Phase synchronization of epicyclic motion due to gravitational scattering by wakes

The swing amplification is one of the mechanisms for spiral arm formation and gravitational scattering of stellar orbits by a high-density region in a disc galaxy is considered as its elementary process. During the swing amplification, the epicycle phases of stars are synchronized. We previously showed that gravitational scattering by a softened point mass can synchronize the epicycle phases. Here, we expand upon our previous work to consider gravitational scattering by a finite-sized wake, which we model by using a prolate body. We numerically simulate the stellar motion under the influence of the wake gravity, and we investigate the dependence of the orbital evolution on the wake properties. We find that phase synchronization is more effective for a wake with a pitch angle around π/2, and that the phase synchronization depends on the wake shape. Even for realistic pitch angles i ≲ π/4 the phase synchronization can be more effective than that by the softened point mass. Increasing the impact parameter of stars and decreasing the wake pitch angle are shown to increase the axis ratio at which synchronization occurs. Linear trailing high-density patterns form around the wake and enlarge the wake itself.