When Growing Giants Push Back, How Gas Accretion Drives Planets Outward
The paper “Outward Migration of a Gas Accreting Planet: A Semi-Analytical Formula” by Shigeru Ida and collaborators explores how giant planets can move outward through their birth disks, challenging older models that predict rapid inward drift. Traditionally, “Type II migration”, the motion of a massive planet that opens a gap in its surrounding gas disk, was thought to drag planets inward toward their stars too quickly to match the population of exoplanets seen beyond 1 astronomical unit (au). Ida and colleagues use results from recent high-resolution simulations to develop a new semi-analytical model that explains when and why planets can instead migrate outward.
From Inward to Outward Motion
The study begins by describing the observed “pile-up” of gas giants beyond 1 au, found by radial velocity surveys. Earlier theories tried to explain this using slower disk accretion rates or disk winds, but those mechanisms alone were insufficient. Recent hydrodynamical simulations, especially by Li et al. (2024) and Pan et al. (2025), revealed that a planet still forming and actively accreting gas can experience outward migration. This motion arises from an azimuthal (directional) imbalance in forces around the planet, rather than the radial imbalance traditionally considered. As gas spirals into the planet, it creates a slightly denser region ahead of the planet than behind it, this asymmetry pushes the planet outward.
Modeling Gaps and Gas Flow
To capture this behavior, Ida and colleagues model two key processes: how deeply a planet carves a gap in the disk, and how fast it accretes gas. They describe the gap depth using a parameter (K′), which depends on the planet’s mass, the disk’s viscosity (denoted by α), and its thickness (h). The authors also adopt previous results on gas accretion, distinguishing between “Bondi” accretion for smaller planets and “Hill” accretion for larger ones, to determine how efficiently a planet captures disk material. When a planet accretes most of the surrounding gas flow, it strongly alters the local gas density, setting the stage for the outward torque that drives migration.
The Condition for Outward Migration
By analyzing the simulation data, Ida finds that outward migration occurs only for a specific range of gap depths, defined by the surface-density reduction factor (1/(1+K′)). Migration is outward when (0.03 <= K′ <= 50). In simpler terms, the gap must be deep enough to influence gas flow but not so deep that the planet becomes isolated from the disk. Within this “sweet spot,” gas flowing around the planet creates the leading–trailing asymmetry responsible for the outward push. When the gap is too shallow or too deep, the torque balance shifts, and migration turns inward again.
A Unified Migration Formula
Using these results, the authors construct a general semi-analytical formula, the “Type II (full)” model, that captures both inward and outward migration. This new formula expands on earlier “Type II (gap)” and “Type II (gap + depletion)” models by incorporating the azimuthal asymmetry from gas accretion. The model matches hydrodynamical simulations within a factor of two, providing a practical tool for population-synthesis studies. The magnitude of the outward torque is comparable to that of inward migration predicted by older models, but the direction reverses due to the leading-side density enhancement in the circumplanetary disk.
Growing and Moving Together
In Section 3.4, Ida demonstrates how growth and migration occur simultaneously. As a forming giant planet accretes gas and gains mass, it may first migrate outward before eventually moving inward again once its gap becomes too deep. Using a disk model typical of young stars, the authors show that planets forming between 3 and 30 au can temporarily reverse direction, with some moving to hundreds of au. This outward migration helps explain the retention of gas giants beyond 1 au and could even relate to wide-orbit planetary systems like HR 8799.
Implications and Future Directions
The study concludes that outward migration driven by gas accretion plays a crucial role in shaping planetary systems. By linking the physics of accretion, disk viscosity, and torque asymmetry, Ida’s new formula provides a more complete framework for modeling how gas giants settle into their observed orbits. Future work will include population-synthesis simulations to test whether this mechanism can reproduce the full distribution of known exoplanets. In short, as gas giants grow, they do not always fall toward their stars, sometimes, by feeding on their disks, they can push themselves outward instead.
Source: Ida
