We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disks self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of disks gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disks self-gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, Sigma_I and Sigma_II. When the surface density of the disk is lower than the first one, Sigma_0 < Sigma_I, the effect of self-gravity suppresses the formation of a gap. When Sigma_0 > Sigma_I, the self-gravity of the gas tends to benefit the gap formation process and enlarge the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density Sigma_I approx 0.8MMSN. This effect increases until the surface density reaches the second critical value Sigma_II. When Sigma_0 > Sigma_II, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disks self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale associates with the effective viscosity and can be up to 10^4 yr.
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