octiles in distribution of ΔE / E for bulge bodies, while blue is likewise for disk bodies. The distribution of ΔE / E values shows a random patterns of fluctuations superimposed on a general trend.

Joshua E. Barnes (
Last modified: May 8, 2002