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Title: Planetary Torque in 3D Isentropic Disks

Abstract

Planetary migration is inherently a three-dimensional (3D) problem, because Earth-size planetary cores are deeply embedded in protoplanetary disks. Simulations of these 3D disks remain challenging due to the steep resolution requirements. Using two different hydrodynamics codes, FARGO3D and PEnGUIn, we simulate disk–planet interaction for a one to five Earth-mass planet embedded in an isentropic disk. We measure the torque on the planet and ensure that the measurements are converged both in resolution and between the two codes. We find that the torque is independent of the smoothing length of the planet’s potential ( r {sub s}), and that it has a weak dependence on the adiabatic index of the gaseous disk ( γ ). The torque values correspond to an inward migration rate qualitatively similar to previous linear calculations. We perform additional simulations with explicit radiative transfer using FARGOCA, and again find agreement between 3D simulations and existing torque formulae. We also present the flow pattern around the planets that show active flow is present within the planet’s Hill sphere, and meridional vortices are shed downstream. The vertical flow speed near the planet is faster for a smaller r {sub s} or γ , up to supersonic speeds for themore » smallest r {sub s} and γ in our study.« less

Authors:
 [1]; ;  [2];  [3]
  1. Department of Astronomy, University of California at Berkeley, Campbell Hall, Berkeley, CA 94720-3411 (United States)
  2. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Av. Universidad s/n, 62210 Cuernavaca, Mor. (Mexico)
  3. Université de la Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange UMR 7293, Nice (France)
Publication Date:
OSTI Identifier:
22663758
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astronomical Journal (Online); Journal Volume: 153; Journal Issue: 3; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; COMPUTERIZED SIMULATION; F CODES; HYDRODYNAMICS; INDEXES; ISENTROPIC PROCESSES; MASS; P CODES; PLANETS; PROTOPLANETS; RADIANT HEAT TRANSFER; RESOLUTION; SATELLITES; THREE-DIMENSIONAL CALCULATIONS; TORQUE; VORTICES

Citation Formats

Fung, Jeffrey, Masset, Frédéric, Velasco, David, and Lega, Elena, E-mail: jeffrey.fung@berkeley.edu. Planetary Torque in 3D Isentropic Disks. United States: N. p., 2017. Web. doi:10.3847/1538-3881/153/3/124.
Fung, Jeffrey, Masset, Frédéric, Velasco, David, & Lega, Elena, E-mail: jeffrey.fung@berkeley.edu. Planetary Torque in 3D Isentropic Disks. United States. doi:10.3847/1538-3881/153/3/124.
Fung, Jeffrey, Masset, Frédéric, Velasco, David, and Lega, Elena, E-mail: jeffrey.fung@berkeley.edu. Wed . "Planetary Torque in 3D Isentropic Disks". United States. doi:10.3847/1538-3881/153/3/124.
@article{osti_22663758,
title = {Planetary Torque in 3D Isentropic Disks},
author = {Fung, Jeffrey and Masset, Frédéric and Velasco, David and Lega, Elena, E-mail: jeffrey.fung@berkeley.edu},
abstractNote = {Planetary migration is inherently a three-dimensional (3D) problem, because Earth-size planetary cores are deeply embedded in protoplanetary disks. Simulations of these 3D disks remain challenging due to the steep resolution requirements. Using two different hydrodynamics codes, FARGO3D and PEnGUIn, we simulate disk–planet interaction for a one to five Earth-mass planet embedded in an isentropic disk. We measure the torque on the planet and ensure that the measurements are converged both in resolution and between the two codes. We find that the torque is independent of the smoothing length of the planet’s potential ( r {sub s}), and that it has a weak dependence on the adiabatic index of the gaseous disk ( γ ). The torque values correspond to an inward migration rate qualitatively similar to previous linear calculations. We perform additional simulations with explicit radiative transfer using FARGOCA, and again find agreement between 3D simulations and existing torque formulae. We also present the flow pattern around the planets that show active flow is present within the planet’s Hill sphere, and meridional vortices are shed downstream. The vertical flow speed near the planet is faster for a smaller r {sub s} or γ , up to supersonic speeds for the smallest r {sub s} and γ in our study.},
doi = {10.3847/1538-3881/153/3/124},
journal = {Astronomical Journal (Online)},
number = 3,
volume = 153,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}
  • We provide torque formulae for low-mass planets undergoing type I migration in gaseous disks. These torque formulae put special emphasis on the horseshoe drag, which is prone to saturation: the asymptotic value reached by the horseshoe drag depends on a balance between coorbital dynamics (which tends to cancel out or saturate the torque) and diffusive processes (which tend to restore the unperturbed disk profiles, thereby desaturating the torque). We entertain the question of this asymptotic value and derive torque formulae that give the total torque as a function of the disk's viscosity and thermal diffusivity. The horseshoe drag features twomore » components: one that scales with the vortensity gradient and another that scales with the entropy gradient and constitutes the most promising candidate for halting inward type I migration. Our analysis, which is complemented by numerical simulations, recovers characteristics already noted by numericists, namely, that the viscous timescale across the horseshoe region must be shorter than the libration time in order to avoid saturation and that, provided this condition is satisfied, the entropy-related part of the horseshoe drag remains large if the thermal timescale is shorter than the libration time. Side results include a study of the Lindblad torque as a function of thermal diffusivity and a contribution to the corotation torque arising from vortensity viscously created at the contact discontinuities that appear at the horseshoe separatrices. For the convenience of the reader mostly interested in the torque formulae, Section 8 is self-contained.« less
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  • The kinetic theory of planetary rings developed by Araki and Tremaine (1986) and Araki (1988) is extended and refined, with a focus on the implications of finite particle size: (1) nonlocal collisions and (2) finite filling factors. Consideration is given to the derivation of the equations for the local steady state, the low-optical-depth limit, and the steady state at finite filling factors (including the effects of collision inelasticity, spin degrees of freedom, and self-gravity). Numerical results are presented in extensive graphs and characterized in detail. The importance of distinguishing effects (1) and (2) at low optical depths is stressed, andmore » the existence of vertical density profiles with layered structures at high filling factors is demonstrated. 17 refs.« less
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