Effect of finite disk-thickness on swing amplification of non-axisymmetric perturbations in a sheared galactic disk

Abstract

A typical galactic disk is observed to have a finite thickness. Here, we present the study of the physical effect of introduction of finite thickness on the generation of small-scale spiral arms by swing amplification in a differentially rotating galactic disk. The galactic disk is modelled first as a one-fluid system, and then as a gravitationally-coupled two-fluid (stars and gas) system where each fluid is taken as isothermal, and corotating with each other. We derived the equations governing the evolution of the non-axisymmetric perturbations in a sheared frame of reference while incorporating the effect of finite thickness of a galactic disk. We found that the finite thickness of a galactic disk has a generic trend of suppressing the growth of the non-axisymmetric perturbations via swing amplification. Moreover, even the observed range of disk-thickness values (∼300–500 pc) can lead to a complete suppression of swing amplification for Q ∼ 1.7, whereas for an infinitesimally-thin disk, the corresponding critical value is Q ∼ 2. For a two-fluid (stars and gas) system, the net amplification is shown to be set by the mutual interplay of the effect of interstellar gas in promoting the spiral features and the effect of finite thickness in preventing the spiral arms. The coexistence of these two opposite effects is shown to be capable of giving rise to diverse and complex dynamical behaviour.