Outward Migration of a Gas Accreting Planet: A Semi-Analytical Formula

TL;DR

This paper derives a semi-analytical formula explaining conditions under which gas accreting planets undergo outward migration, challenging traditional inward migration models and helping to explain observed exoplanet distributions.

Contribution

It introduces a new semi-analytical formula for planetary migration that accounts for azimuthal asymmetry caused by planetary gas accretion, enabling broader application across different planet and disk conditions.

Findings

Outward migration occurs when the gap depth parameter is within a specific range.

Azimuthal asymmetry in corotation torque dominates over radial asymmetry.

The new formula can reproduce the observed pile-up of gas giants beyond 1 au.

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 pile-up of gas giant beyond 1 au. Analyzing the recent high-resolution hydrodynamical simulations by Li et al. (2024) and Pan et al. (2025) 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 semi-analytical formula that can be applied for broad range of planet mass and disk conditions. The striking outward migration is caused by azimuthal asymmetry in corotation torque exerted from cicumplanetary disk regions (connecting to horseshoe flow) 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 protoplanetry 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 $1/(1+K')$ is in the range of $0.03 \lesssim K' \lesssim 50$. 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 pile-up of exoplanetary gas giants beyond 1 au, although more detailed planet population synthesis calculations are needed in the future.