  Spiral density wave theory attempts to describe the spiral pattern in spiral
galaxies in terms of a long-lived wave structure with a constant pattern speed
in order to avoid the winding dilemma. The pattern is consequently a rigidly
rotating, long-lived feature. We run N-body simulations of a giant disc galaxy
consisting of a pure stellar disc and a static dark matter halo, and find that
the spiral arms are transient features whose pattern speeds decrease with
radius, in such a way that the pattern speed is almost equal to the rotation
curve of the galaxy. We trace particle motion around the spiral arms. We show
that particles from behind and in front of the spiral arm are drawn towards and
join the arm. Particles move along the arm in the radial direction and we find
a clear trend that they migrate toward the outer (inner) radii on the trailing
(leading) side of the arm. Our simulations demonstrate that because the spiral
arm feature is co-rotating, the particles continue to be accelerated
(decelerated) by the spiral arm for long periods, which leads to strong and
efficient migration, at all radii in the disc.
