Wave Propagation in Accretion Disks with Self-Gravity

We extend the research by Lubow and Pringle of axisymmetric waves in accretion disks to the case where self-gravity of disks should be considered. We derive and analyse the dispersion relations with the effect of self-gravity. Results show that self-gravity extends the forbidden region of the wave propagation: for high frequency p-modes, self-gravity makes the wavelength shorter and the group velocity larger; for low frequency g-modes, the effect is opposite.