Type I Migration in Protoplanetary Disks

• Type I migration is the rapid orbital drift of low-mass planets in gaseous disks, where the net torque is the sum of differential Lindblad and corotation effects.
• Disk properties such as temperature gradients, opacity transitions, magnetic fields, and turbulence critically alter migration rates and may even reverse drift direction.
• The interplay of Type I migration with runaway gas-accretion and gap opening marks a transition in planet formation, highlighting the complex and regime-dependent dynamics.

Type I migration is the orbital drift of a low-mass, non-gap-opening body embedded in a gaseous disk. In this regime the planet does not significantly perturb the disk surface-density profile, so the torque is computed from the response of an almost unperturbed disk. The standard formulation writes the total torque as the sum of a differential Lindblad torque and a corotation torque, with the net sign set by local gradients, thermodynamics, and saturation physics rather than by planet mass alone. In classical locally isothermal disks the drift is usually rapid and inward, but modern work shows that opacity transitions, viscous heating, corotation saturation, multi-planet resonant dynamics, magnetic stresses, disk winds, and strong turbulence can all modify, stall, or qualitatively alter the canonical picture (Crida et al., 2016, Cossou et al., 2013, Masset, 2012).

1. Canonical regime and torque budget

In the standard low-mass regime, small planets do not affect the gas profile and migrate in fast Type I migration. A convenient decomposition is

$\Gamma=\Gamma_L+\Gamma_C,$

where $\Gamma_L<0$ is the differential Lindblad torque and $\Gamma_C$ is the corotation torque, which can be positive or negative depending on disk structure (Cossou et al., 2013). In one commonly used locally isothermal normalization,

$$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$

with the migration rate

$$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$

For the standard disk used most often by Crida and Bitsch, $\Sigma\propto r^{-1}$, $h=0.05$, and $\alpha=10^{-3}$, which gives $A\simeq 2.73$ in their isothermal setup (Crida et al., 2016).

The classical danger of Type I migration is that once planets exceed the mass range where non-isothermal corotation torques can halt or reverse migration, they are expected to drift inward on a timescale much shorter than the gas-disk lifetime. In the broader literature reviewed by Crida and Bitsch, migration can be inward or outward for planets below about $20$–$\Gamma_L<0$0 in non-isothermal regions with strong entropy gradients, but above a critical mass $\Gamma_L<0$1 the corotation torque saturates and vanishes, so the net torque becomes negative and migration is expected to be inward. They quote a typical migration time-scale of only $\Gamma_L<0$2 orbits for a $\Gamma_L<0$3 planet (Crida et al., 2016).

A central implication is that Type I migration is not a single rate law but a family of torque regimes. The low-mass condition, the degree of corotation saturation, and the local disk gradients jointly determine whether the process appears as rapid inward drift, slowed migration, or temporary outward motion.

2. Thermodynamics, opacity transitions, and migration traps

Thermal structure is a primary control parameter because the corotation torque depends sensitively on entropy and vortensity gradients. In radiatively efficient disks, the positive corotation torque seen in adiabatic disks is weakened because gas on horseshoe orbits can radiate away compressional heating rather than preserving the entropy contrast that builds a density asymmetry. In the $\Gamma_L<0$4 case of Tsang’s global 2D simulations, with $\Gamma_L<0$5, the total normalized torque at $\Gamma_L<0$6 was $\Gamma_L<0$7 in the adiabatic disk, but $\Gamma_L<0$8 in both the isothermal disk and a radiative disk with $\Gamma_L<0$9; the total torque becomes more negative as $\Gamma_C$0 increases, approaches the isothermal value for $\Gamma_C$1, and is always negative for $\Gamma_C$2 in the explored models (Yamada et al., 2010).

In simplified steady-state $\Gamma_C$3-disk models using the Paardekooper et al. (2011) prescription, outward migration requires a sufficiently steep temperature slope. The adopted criterion is approximately

$\Gamma_C$4

and the outward torque is strongest when thermal diffusion modestly exceeds viscosity,

$\Gamma_C$5

The same study emphasizes that the permitted mass range is narrow because saturation worsens as planet mass increases, while pebble accretion tends to drive planets to the pebble isolation mass

$\Gamma_C$6

which often exceeds the maximum mass that can remain in the outward-migration regime in hot young disks (Brasser et al., 2017).

