Group velocity of the density waves in galactic disks

The letter is emphasized on the discussion of the group velocity of disturb ed galactic density waves (GDW), which is one of the two most insurmountabl e problems in the density waves theory. In our calculation, we find that th e galactic thickness has an important effect on the GDW. The dynamic time s cale of GDW in our three-dimensional model can be prominently prolonged, fr om 36% to 60% contrasting to that of two-dimensional galactic model. Howeve r, it is still less than the lifetime of our Galaxy, which means that it is necessary to seek some other physical mechanisms to excite and sustain the GDW.