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Dynamics of Non-Steady Spiral Arms in Disk Galaxies

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.