A dynamical study of three-dimensional spiral galaxies

On the basis of a rigorous solution of the three-dimensional (3D) gravitati onal Poisson equation for density disturbance of logarithmic spiral type, a dispersion relation of 3D mixed disk density wave in the plane of symmetry (z = 0) has been derived. With this result the local stability for disturb ed disks of various types is investigated and the group velocity of density waves on the disk surface is calculated. As shown by numerical computation s, the logarithmic spiral density disturbance can well satisfy the antiphas e relation between the disturbed density and potential. An increase in the thickness or in the number of spiral arms is favourable to the stability of the disk, while a gaseous content may lead to instability. When the effect of thickness is considered, the dynamic time scale of the propagation of d ensity waves in the Galaxy will be very much longer than Toomre's estimate and it may be at least 4.17 x 10(9) yr, or about one third of the cosmic ag e. So the problem of too large a group velocity in the previous theories of density waves may be alleviated.