Disk Stability of the Milky Way Near the Sun

By solving Poisson's equation for logarithmic density disturbance in three-dimensional (3D) spiral galaxies, the disturbed potential can be given on the disk. Combining it with the corresponding dispersion relation, the local gravitational stability of our galaxy is discussed here. We have generalized the Toomre's stability criterion to the more realistic 3D galaxy models. The generalized Toomre's parameter Q near the sun is 2.08 or 2.20 for two or four armed spiral galaxy models, respectively.