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.

摆动放大是盘状星系中螺旋臂形成的模型。上一页ñ体模拟表明旋臂中恒星的本轮相位是同步的。然而，相位同步的基本过程还不是很清楚。为了研究相位同步，我们研究了由于本轮近似下扰动器的引力散射引起的恒星轨道演化及其对轨道元素和圆盘参数的依赖性。我们发现扰动器的引力散射会导致恒星轨道的相位同步。对于较小的恒星初始本轮振幅和较大的星系盘剪切率，本轮相位更好地同步。恒星的垂直运动不影响相位同步。相位同步形成拖尾密集区域，这可能对应于螺旋臂。