# PLANET-DISK INTERACTION IN THREE DIMENSIONS: THE IMPORTANCE OF BUOYANCY WAVES

## Abstract

We carry out local three-dimensional (3D) hydrodynamic simulations of planet-disk interaction in stratified disks with varied thermodynamic properties. We find that whenever the Brunt-Vaeisaelae frequency (N) in the disk is non-zero, the planet exerts a strong torque on the disk in the vicinity of the planet, with a reduction in the traditional 'torque cutoff'. In particular, this is true for adiabatic perturbations in disks with isothermal density structure, as should be typical for centrally irradiated protoplanetary disks. We identify this torque with buoyancy waves, which are excited (when N is non-zero) close to the planet, within one disk scale height from its orbit. These waves give rise to density perturbations with a characteristic 3D spatial pattern which is in close agreement with the linear dispersion relation. The torque due to these waves can amount to as much as several tens of percent of the total planetary torque, which is not expected based on analytical calculations limited to axisymmetric or low-m modes. Buoyancy waves should be ubiquitous around planets in the inner, dense regions of protoplanetary disks, where they might possibly affect planet migration.

- Authors:

- Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States)

- Publication Date:

- OSTI Identifier:
- 22078480

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal Letters

- Additional Journal Information:
- Journal Volume: 758; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 2041-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AXIAL SYMMETRY; COMPUTERIZED SIMULATION; DENSITY; DISPERSION RELATIONS; DISTURBANCES; INTERACTIONS; MIGRATION; ORBITS; PLANETS; PROTOPLANETS; SCALE HEIGHT; THERMODYNAMIC PROPERTIES; THREE-DIMENSIONAL CALCULATIONS; TORQUE

### Citation Formats

```
Zhu Zhaohuan, Stone, James M., and Rafikov, Roman R., E-mail: zhzhu@astro.princeton.edu, E-mail: jstone@astro.princeton.edu, E-mail: rrr@astro.princeton.edu.
```*PLANET-DISK INTERACTION IN THREE DIMENSIONS: THE IMPORTANCE OF BUOYANCY WAVES*. United States: N. p., 2012.
Web. doi:10.1088/2041-8205/758/2/L42.

```
Zhu Zhaohuan, Stone, James M., & Rafikov, Roman R., E-mail: zhzhu@astro.princeton.edu, E-mail: jstone@astro.princeton.edu, E-mail: rrr@astro.princeton.edu.
```*PLANET-DISK INTERACTION IN THREE DIMENSIONS: THE IMPORTANCE OF BUOYANCY WAVES*. United States. doi:10.1088/2041-8205/758/2/L42.

```
Zhu Zhaohuan, Stone, James M., and Rafikov, Roman R., E-mail: zhzhu@astro.princeton.edu, E-mail: jstone@astro.princeton.edu, E-mail: rrr@astro.princeton.edu. Sat .
"PLANET-DISK INTERACTION IN THREE DIMENSIONS: THE IMPORTANCE OF BUOYANCY WAVES". United States. doi:10.1088/2041-8205/758/2/L42.
```

```
@article{osti_22078480,
```

title = {PLANET-DISK INTERACTION IN THREE DIMENSIONS: THE IMPORTANCE OF BUOYANCY WAVES},

author = {Zhu Zhaohuan and Stone, James M. and Rafikov, Roman R., E-mail: zhzhu@astro.princeton.edu, E-mail: jstone@astro.princeton.edu, E-mail: rrr@astro.princeton.edu},

abstractNote = {We carry out local three-dimensional (3D) hydrodynamic simulations of planet-disk interaction in stratified disks with varied thermodynamic properties. We find that whenever the Brunt-Vaeisaelae frequency (N) in the disk is non-zero, the planet exerts a strong torque on the disk in the vicinity of the planet, with a reduction in the traditional 'torque cutoff'. In particular, this is true for adiabatic perturbations in disks with isothermal density structure, as should be typical for centrally irradiated protoplanetary disks. We identify this torque with buoyancy waves, which are excited (when N is non-zero) close to the planet, within one disk scale height from its orbit. These waves give rise to density perturbations with a characteristic 3D spatial pattern which is in close agreement with the linear dispersion relation. The torque due to these waves can amount to as much as several tens of percent of the total planetary torque, which is not expected based on analytical calculations limited to axisymmetric or low-m modes. Buoyancy waves should be ubiquitous around planets in the inner, dense regions of protoplanetary disks, where they might possibly affect planet migration.},

doi = {10.1088/2041-8205/758/2/L42},

journal = {Astrophysical Journal Letters},

issn = {2041-8205},

number = 2,

volume = 758,

place = {United States},

year = {2012},

month = {10}

}