Vertical Oscillations of Fluid and Stellar Disks

TL;DR

This paper investigates the vertical oscillation modes in self-gravitating stellar and fluid disks, revealing a spectrum of normal and damped modes that can explain observed vertical perturbations in galactic disks.

Contribution

It provides a comprehensive analysis of vertical oscillation modes in self-gravitating disks using the matrix method, including the discovery of infinite mode series and Landau damping effects.

Findings

Identified an infinite series of modes in fluid disks.

Found double series of modes in collisionless stellar systems.

Demonstrated that Landau damping can allow modes to persist for hundreds of Myr.

Abstract

A satellite galaxy or dark matter subhalo that passes through a stellar disk may excite coherent oscillations in the disk perpendicular to its plane. We determine the properties of these modes for various self-gravitating plane symmetric systems (Spitzer sheets) using the matrix method of Kalnajs. In particular, we find an infinite series of modes for the case of a barotropic fluid. In general, for a collisionless system, there is a double series of modes, which include normal modes and/or Landau-damped oscillations depending on the phase space distribution function of the stars. Even Landau-damped oscillations may decay slowly enough to persist for several hundred Myr. We discuss the implications of these results for the recently discovered vertical perturbations in the kinematics of solar neighborhood stars and for broader questions surrounding secular phenomena such as spiral structure in disk galaxies.