Since the work of Orr (1907) it has been known that certain perturbations in stable shearing flows show a transient exponential growth. This phenomenon was discussed extensively by Goldreich & Lynden-Bell (1965) and Julian & Toomre (1966) in the context of galactic dynamics, using hydrodynamics and statistical mechanics, respectively. Both papers examine the dynamics of a small patch within a larger disk and find strong transient growth of density perturbations as they "swing by" from leading to trailing. Toomre (1990) has argued that this amplification mechanism is the principal dynamical process responsible for spiral arms in disk galaxies.
While gas is known to play a major role in quasi-stationary density waves (Roberts 1969), there has been little research on the dynamical behavior of the interstellar medium (ISM) in transient density waves. It is this issue the present paper addresses. The key question we want to answer is whether the short lifetime of a swing-amplified perturbation still allows a noticeable response of the ISM. Additionally, we look for kinematical signatures that might allow a discrimination of quasi-stationary versus transient density waves.
So far, the only study of swing amplification in a two-component medium was undertaken by Jog (1992) who extended the formalism of Goldreich & Tremaine (1978) to include two fluids with different stability numbers. While these works used Lagrangian coordinates to solve the dynamical equations, in this paper we employ a different approach using Eulerian coordinates. This enables us to consider a succession of swing amplification events in a consistent way.
The outline of this paper is as follows: In Sect. 2 we describe our model with a brief review of the results of Fuchs (1991) important to this work and a discussion of our treatment of an ISM consisting of discrete clouds. Sect. 3 presents the main results. In a first part, we describe the behavior of our model under a single perturbation. This behavior is interpreted in the second part. After a discussion of the model with repeated perturbations, Sect. 3 closes with an investigation of the effects of self gravity in the ISM. In Sect. 4 we briefly summarize the main conclusions we draw from this work.
© European Southern Observatory (ESO) 1998
Online publication: February 16, 1998