Modeling protoplanetary disks with adaptive mesh refinement techniques

So far, most numerical approaches in planet formation or accretion disks make use of Lagrangian-based smoothed-particle hydrodynamics (SPH) techniques or grid-based 2D axisymmetric simulations. Here, we present a new setup to model gravitational instabilities in 3D with the adaptive mesh refinement (AMR) hydrodynamics code Enzo. We explore the potential impact of AMR techniques to model the first stages of giant planet formation via gravitational instabilities (GI), in particular the fragmentation and clumping due to large-scale instabilities using different numerical setups. As our reference model we consider the temporal evolution of a compact (r = 10 AU) and massive (Mdisk ≈ 0.05M⊙) protoplanetary disk around a central object of subsolar mass (M⋆ = 0.646M⊙), which was suggested to form through common-envelope events by Schleicher & Dreizler (2014). Adopting a simple thermodynamical profile corresponding to a marginally stable disk, we show that fragmentation and clumping can be observed in the disk structure. In the numerical model, clumps are formed by GI but eventually vanish due to tidal disruptions. The latter reflects the absence of radiative feedback from the central star, which may stabilize the clumps on larger scales. Our simulations illustrate the capabilities of AMR-based modeling techniques for planet formation simulations. We expect that the inclusion of additional physics like radiative feedback and the formation of sink particles will provide a detailed framework to study the formation of planets via gravitational instabilities.