The effects of viscosity on the circumplanetary disks
The effects of viscosity on the circumplanetary disks residing in the vicinity of protoplanets are investigated through two-dimensional hydrodynamical simulations with the shearing sheet model. We find that viscosity can affect properties of the circumplanetary disk considerably when the mass of the protoplanet is $M_p \lesssim 33M_\oplus$, where $M_\oplus$ is the Earth mass. However, effects of viscosity on the circumplanetary disk are negligibly small when the mass of the protoplanet $M_p \gtrsim 33M_\oplus$. We find that when $M_p \lesssim 33M_\oplus$, viscosity can disrupt the spiral structure of the gas around the planet considerably and make the gas smoothly distributed, which makes the torques exerted on the protoplanet weaker. Thus, viscosity can make the migration speed of a protoplanet lower. After including viscosity, size of the circumplanetary disk can be decreased by a factor of $\gtrsim 20%$. Viscosity helps to transport gas into the circumplanetary disk from the differentially rotating circumstellar disk. The mass of the circumplanetary disk can be increased by a factor of 50% after viscosity is taken into account when $M_p \lesssim 33M_\oplus$. Effects of viscosity on the formation of planets and satellites are briefly discussed.