Axisymmetric Waves in Isothermal Accretion Discs with Vertical Self-Gravity

We extend the research of axisymmetric waves in accretion discs with three-dimensional structure to the case that vertical self-gravity of the discs is included. We derive and analyze the dispersion relation and solve the eigenfunctions numerically. The following results have been reached: vertical self-gravity expands the forbidden region of the wave propagation. As the influence of the vertical self-gravity increases, the group velocities of the waves get smaller and the vertical nodes of the wave shrink to the middle plane of the disc.