Gap formation in a self-gravitating disk and the associated migration of the embedded giant planet

Abstract

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 disk's 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 the disk's gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disk's self-gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, ΣI and ΣII. When the surface density of the disk is lower than the first one, Σ0 < ΣI, the effect of self-gravity suppresses the formation of a gap. When Σ0 > ΣI, the self-gravity of the gas tends to benefit the gap formation process and enlarges the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density to be ΣI ≈ 0.8 MMSN. This effect increases until the surface density reaches the second critical value ΣII. When Σ0 > ΣII, 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 3.5 MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disk's self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale correlates with the effective viscosity and can be up to 104 yr.