Plasma Echo Analogues in Galactic Disk Dynamics

Abstract

Because both Newton's law of gravitation and Coulomb's law are inverse-square in distance, the equations that govern stellar dynamics are remarkably similar to those that govern electrostatic plasmas. In plasmas, an "echo" effect occurs when a homogeneous plasma is given a small perturbation twice; after the second perturbation, an echo manifesting as a third perturbation appears in the plasma. However, this phenomenon, which was first observed in the 1960s, has not yet been studied in the stellar dynamical context. In this work, I investigate the so-called plasma echo effect in the stellar dynamical context. Beginning from the collisionless Boltzmann equation, I perform pen-and-paper calculations to show that an analogous galactic echo effect can occur for a one-dimensional model of a galactic disk and at a potentially observable amplitude. I then perform numerical experiments to try to verify our analytical prediction of the galactic echo effect. Within the existing research literature, first- and second-order perturbations in plasma systems have been widely explored, while only first-order perturbations have been well-explored in the context of stellar dynamics. This work provides an in-depth illustration of second-order perturbations within the context of stellar dynamics.