ON LOOSELY WOUND SPIRAL DENSITY WAVES OF GALAXIES

In this paper the loosely wound galactic spiral density wave is studied using a hydrodynamic model. The basic equation of wave propagation is derived, and the calculation is made for Toomre’s (=2) galactic model. The result shows that the behayiours of loosely wound spiral density waves are considerably different from those of tightly wound ones. Owing to the existence of the "loosely wound effect", a linear density wave with real wave mumber, generally speaking, will always be unstable. For a trailing wave, its amplitude will grow within the corotation circle and decay outside the corotation circle. For a leading wave, the behaviour is just the opposite.