The Hydrodynamic Flow Around an Exoplanet in a Protoplanetary Disk

The 3D Flow Field Around an Embedded Planet

Authors:

Fung et al

Abstract:

Understanding the 3D flow topology around a planet embedded in its natal disk is crucial to the study of planet formation. 3D modifications to the well-studied 2D flow topology have the potential to resolve longstanding problems in both planet migration and accretion. 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 high-resolution multi-GPU hydrodynamics code PEnGUIn. We show 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 and converges rapidly toward the planet, enters its Bondi sphere, performs one horseshoe turn, and exits radially in the midplane. A portion of this flow gathers enough speed to exit the horseshoe region altogether. We call this newly identified feature the "transient" horseshoe flow. As the flow continues close to the disk midplane, it splits into the up-down symmetric parts, and rolls up into a pair of counter-rotating, horizontal vortex lines shed downstream into the wake of the planet. This flow, unique to 3D, affects both planet migration and accretion. It prevents the planet from sustaining a hydrostatic atmosphere due to its intrusion into the Bondi sphere, and it also leads to a significant corotation torque on the planet, unanticipated by 2D analysis. In the reported simulation, starting with a Σ∼r−3/2 radial surface density profile, this torque is positive and largely cancels with the negative differential Lindblad torque, resulting in an almost 2 orders of magnitude reduction in the inferred rate of planet migration. Finally, we report that 3D effects can be suppressed by a sufficiently large disk viscosity, leading to results similar to those in 2D.