  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.
