Dynamical interplay of disc thickness and the interstellar gas:
  implication for the longevity of spiral density waves
  A typical galactic disc has a finite thickness and in addition to stars it
also contains a finite amount of interstellar gas. Here, we investigate the
physical impact of the finite thickness of a galactic disc on the disc
stability against the non-axisymmetric perturbations and on the longevity of
the spiral density waves, with and without the presence of gas. The longevity
is quantified via group velocity of density wavepackets. The galactic disc is
first modelled as a collisionless stellar disc with finite height and then more
realistically as a gravitationally-coupled stars plus gas system (with
different thickness for stars and gas). For each case, we derive the
appropriate dispersion relation in the WKB approximation, and study the
dynamical effect of the disc thickness on the life-time of spiral density waves
via a parametric approach. We find the generic trend that the effective
reduction in disc self-gravity due to disc thickness makes it more stable
against the non-axisymmetric perturbations, and shortens the life-span of the
spiral density waves. Further, the interstellar gas and the disc thickness are
shown to have a mutually opposite dynamical effect on the disc stability as
well as the longevity of the spiral density waves. While the gas supports the
non-axisymmetric features for a longer time, the disc thickness has an
opposite, quenching effect. Consequently, the net change is set by the relative
dominance of the opposite effects of the interstellar gas and the disc
thickness.
