Dynamical effect of gas on spiral pattern speed in galaxies
  In the density wave theory of spiral structure, the grand-design two-armed
spiral pattern is taken to rotate rigidly in a galactic disc with a constant,
definite pattern speed. The observational measurement of the pattern speed of
the spiral arms, though difficult, has been achieved in a few galaxies such as
NGC 6946, NGC 2997, and M 51 which we consider here. We examine whether the
theoretical dispersion relation permits a real solution for wavenumber
corresponding to a stable wave, for the observed rotation curve and the pattern
speed values. We find that the disc when treated to consist of stars alone, as
is usually done in literature, does not generally support a stable density wave
for the observed pattern speed. Instead the inclusion of the low velocity
dispersion component, namely, gas, is essential to obtain a stable density
wave. Further, we obtain a theoretical range of allowed pattern speeds that
correspond to a stable density wave at a certain radius, and check that for the
three galaxies considered, the observed pattern speeds fall in the respective
prescribed range. The inclusion of even a small amount (~ 15 %) of gas by mass
fraction in the galactic disc is shown to have a significant dynamical effect
on the dispersion relation and hence on the pattern speed that is likely to be
seen in a real, gas-rich spiral galaxy.
