## 1. Spontaneous Spiral Structure

Swing amplification of particle noise can bring forth trailing
multi-armed spiral patterns. Shown here is an N-body experiment with
a central bulge (yellow), an exponential disk (blue), and a dark halo
(red). Apart from Poissonian fluctuations due to particle noise, this
disk is initially featureless. Later frames, separated by about half
a rotation period at three exponential scale lengths, show the
development of transient spiral patterns.

## 2. Tidal Spiral Structure

Tides between galaxies provoke a two-sided response. Such
perturbations, if further swing-amplified in differentially-rotating
disks, may produce striking `grand-design' spiral patterns. In the
experiment shown here, an artificial tide was applied by taking the
unperturbed disk above and instantaneously replacing each
`x` velocity with

v_x <- v_x + k x ,

where `k` is a constant used to adjust the strength of the
perturbation. No perturbation was applied to the `y` and
`z` velocities. Frames made after `1.5` rotation
periods show the development of an open, two-armed spiral pattern
which becomes more tightly wound with time.

Joshua E. Barnes
(barnes@zeno.ifa.hawaii.edu)
Last modified: September 3, 1996