Gas Giant Protoplanet Formation: Disk Instability Models with Detailed Thermodynam- Ics and Varied Artificial Viscosity

Three dimensional (3D) hydrodynamical models of the evolution of marginally gravitationally unstable protoplanetary disks have shown that such disks are likely to form selfgravitating clumps that could become gas giant protoplanets, even when detailed thermodynamics is included [1]. Vertical convective motions appear to be crucial for providing a means of cooling the disk midplane sufficiently for clump formation [2]. Clump survival to form gas giant planets seems possible, provided that the clumps are sufficiently well-resolved [3]. However, calculations where artificial viscosity is employed generally have not found robust clump formation in either fully 3D [4] or thin disk models [5]. The lack of clump formation in the latter models [5] may be due to the prohibition against vertical convection in thin disk models. Here we show that when artificial viscosity is included in 3D disk models with radiative and convective cooling, the tendency to form clumps is reduced somewhat, but not eliminated, unless the artificial viscosity is increased by a factor of ten. This result suggests that disk instability remains as a possible means for forming the giant planets of our Solar System [7]. Artificial viscosity can be used to help stabilize numerical schemes and to provide microphysical heating within shocks. We use a tensor artificial viscosity [8], which enters into the momentum equations as follows, where the other terms on the right hand sides of these equations are suppressed for clarity,