Start with a planet that keeps coming around
Imagine marking a young planet’s position each time it crosses the same direction from its star. If the marks gradually approach the star, the planet is migrating. It is still orbiting; its orbital size is changing on a much longer clock.
The dashed circles in the Lab remember the initial orbital sizes. The bright planets follow a later section of an actual synthetic integration. Both planets use the same clock. Their revolutions and migration share that physical clock.
Reading: Paardekooper · Ogilvie & Lubow
The disk does not pull equally from every direction
An exactly axisymmetric ring cannot give a planet a sustained azimuthal push. A planet disturbs that symmetry. It launches spiral waves into the gas on both sides of its orbit. Inner and outer responses exchange angular momentum with it in opposite directions.
For many smooth disks the outer contribution wins, leaving a negative net wave torque and inward migration. The outer disk is not simply “behind” the planet: the spiral response, its phase and the disk gradients matter. The picture follows a calculated linear wake phase; gas density and complete fluid motion require a separate model.
Reading: Paardekooper · Ogilvie & Lubow
Some gas turns around the planet’s orbit
Gas slightly inside the orbit moves around the star faster than the planet. Gas just outside moves more slowly. Near the planet, some trajectories make a U-turn and exchange sides, outlining a horseshoe in the rotating frame.
These turns carry angular momentum and can give a positive or negative corotation torque. A temperature gradient can help the positive contribution overcome the negative wave torque. Change the gradient in the Lab and inspect the signed contributions before guessing the direction.
Reading: Paardekooper · Ogilvie & Lubow
Diffusion can keep an imbalance alive
A trapped patch of gas can gradually mix away the contrast that made its first turn effective. The nonlinear corotation torque then saturates. Heat diffusion and viscosity can restore the contrast, but extremely rapid diffusion also weakens the nonlinear horseshoe response.
That is why a viscosity slider is not just a speed control. At fixed temperature gradient it can change the balance of two torques, even reversing the migration direction. There is no universal inward conveyor belt.
Reading: Paardekooper · Fendyke & Nelson
Two planets may briefly share a rhythm
When the outer orbit shrinks faster, the planets approach a simple period ratio. Their repeated gravitational kicks may settle into a resonant pattern. The angles of those kicks then turn back and forth instead of sweeping around a full circle.
Open “Temporary capture”, then “Later: let go”. The physical parameters are identical. The first record ends at twelve thousand initial inner periods; the second continues to fifty thousand. Both angles are bounded in the first record’s later half, yet circulate later. The finite record diagnoses a temporary capture window. Its lifetime and the cause of escape remain open questions.
Reading: Izidoro et al. · Mills et al.
A present-day orbit is a clue, not a birth certificate
Kepler-223 supplies a real example of a carefully modeled resonant chain. Its measured transit timing shifts let us build a limited angle diagnostic in the tutorial. The published work goes further, fitting the interacting orbits and testing their stability.
Neither those timing measurements nor our two synthetic planets tell us a unique birth disk. Growth, disk evolution and later interactions can change the route. The next chapter starts with the quantity every proposed route must account for: angular momentum.
Reading: Mills et al. · Izidoro et al.