Planet Migration in Windy Discs

TL;DR

This study uses 2D simulations to explore how magnetized disc winds affect planet migration in protoplanetary discs, revealing conditions that can lead to outward or inward migration depending on wind strength and timescales.

Contribution

It introduces a dynamical model for angular momentum transport by disc winds and systematically analyzes their impact on planet migration directions and rates.

Findings

Strong disc winds can induce outward planet migration.

Migration direction depends on the hierarchy of timescales $ au_{dw}$, $ au_{lib}$, and $ au_{U-turn}.

A zone of outward migration exists for planets at 10-100 au in typical PPDs.

Abstract

Accretion of protoplanetary discs (PPDs) could be driven by MHD disc winds rather than turbulent viscosity. With a dynamical prescription for angular momentum transport induced by disc winds, we perform 2D simulations of PPDs to systematically investigate the rate and direction of planet migration in a windy disc. We find that the the strength of disc winds influences the corotation region similarly to the "desaturation" effect of viscosity. The magnitude and direction of torque depend sensitively on the hierarchy between the radial advection timescale across the horseshoe due to disc wind $\tau_{\rm dw}$, the horsehoe libration timescale $\tau_{\rm lib}$ and U-turn timescale $\tau_{\rm U-turn}$. Initially, as wind strength increases and the advection timescale shortens, a non-linear horseshoe drag emerges when $\tau_{\rm dw} \lesssim \tau_{\rm lib}$, which tends to drive strong outward migration. Subsequently, the drag becomes linear and planets typically still migrate inward when $\tau_{\rm dw} \lesssim \tau_{\rm U-turn} \sim \tau_{\rm lib}h$, where $h$ is the disc aspect ratio. For a planet with mass ratio of $\sim 10^{-5}$, the zone of outward migration sandwiched between inner and outer inward migration zones corresponds to $\sim $ 10-100 au in a PPD with accretion rates between $10^{-8}$ and $10^{-7}$ $M_\odot \text{yr}^{-1}$.