Opacity transitions provide an additional structural route to stalling Type I migration. Masset’s generalized locally isothermal Lindblad torque formula shows that near an opacity transition the dominant correction is controlled not just by the local slopes $\Gamma_C$7 and $\Gamma_C$8, but by higher-order temperature structure, especially the third derivative of temperature. Their final expression is

$\Gamma_C$9

with $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$0 and $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$1 evaluated at $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$2 and $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$3. Near such transitions, the vortensity-related corotation torque can also be boosted strongly enough that the total torque reverses sign, so opacity transitions can act as migration traps or convergence zones (Masset, 2012).

Kretke and Lin place these results in a broader disk-structure framework. In their models, the inner viscously heated regions of typical protostellar disks can support outward migration because horseshoe and corotation torques exceed the differential Lindblad torque, whereas passive stellar irradiation causes Type I migration to be inward throughout much of the disk. The location and mass range of planet traps then depend on the adopted viscous-disk, irradiated-disk, or layered-accretion structure, and on whether the relevant corotation torques remain unsaturated (Kretke et al., 2012).

3. Saturation, convergence zones, and resonant chains

Once more than one low-mass planet migrates in the same disk, the single-planet zero-torque picture ceases to be adequate. In radiative disks with nominal convergence zones, convergently migrating planets do not simply pile up at the classical zero-torque radius. Instead, they are captured into mean-motion resonances, their eccentricities are maintained at nonzero values, the positive corotation torque is weakened, and the resonant chain settles at an inwardly shifted effective equilibrium. The relevant condition becomes

$$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$4

not the vanishing of each individual planet’s torque. Cossou, Raymond, and Pierens show that two planets captured in resonance can halt more than $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$5 AU interior to the nominal convergence zone, that the inward shift increases with eccentricity and lower-order resonances, and that systems with several planets can undergo stochastic collective migration because resonances are repeatedly broken and re-formed (Cossou et al., 2013).

Convergent Type I migration also naturally generates first-order resonant capture. Delisle and collaborators model two planets under convergent Type I migration and show that capture into a first-order resonance requires not only slow migration but also sufficiently weak eccentricity damping. Once capture occurs, the subsequent behavior falls into three regimes—stable trap, overstable trap, and escape—and the organization of outcomes can be displayed in a $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$6-$$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$7 diagram. Their central point is that weak eccentricity damping is a capture condition in its own right, rather than merely a post-capture modifier (Lin et al., 22 Jan 2025).

Hydrodynamic calculations then show that resonant trapping is often temporary. In 2D locally isothermal simulations of $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$8 and $$\Gamma=-A\Gamma_0,\qquad \Gamma_0=\left(\frac{M_p}{M_*}\right)^2\Sigma a^4\Omega^2 h^{-2},$$9 planets, convergent Type I migration captures the pair into the 2:1 mean-motion resonance, the inner planet’s eccentricity rises to about $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$0–$$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$1, and disc torques drive escape from resonance on a timescale of a few hundred orbits. The effect is more pronounced in highly viscous discs, but operates efficiently even in inviscid discs. The interpretation advanced by Hands and Alexander is overstable libration driven by moderate eccentricity damping, although the hydrodynamic implementation differs from simpler analytic models with fixed damping laws (Hands et al., 2017).

Higher-order resonances are not excluded from Type I migration. In more than $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$2 migration simulations of multi-planet systems interacting with a disk inner edge, second-order and third-order resonances in a state of libration formed in $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$3 and $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$4 of resonant-chain systems, respectively. Their formation favored slower disk migration and a smaller outer planet mass, and did not require a Laplace-like three-body resonance. Instead, higher-order capture was assisted by breaking a pre-existing first-order resonance, which generated small but non-zero initial eccentricities, $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$5 to $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$6. The same study predicts that librating higher-order resonances have higher equilibrium $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$7 ($$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$8), are more likely to appear as isolated pairs in otherwise first-order chains, and are more likely to emerge in the inner pairs of a chain (Keller et al., 17 Apr 2025).

4. Runaway accretion, gap opening, and the end of the classical Type I regime

A major problem in planet formation theory is the interval between the saturation of the positive corotation torque at roughly $$\dot a=-2A\left(\frac{M_p}{M_*}\right)\frac{\Sigma a^3\Omega}{M_*h^2}=-\frac{a}{\tau_m}.$$9–$\Sigma\propto r^{-1}$0 and the onset of gap opening. Crida and Bitsch analyze this interval by coupling a standard Type I migration law to a runaway gas-accretion prescription from Machida et al. (2010), using isothermal 2D FARGO-2D1D simulations and analytic estimates (Crida et al., 2016).

