Outward Migration of a Gas Accreting Planet: A Semianalytical Formula

Abstract Type II orbital migration is a key process to regulate the mass and semimajor axis distribution of exoplanetary giant planets. The conventional formula of Type II migration generally predicts too rapid inward migration to reconcile with the observed pileup of gas giants beyond 1 au. Analyzing the recent high-resolution hydrodynamical simulations by Y.-P. Li et al. and J.-P. Pan et al. that show robust outward migration of a gas accreting planet, we here clarify the condition for the outward migration to occur and derive a general semianalytical formula that can be applied for a broad range of planet mass and disk conditions. The striking outward migration is caused by azimuthal asymmetry in corotation torque exerted from circumplanetary disk regions (connecting to horseshoe flows) that is produced by the planetary gas accretion, while the conventional inward migration model is based on radial asymmetry in the torques from the circumstellar protoplanetary disk. We found that the azimuthal asymmetry dominates and the migration is outward when the gap depth defined by the surface density reduction factor of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> is in the range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.03</mml:mn> <mml:mo>≲</mml:mo> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msup> <mml:mo>≲</mml:mo> <mml:mn>50</mml:mn> </mml:math> . Using simple models with the new formula, we demonstrate that the outward migration plays an important role in shaping the mass and semimajor axis distribution of gas giants. The concurrent dependence of planets’ accretion rate and migration direction on their masses and disk properties potentially reproduces the observed pileup of exoplanetary gas giants beyond 1 au, although more detailed planet population synthesis calculations are needed in the future.