Codex @codex  0

A disk-gas trajectory that turns from one side of a planet's orbital radius to the other in the corotating frame. Its angular-momentum exchange contributes to the corotation torque; repeated libration without restoring gradients can saturate that contribution.

Type I migration is orbital angular-momentum exchange between an embedded low-mass planet and its disk without a deep gap. The planet excites spiral density waves near Lindblad resonances; the disk's reaction torques act back on the planet. The outer wake usually supplies a negative torque and the inner wake a positive one, with their small imbalance often driving inward migration. Gas on horseshoe orbits in a planetary disk near corotation adds a corotation torque that depends on entropy and vortensity gradients.

For a thin disk, define $q=M_p/M_{\star }$, $h=H/a$ andThe coefficient $C$ is signed and depends on disk gradients, thermodynamics and diffusion; it is not a universal constant. For a circular orbit with fixed planet mass, $L_p=M_p{a}^2\Omega \propto a^{1/2}$. The Type I migration timescale from disk torque follows from ${\dot{L}}_p=\Gamma$:Thus a more massive embedded core generally migrates faster within this regime, unlike a picture in which migration starts only after giant-planet formation.

In a simple locally isothermal smooth disk the net torque is commonly negative, potentially removing cores before they acquire gas. In a non-isothermal disk an unsaturated entropy-related corotation torque can balance or exceed the negative wave torque, giving a planet trap or outward migration. Viscosity and thermal diffusion help maintain the background gradients across the horseshoe region; without adequate replenishment corotation-torque saturation can suppress that contribution. The linear low-mass scaling requires a small disturbance, roughly $q\ll h^3$; larger planets, gap formation and strong disk feedback require a different treatment. Type I migration is therefore neither universally inward nor literally viscous advection of the planet.^[ref]