Planet migration in windy discs

ABSTRACT Accretion of protoplanetary discs (PPDs) could be driven by magnetohydrodynamic 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 time-scale across the horseshoe due to disc wind $\tau _{\rm dw}$, the horseshoe libration time-scale $\tau _{\rm lib}$ and U-turn time-scale $\tau _{\rm U-turn}$. Initially, as wind strength increases and the advection time-scale 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 $10^{-7}\, \mathrm{ M}_\odot \text{yr}^{-1}$.