Their basic result is that genuine runaway accretion can outpace or at least match Type I drift over the critical mass interval. For the Machida rate,

$\Sigma\propto r^{-1}$1

they define a growth-to-migration ratio

$\Sigma\propto r^{-1}$2

and show that it is independent of $\Sigma\propto r^{-1}$3, $\Sigma\propto r^{-1}$4, and $\Sigma\propto r^{-1}$5. For $\Sigma\propto r^{-1}$6 and $\Sigma\propto r^{-1}$7, they find $\Sigma\propto r^{-1}$8 at $\Sigma\propto r^{-1}$9, so below that mass, in runaway accretion, growth is faster than Type I migration (Crida et al., 2016).

Gap opening is treated with the Crida et al. (2006) criterion. In the standard case $h=0.05$0, $h=0.05$1, the quoted threshold is

$h=0.05$2

or $h=0.05$3 in one numerical setup. Their analytic map in the $h=0.05$4 plane shows that for standard disks, roughly $h=0.05$5, a planet can reach $h=0.05$6 while losing less than $h=0.05$7 of its semi-major axis under pure Type I migration (Crida et al., 2016).

The transition is not fully smooth. In dense disks, partial gap opening creates a coorbital mass deficit,

$h=0.05$8

which can temporarily accelerate migration above the nominal Type I rate. Nonetheless, the simulations show that migrating giant planets always open gaps in the disk, and that migration does not prevent gap opening because the planet carries its horseshoe region with it and continues depleting it (Crida et al., 2016).

A second new point is that actual gas removal from the disk matters. If the planet accretes from its horseshoe region using the Kley sink prescription, gap opening is accelerated because the corotation region itself is depleted. This can move the planet out of the embedded Type I state before the nominal gravitational gap-opening mass is reached. By contrast, if accretion is limited to the radial disk flow,

$h=0.05$9

growth is too slow: the planet can lose about $\alpha=10^{-3}$0 of its semi-major axis before reaching the nominal gap-opening mass (Crida et al., 2016).

5. Magnetic fields, disk winds, and turbulence

Magnetic fields modify Type I migration by changing the wave spectrum, the coorbital flow, or the global disk profile. In weakly magnetized 2D laminar disks threaded by a toroidal field, McNally, Nelson, and Paardekooper identify an additional corotation torque—the “MHD torque excess”—caused by magnetic-flux accumulation along the downstream separatrices of the horseshoe region, which creates an azimuthally asymmetric underdense region. Its sign depends only on the density and temperature gradients, approximately through

$\alpha=10^{-3}$1

and the paper argues that it is positive for outer-disk profiles expected in protoplanetary disks. Its magnitude depends mainly on field strength and especially resistivity, and it can be strong enough to reverse migration even when magnetic pressure is less than one percent of thermal pressure (Guilet et al., 2013).

Large-scale ordered fields in ideal MHD behave differently in 3D. For pure $\alpha=10^{-3}$2, a vertical field mainly increases the effective stiffness of the disk and reduces the magnitude of the inward torque; when magnetic pressure approaches thermal pressure, inward migration is slowed by up to a factor of $\alpha=10^{-3}$3, but not reversed. A previous inference that a pure-$\alpha=10^{-3}$4 field whose amplitude decreases fast enough with radius leads to outward migration applies only in 2D; in 3D, the net torque remains negative, and a pure-$\alpha=10^{-3}$5 disk undergoes a rapid transition to turbulence because the planet-induced $\alpha=10^{-3}$6 perturbation can trigger MRI (Uribe et al., 2015).

In an ideal-MHD linear treatment of wind-driving disks, the field geometry $\alpha=10^{-3}$7 produces a qualitatively different result. In that case the dominant contributions to the torque add with the same sign from the two sides of the planet, because the planet couples directly to the disk’s underlying vertical angular-momentum transport mechanism. For slightly subthermal fields, the total torque can speed up inward migration by a factor $\alpha=10^{-3}$8, although the authors explicitly caution that dissipation and magnetic diffusivity could reduce this factor in a real disk (Bans et al., 2015).

