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

Planets in their formative years can migrate due to the influence of\ngravitational torques in the protoplanetary disk they inhabit. For low-mass\nplanets in an isothermal disk, it is known that there is a strong negative\ntorque on the planet due to its linear perturbation to the disk, causing fast\ninward migration. The current investigation demonstrates that in these same\nisothermal disks, for intermediate-mass planets, there is a strong positive\nnonlinear corotation torque due to the effects of gas being pulled through a\ngap on horseshoe orbits. For intermediate-mass planets, this positive torque\ncan partially or completely cancel the linear (Type I) torque, leading to\nslower or outward migration, even in an isothermal disk. The effect is most\nsignificant for Super-Earth and Sub-Jovian planets, during the transition from\na low-mass linear perturber to a non-linear gap-opening planet, when the planet\nhas opened a so-called 'partial gap'. In this study, numerical calculations of\nplanet-disk interactions calculate these torques explicitly, and scalings are\nempirically constructed for migration rates in this weakly nonlinear regime.\nThese results find outward migration is possible for planets with masses in the\n20 - 100 Earth Mass range.\n

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