Planet-disk-wind interaction: The magnetized fate of protoplanets
Authors: Wafflard-Fernandez Gaylor , Lesur Geoffroy 
Published: July 2023

Context. Models of a planet-disk interaction are mainly based on 2D and 3D viscous hydrodynamic simulations. In such models, accretion is classically prescribed by an αv parameter which characterizes the turbulent radial transport of angular momentum in the disk. This accretion scenario has been questioned for a few years and an alternative paradigm has been proposed that involves the vertical transport of angular momentum by magneto-hydrodynamic (MHD) winds.

Aims. We revisit planet–disk interactions in the context of MHD wind-launching protoplanetary disks. In particular, we focus on the planet’s ability to open a gap and produce meridional flows. The accretion, magnetic field, and wind torque in the gap are also explored, as well as the evaluation of the gravitational torque exerted by the disk onto the planet.

Methods. We carried out high-resolution 3D global nonideal MHD simulations of a gaseous disk threaded by a large-scale vertical magnetic field harboring a planet in a fixed circular orbit using the code IDEFIX, which is accelerated with graphics processing units. We considered various planet masses (10 Earth masses, 1 Saturn mass, 1 Jupiter mass, and 3 Jupiter masses for a solar-mass star) and disk magnetizations (104 and 103 for the β-plasma parameter, defined as the ratio of the thermal pressure over the magnetic pressure).

Results. We find that a gap opening always occurs for sufficiently massive planets, typically on the order of a few Saturn masses for β0 = 103, with deeper gaps when the planet mass increases and when the initial magnetization decreases. We propose an expression for the gap-opening criterion when accretion is dominated by MHD winds. We show that accretion is unsteady and comes from surface layers in the outer disk, bringing material directly toward the planet poles. A planet gap is a privileged region for the accumulation of a large-scale magnetic field, preferentially at the gap center or at the gap edges in some cases. This results in a fast accretion stream through the gap, which can become sonic at high magnetizations. The torque due to the MHD wind responds to the planet presence in a way that leads to a more intense wind in the outer gap compared to the inner gap. More precisely, for massive planets, the wind torque is enhanced as it is fed by the planet torque above the gap’s outer edge, whereas the wind torque is seemingly diminished above the gap’s inner edge due to the planet-induced deflection of magnetic field lines at the disk surface. This induces an asymmetric gap, both in depth and in width, that progressively erodes the outer gap edge, reducing the outer Lindblad torque and potentially reversing the migration direction of Jovian planets in magnetized disks after a few hundreds of orbits. For low-mass planets, we find strongly fluctuating gravitational torques that are mostly positive on average, indicating a stochastic outward migration.

Conclusions. The presence of MHD winds strongly affects planet-disk interaction, both in terms of flow kinematics and protoplanet migration. This work illustrates the tight dependence between the planet torque, the wind torque, and magnetic field transport that is required to get the correct dynamics of such systems. In particular, many of the predictions from “effective” models that use parameterized wind torques are not recovered (such as gap formation criteria, the migration direction, and speed) in our simulations.