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

TL;DR

This paper investigates how gravitational scattering causes phase synchronization of stellar orbits, leading to spiral arm formation in disk galaxies, by analyzing orbital evolution under the epicycle approximation.

Contribution

It demonstrates that gravitational scattering can synchronize stellar epicycle phases, clarifying an elementary process behind spiral arm formation.

Findings

Gravitational scattering induces phase synchronization of stellar orbits.

Synchronization is more effective with smaller initial epicycle amplitudes and higher shear rates.

Vertical stellar motion does not influence phase synchronization.

Abstract

Swing amplification is a model of spiral arm formation in disk galaxies. Previous $N$-body simulations show that the epicycle phases of stars in spiral arms are synchronized. However, the elementary process of the phase synchronization is not well understood. In order to investigate phase synchronization, we investigate the orbital evolution of stars due to gravitational scattering by a perturber under the epicycle approximation and its dependence on orbital elements and a disk parameter. We find that gravitational scattering by the perturber can cause phase synchronization of stellar orbits. The epicycle phases are better synchronized for smaller initial epicycle amplitudes of stars and larger shear rates of galactic disks. The vertical motion of stars does not affect the phase synchronization. The phase synchronization forms trailing dense regions, which may correspond to spiral arms.