  In order to understand the physical mechanisms underlying non-steady stellar
spiral arms in disk galaxies, we analyzed the growing and damping phases of
their spiral arms using three-dimensional $N$-body simulations. We confirmed
that the spiral arms are formed due to a swing amplification mechanism that
reinforces density enhancement as a seeded wake. In the damping phase, the
Coriolis force exerted on a portion of the arm surpasses the gravitational
force that acts to shrink the portion. Consequently, the stars in the portion
escape from the arm, and subsequently they form a new arm at a different
location. The time-dependent nature of the spiral arms are originated in the
continual repetition of this non-linear phenomenon. Since a spiral arm does not
rigidly rotate, but follows the galactic differential rotation, the stars in
the arm rotate at almost the same rate as the arm. In other words, every single
position in the arm can be regarded as the co-rotation point. Due to
interaction with their host arms, the energy and angular momentum of the stars
change, thereby causing the radial migration of the stars. During this process,
the kinetic energy of random motion (random energy) of the stars does not
significantly increase, and the disk remains dynamically cold. Owing to this
low degree of disk heating, the short-lived spiral arms can recurrently develop
over many rotational periods. The resultant structure of the spiral arms in the
$N$-body simulations is consistent with some observational nature of spiral
galaxies. We conclude that the formation and structure of spiral arms in
isolated disk galaxies can be reasonably understood by non-linear interactions
between a spiral arm and its constituent stars.
