Planetary Torque in 3D Isentropic Disks

TL;DR

This study investigates the 3D torque exerted on Earth-mass planets in protoplanetary disks through high-resolution simulations, confirming the torque's independence from smoothing length and its weak dependence on the adiabatic index, with implications for planet migration.

Contribution

The paper provides the first detailed 3D simulation analysis of planetary torque in isentropic disks, validating torque formulae and exploring flow patterns around embedded planets.

Findings

Torque is independent of smoothing length ($r_s$).

Torque shows weak dependence on the adiabatic index ($b3$).

Flow within the Hill sphere includes active flow and meridional vortices.

Abstract

Planet 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 requirement in resolution. Using two different hydrodynamics code, FARGO3D and PEnGUIn, we simulate disk-planet interaction for a 1 to 5 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 ($r_{\rm s}$), and that it has a weak dependence on the adiabatic index of the gaseous disk ($\gamma$). 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, and show that 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 $r_{\rm s}$ or $\gamma$, up to supersonic speeds for the smallest $r_{\rm s}$ and $\gamma$ in our study.