Abstract

The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. The use of numerical approaches provides a method to tackle the weaknesses of current models and is an important tool to close gaps in poorly constrained areas such as the rapid formation of giant planets in highly evolved systems. So far, most numerical approaches make use of Lagrangian-based smoothed-particle hydrodynamics techniques or grid-based 2D axisymmetric simulations. We present a new global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code enzo. With this setup, we explore the potential impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison. Additionally, we study the effects of varying the disk radius. The physical settings involve disks with R$_{disk}$ = 10,100 and 300 AU, with a mass of M$_{disk}$ {\ap} 0.05 M$_{⊙}$ and a central object of subsolar mass (M$_{⋆}$ = 0.646 M$_{⊙}$). To validate our thermodynamical approach we include a set of simulations with a dynamically stable profile (Q$_{init}$ = 3) and similar grid parameters. The development of fragmentation and the buildup of distinct clumps in the disk is strongly dependent on the chosen AMR grid settings. By combining our findings from the resolution and parameter studies we find a general lower limit criterion to be able to resolve GI induced fragmentation features and distinct clumps, which induce turbulence in the disk and seed giant planet formation. Irrespective of the physical extension of the disk, topologically disconnected clump features are only resolved if the fragmentation-active zone of the disk is resolved with at least 100 cells. The latter corresponds to a minimum requirement for all global disk setups. Our simulations illustrate the capabilities of AMR-based modeling techniques for planet formation simulations and underline the importance of balanced refinement settings to reproduce fragmenting structures. The clumps in our models are migrating inward and are eventually destroyed because of tidal disruptions, reflecting the absence of radiative feedback from the central star, which may stabilize the clumps on larger scales. We expect that the inclusion of additional physics, like a radiation transport mechanism and the formation of sink particles, will provide a detailed framework to study the formation of planets via gravitational instabilities in a global disk view.