Halting Exoplanetary Migration in Protoplanetary Disks

Halting Migration: Numerical Calculations of Corotation Torques in the Weakly Nonlinear Regime

Author:

Duffell

Abstract:

Planets in their formative years can migrate due to the influence of gravitational torques in the protoplanetary disk they inhabit. For low-mass planets in an isothermal disk, it is known that there is a strong negative torque on the planet due to its linear perturbation to the disk, causing fast inward migration. The current investigation demonstrates that in these same isothermal disks, for intermediate-mass planets, there is a strong positive nonlinear corotation torque due to the effects of gas being pulled through a gap on horseshoe orbits. For intermediate-mass planets, this positive torque can partially or completely cancel the linear (Type I) torque, leading to slower or outward migration, even in an isothermal disk. The effect is most significant for Super-Earth and Sub-Jovian planets, during the transition from a low-mass linear perturber to a non-linear gap-opening planet, when the planet has opened a so-called 'partial gap'. In this study, numerical calculations of planet-disk interactions calculate these torques explicitly, and scalings are empirically constructed for migration rates in this weakly nonlinear regime. These results find outward migration is possible for planets with masses in the 20 - 100 Earth Mass range.

Tidal Torques on Misaligned Protoplanetary Disks in Binary Systems

Tidal Torques on Misaligned Disks in Binary Systems

Authors:

Lubow et al

Abstract:

We extend previous studies of the tidal truncation of coplanar disks in binary systems to the more general case of noncoplanar disks. As in the prograde coplanar case, Lindblad resonances play a key role in tidal truncation. We analyze the tidal torque acting on a misaligned nearly circular disk in a circular orbit binary system. We concentrate on the 2:1 inner Lindblad resonance associated with the m=2 tidal forcing (for azimuthal wavenumber m) that plays a major role in the usual coplanar case. We determine the inclination dependence of this torque, which is approximately cos^8(i/2) for misalignment angle i. Compared to the prograde coplanar case (i=0), this torque decreases by a factor of about 2 for i = pi/6 and by a factor of about 20 for i=pi/2. The Lindblad torque decreases to zero for a tilt angle of pi (counter-rotation), consistent with previous investigations. The effects of higher order resonances associated with m greater than 2 tidal forcing may contribute somewhat, but are much more limited than in the i=0 case. These results suggest that misaligned disks in binary systems can be significantly extended compared to their coplanar counterparts. In cases where a disk is sufficiently inclined and viscous, it can overrun all Lindblad resonances and overflow the Roche lobe of the disk central object.