DENSITY WAVES EXCITED BY LOW-MASS PLANETS IN PROTOPLANETARY DISKS. II. HIGH-RESOLUTION SIMULATIONS OF THE NONLINEAR REGIME
We investigate numerically the propagation of density waves excited by a low-mass planet in a protoplanetary disk in the nonlinear regime, using two-dimensional local shearing box simulations with the grid-based code Athena at high spatial resolution (256 grid points per scale height h). The nonlinear evolution results in the wave steepening into a shock, causing damping and angular momentum transfer to the disk. On long timescales this leads to spatial redistribution of the disk density, causing migration feedback and potentially resulting in gap opening. Previous numerical studies concentrated on exploring these secondary phenomena as probes of the nonlinear wave evolution. Here we focus on exploring the evolution of the basic wave properties, such as its density profile evolution, shock formation, and post-shock wave behavior, and provide comparison with analytical theory. The generation of potential vorticity at the shock is computed analytically and is subsequently verified by simulations and used to pinpoint the shock location. We confirm the theoretical relation between the shocking length and the planet mass (including the effect of the equation of state), and the post-shock decay of the angular momentum flux carried by the wave. The post-shock evolution of the wave profile is explored, and we quantitatively confirm its convergence to the theoretically expected N-wave shape. The accuracy of various numerical algorithms used to compute the nonlinear wave evolution is also investigated: we find that higher order spatial reconstruction and high resolution are crucial for capturing the shock formation correctly.
- OSTI ID:
- 21612731
- Journal Information:
- Astrophysical Journal, Vol. 741, Issue 1; Other Information: DOI: 10.1088/0004-637X/741/1/57; Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
COSMOLOGY AND ASTRONOMY
97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
ANGULAR MOMENTUM
ANGULAR MOMENTUM TRANSFER
COMPUTERIZED SIMULATION
COSMOLOGICAL MODELS
EQUATIONS OF STATE
HYDRODYNAMICS
MASS
MATHEMATICAL EVOLUTION
NONLINEAR PROBLEMS
NUMERICAL ANALYSIS
PLANETS
PROTOPLANETS
SATELLITES
SCALE HEIGHT
SHOCK WAVES
SPATIAL RESOLUTION
STAR EVOLUTION
TWO-DIMENSIONAL CALCULATIONS
DIMENSIONS
EQUATIONS
EVOLUTION
FLUID MECHANICS
HEIGHT
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICS
MECHANICS
MOMENTUM TRANSFER
RESOLUTION
SIMULATION