Elementary Process of Galactic Spiral Arm Formation: Synchronization of Epicycle Motion by Gravitational Scattering

Speaker: Yuki Yoshida (Univ. of Tokyo ,
*Student talk, *in Japanese)


The formation of galactic spiral arms is one of the main problems in the galactic dynamics. Recent studies have shown that spiral arms are transient and recurrent, and are considered to be stellar material arms that move as a group. As one of the formation processes, the swing amplification has been considered, in which the leading wave becomes a trailing one by differential rotation and the surface density is amplified by self-gravity (Julian & Toomre 1966; Toomre 1981). As a mechanism of the swing amplification, the gravitational scattering from density fluctuations in the galactic disk is considered to make a spiral-like structure. Also, N-body simulation of the formation of spiral arms has confirmed that the phase of the stellar orbits is synchronized during the formation of spiral arms (Michikoshi & Kokubo 2016; 2018). Although Julian & Toomre (1966) suggested that there is a relation between the spiral arm formation and the phase synchronization, no study investigates the relation in detail. We focus on the gravitational scattering by this perturber and consider the elementary process of swing amplification reduced to the restricted three-body problem. To investigate the orbital evolution and the phase synchronization of the stellar orbits, we use the epicycle approximation, consider the perturber as a point mass, and simulate the gravitational scattering by the perturber. We show that the gravitational scattering by the perturber synchronizes the epicycle phase of the stellar orbits. We also investigate the dependence of the phase synchronization on the disk parameter and the initial stellar orbital elements to identify the conditions of the synchronization. Also, we prepare uniformly distributed groups of stars and solve the restricted three-body problem of the orbital evolution of each star. We then study the structure of the surface distribution caused by gravitational scattering and identified the high-density region formed by the swing amplification. The dependence of the structure of the high-density region on the disk parameters and the initial stellar orbital elements is also studied. From these results, we discuss the conditions of the phase synchronization and how the condition corresponds to the actual galactic spiral arms.