Disk winds change Type I migration even without ideal-MHD wave coupling, simply by reshaping the inner disk. Ogihara, Suzuki, and collaborators define

$\alpha=10^{-3}$9

the ratio of viscous diffusion to disk-wind strength. Their migration maps show that Type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong, $A\simeq 2.73$0, because the inner surface-density profile becomes shallow or even positive and the corotation torque strengthens relative to the Lindblad torque (Ogihara et al., 2015). A related wind-torque model distinguishes whether wind-driven accretion reaches the midplane. In MRI-inactive disks, if the midplane participates in wind-driven accretion, the outward-migration region extends to smaller $A\simeq 2.73$1 and larger $A\simeq 2.73$2, including the super-Earth mass range; in the corresponding N-body runs no planets fall onto the central star, and some super-Earths migrate outward to $A\simeq 2.73$3 au (Ogihara et al., 2017).

Strong turbulence can invalidate the laminar Type I picture altogether. Global 2D simulations with driven turbulence show that when turbulence is weak, the classical linear Lindblad torque persists beneath stochastic forcing and can dominate over sufficiently long timescales. In strong turbulence, however, the wake and local flow structure are disrupted, the running-time average torque does not recover the classical value, and migration becomes random-walk-dominated. Wu, Chen, and Lin propose a transition criterion

$A\simeq 2.73$4

with $A\simeq 2.73$5 tentatively, and interpret the high-turbulence regime as genuinely chaotic Type I migration (Wu et al., 2023).

6. Regime limits, competing processes, and broader extensions

Type I migration is also sensitive to how angular momentum is deposited in low-viscosity disks. Long-duration 2D simulations in nearly laminar disks show two damping regimes for planet-driven density waves. At $A\simeq 2.73$6, corresponding to $A\simeq 2.73$7, angular momentum transport is viscosity dominated and migration agrees with Tanaka et al. (2002). At $A\simeq 2.73$8, or $A\simeq 2.73$9, shock-dominated damping produces a broad density depression and the migration rate falls to the viscous drift rate. At $20$0, or $20$1, migration is essentially halted and tends to slowly reverse outward at late times, while inviscid runs become nonmonotonic because Rossby vortex instability produces large transient torques (Yu et al., 2010). This suggests that the classical Type I limit is not universal even in non-magnetized, locally isothermal disks.

A second complication is that Type I migration need not be the only active radial-transport mechanism. High-resolution self-consistent $20$2-body simulations that include planetesimal-driven migration, gas drag, and a Type I force law show that outward planetesimal-driven migration can occur even in the presence of inward Type I torque. The comparison runs establish that the fraction of outward migrators is lowest when both gas drag and Type I are active, but outward migration due to planetesimal scattering still occurs, and the appendix shows that it persists even for MMSN-like gas-to-dust ratios (Jinno et al., 2024). A plausible implication is that the practical outcome of “Type I migration” in formation models can be set by competition between multiple transport channels rather than by gas torque alone.

The term has also been extended beyond classical planet–gas-disk systems. In Saturn’s rings, a modified particulate-disk version of Type I migration has been used to explain the non-Keplerian motion of propeller moons: angular-momentum exchange with a radially structured ring can create an equilibrium semimajor axis, and if the moon is displaced from that equilibrium by a collision or stochastic kick, the torque imbalance drives exponential return (Tiscareno, 2012). In a different direction, strong-turbulence work explicitly applies chaotic Type I migration to low-mass companions embedded in AGN disks as well as to planets in gravito-turbulent protoplanetary disks (Wu et al., 2023).

Across these variants, the main caveat is methodological. Many influential results rely on locally isothermal thermodynamics, 2D hydrodynamics, ideal-MHD linear theory, static disks, or prescribed migration and damping forces rather than fully self-consistent 3D thermochemical or non-ideal-MHD calculations. The literature therefore does not support a single universal Type I migration law. It supports a structured hierarchy of regimes: classical inward drift in laminar low-mass disks, thermally or structurally induced traps, resonant capture and escape in multi-planet systems, rapid transition toward gap opening during runaway growth, magnetic or wind-driven modifications in magnetized disks, and stochastic or chaotic motion when turbulence destroys the wake itself (Crida et al., 2016, Cossou et al., 2013, Bans et al., 2015).