2016MNRAS.459.4057G

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 modelled as a stars-alone case, as is usually done in literature, does not generally give a stable density wave solution 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 per cent) 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.