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