Warped Disk Evolution in Grid-Based Simulations

• Published in: arXiv.org 2024-06
• Main Authors: Kimmig, C N, Dullemond, C P
• Format: Article
• Language: English
• Subjects: Evolution; Kinematics; One dimensional models; Planet formation; Protoplanetary disks; Shearing; Simulation; Smooth particle hydrodynamics; Spherical coordinates; Viscosity
• ISSN: 2331-8422

Observations show evidence that a significant fraction of protoplanetary disks contain warps. A warp in a disk evolves in time affecting the appearance of shadows and greatly influencing kinematic signatures. So far, many theoretical studies of warped disks have been conducted using Smoothed Particle Hydrodynamics (SPH) methods. In our approach, we use a grid-based method in spherical coordinates which has notable advantages: the method allows for accurate modelling of low viscosity values and the resolution does not depend on density or mass of the disk, which allows surface structures to be resolved. We perform 3D simulations using FARGO3D to simulate the evolution of a warped disk and compare the results to one-dimensional models using a ring code. Additionally, we extensively investigate the applicability of grid-based methods to misaligned disks and test their dependency on grid resolution as well as disk viscosity. We find that grid-based simulations are capable of simulating disks not aligned to the grid geometry. Our three-dimensional simulation of a warped disk compares well to one-dimensional models in evolution of inclination. However, we find a twist which is not captured in 1D models. After thorough analysis we suspect this to be a physical effect possibly caused by non-linear effects neglected in the one-dimensional equations. Evaluating the internal dynamics, we find sloshing and breathing motions as predicted in local shearing box analysis. They can become supersonic, which may have consequences on kinematic observations of warped disks. Warped disks can be accurately modelled in 3D grid-based simulations when using reasonably good resolution, especially in the \(\theta\)-direction. We find good agreement with the linear approximation of the sloshing motion which highlights the reliability of 1D models.