The 3D Flow Field Around an Embedded Planet

TL;DR

This study uses 3D hydrodynamic simulations to analyze the flow around an embedded planet, revealing complex vertical structures and flow patterns that influence planet accretion and migration, differing significantly from 2D models.

Contribution

It provides the first detailed 3D analysis of flow topology around a low-mass planet, uncovering flow features that impact migration and accretion processes.

Findings

Horseshoe region has a vertical columnar structure extending beyond the Hill sphere.

Transient horseshoe flow involves high-altitude fluid descending into the Bondi sphere.

3D flow induces a positive corotation torque, slowing planet migration by a factor of three.

Abstract

3D modifications to the well-studied 2D flow topology around an embedded planet have the potential to resolve long-standing problems in planet formation theory. We present a detailed analysis of the 3D isothermal flow field around a 5 Earth-mass planet on a fixed circular orbit, simulated using our multi-GPU hydrodynamics code PEnGUIn. We find that, overall, the horseshoe region has a columnar structure extending vertically much beyond the Hill sphere of the planet. This columnar structure is only broken for some of the widest horseshoe streamlines, along which high altitude fluid descends rapidly into the planet's Bondi sphere, performs one horseshoe turn, and exits the Bondi sphere radially in the midplane. A portion of this flow exits the horseshoe region altogether, which we refer to as the "transient" horseshoe flow. The flow continues as it rolls up into a pair of up-down symmetric horizontal vortex lines shed into the wake of the planet. This flow, unique to 3D, affects both planet accretion and migration. It prevents the planet from sustaining a hydrostatic atmosphere due to its intrusion into the Bondi sphere, and leads to a significant corotation torque on the planet, unanticipated by 2D analysis. In the reported simulation, starting with a $\Sigma\sim r^{-3/2}$ radial surface density profile, this torque is positive and partially cancels with the negative differential Lindblad torque, resulting in a factor of 3 slower planet migration rate. Finally, we report 3D effects can be suppressed by a sufficiently large disk viscosity, leading to results similar to 2D.