2003ApJ...599..548D

With a series of numerical simulations, we analyze the thermohydrodynamic evolution of circumstellar disks containing Jupiter-sized protoplanets. In the framework of a two-dimensional approximation, we consider an energy equation that includes viscous heating and radiative effects in a simplified yet consistent form. Multiple nested grids are used in order to study both global and local features around the planet. By means of different viscosity prescriptions, we investigate various temperature regimes. A planetary mass range from 0.1 to 1 M_Jis examined. Computations show that gap formation is a general property that affects density, pressure, temperature, optical thickness, and radiated flux distributions. However, it remains a prominent feature only when the kinematic viscosity is on the order of 10¹⁵cm2/s or lower, although it becomes rather shallow for 0.1 M_Jperturbers. Around accreting planets, a circumplanetary disk forms that has a surface density profile decaying exponentially with distance and whose mass is 5-6 orders of magnitude smaller than Jupiter's mass. Circumplanetary disk temperature profiles decline roughly as the inverse of the distance from the planet, matching the values measured in the gap toward the border of the Roche lobe. Temperatures range from some 10 to ∼1000 K. Moreover, circumplanetary disks are generally opaque, with optical thicknesses larger than 1 and aspect ratios around a few tenths. Nonaccreting protoplanets provide quite different scenarios, with a clockwise, i.e., reversed flow, rotation around low-mass bodies. Planetary accretion and migration rates depend on the viscosity regime, with discrepancies within an order of magnitude. Co-orbital torques increase as viscosity increases. For high viscosities, type I migration may extend to larger planetary masses. Estimates of growth and migration timescales inferred from these models are on the same orders of magnitude as those previously obtained with locally isothermal simulations, in both two and three dimensions.