Introduction
Star and planet formation begins within the diffuse interstellar medium, where gas and dust concentrate into cold, dense molecular clouds. Within these clouds compact, optically thick condensations such as Bok globules and dark nebulae shield their interiors from external radiation, permitting gravitational fragmentation and collapse. Collapsing fragments accrete material from surrounding envelopes and disks to form protostars, which evolve into pre-main-sequence objects; low-mass examples are classified as T Tauri stars and intermediate-mass examples as Herbig Ae/Be stars. During these early stages, bipolar jets and winds driven by accretion processes interact with the ambient medium to produce shock-excited emission regions observed as Herbig–Haro objects.
The theoretical framework for this sequence invokes several key concepts. Jeans instability delineates when a parcel of gas becomes gravitationally unstable and collapses; the initial mass function characterizes the statistical outcome of stellar masses produced by that collapse; and the Kelvin–Helmholtz mechanism describes how gravitational contraction powers a protostar’s luminosity until sustained nuclear burning commences. The nebular hypothesis places planetary formation within a flattened protoplanetary disk fed by accretion, so planets grow by collecting solids and gas from that disk environment.
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Planetary migration arises when forming planets exchange energy and angular momentum with their gaseous or planetesimal-rich surroundings, producing torques and scattering that alter orbital semimajor axes. Migration driven by disk–planet torques or by cumulative planetesimal encounters provides a natural explanation for hot Jupiters: gas giants formed at several astronomical units can be transported inward to very short-period orbits, since in situ formation at small radii is precluded by low solid mass and high temperatures. Migration also strongly affects lower-mass bodies and giant-planet cores; terrestrial-mass planets embedded in a gas disk may spiral rapidly inward, and the movement of cores during the epoch of core accretion can change the timing, location, and material available for subsequent gas accretion, thereby reshaping the ultimate architecture of planetary systems.
Gas disk
The gaseous component of protoplanetary disks is transient, dispersing on million‑year timescales (typically a few to several Myr), and thus constrains the duration of gas-mediated growth and orbital evolution. Bodies with masses of order one Earth mass or larger couple efficiently to the disk and can exchange enough angular momentum with the gas to modify their orbits appreciably while the disk persists.
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These planet–disk interactions operate through torques that change a planet’s semi‑major axis gradually, with migration occurring on timescales comparable to the disk lifetime. The sign and magnitude of the net torque depend sensitively on the disk’s thermodynamic structure: in locally isothermal models the net torque is usually negative and drives inward migration, whereas disks that sustain radial entropy gradients alter the torque balance and can produce conditions that permit outward migration.
Planetesimal disk
In the late stages of planet formation, strong gravitational encounters between growing protoplanets and a dense swarm of planetesimals drive a dynamically active phase in which many small bodies are scattered onto new trajectories. Each scattering event redistributes angular momentum: planetesimals that gain angular momentum move to higher-energy (larger semimajor axis) orbits while those that lose angular momentum fall inward, and by conservation the interacting planet acquires the opposite change. Cumulative exchanges of angular momentum between planets and the planetesimal population therefore produce systematic orbital migration of the planets; the direction of migration depends on the net sense of the exchanges — a planet that preferentially scatters planetesimals inward gains angular momentum and migrates outward, whereas preferential outward scattering causes inward migration. A canonical example is Neptune, whose inferred outward displacement during the late stages of formation provides a natural explanation for the capture of Pluto and the class of “Plutinos” into the 3:2 mean-motion resonance. As a planet’s resonances sweep through the residual small-body disk during migration, objects encountered by a moving resonance can be trapped into stable librating configurations, altering their eccentricities and long-term stability and thereby contributing to the present-day structure of the outer Solar System.
Types of planetary migration
Planetary orbital migration encompasses several distinct physical processes by which a planet’s semimajor axis, eccentricity, or inclination are altered through exchange of energy and angular momentum with other system components. Different authors organize these processes differently for convenience, but they fall broadly into a few physically motivated classes.
Disk-driven migration arises from gravitational interactions between a planet and the gaseous protoplanetary disk. Within this category three canonical regimes are identified (commonly called Type I, Type II and Type III), each defined by the disk properties and the planet’s ability to excite and exchange angular momentum with surrounding gas. These interactions produce torques that can steadily move a planet inward or outward, and the detailed outcome depends on local disk density, temperature, viscosity and the planet’s mass.
Tidal migration is governed by dissipative tidal forces between massive bodies—most often a planet and its host star. Tidal torques transfer angular momentum between spin and orbital motion and, together with internal dissipation, can alter orbital radius, damp eccentricity, and synchronize rotation. The rate and direction of tidal evolution depend sensitively on the bodies’ internal dissipation efficiencies and structural response to tidal forcing.
Planetesimal-driven migration is a cumulative, stochastic process in which a planet exchanges momentum with a population of smaller solid bodies through repeated scattering and, occasionally, accretion. As planetesimals are redistributed or removed, the net angular-momentum budget of the planet changes, producing gradual radial displacement that tracks the evolving distribution of solid material.
Gravitational scattering refers to impulsive close encounters among planets or between planets and large residual bodies. Such interactions can rapidly reconfigure orbital elements, producing large changes in semimajor axis, excitation of eccentricity and inclination, and in some cases ejection or collision. Scattering is therefore a principal route to dynamically hot and potentially unstable architectures.
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A distinct secular pathway combines Kozai–Lidov cycles with tidal friction. Perturbations from a distant, inclined companion induce long-period oscillations in a planet’s eccentricity and inclination. When those oscillations bring the planet to very small pericenter distances, tidal dissipation becomes effective, removing orbital energy and progressively shrinking and circularizing the orbit.
Which mechanism dominates in a given system is set by the local environment—particularly the presence and state of the gas disk, the inventory of solids, and the arrangement of other massive bodies. As the protoplanetary disk dissipates or solids are depleted, the operative migration regime can shift or cease, and without further efficient mediating processes the system tends toward a quasi-stable configuration.
Disk migration
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Disk migration is the orbital evolution produced when a body massive enough to disturb a gaseous protoplanetary disk gravitationally perturbs the local gas density. These perturbations generate azimuthal and radial asymmetries in the disk mass distribution; by Newton’s third law the distorted gas in turn exerts an equal and opposite gravitational influence on the embedded object. That interaction is most appropriately described as a torque on the orbit rather than as a single-point force, because it changes the body’s orbital angular momentum.
The resulting torque alters orbital elements over time: net removal of angular momentum causes the semi‑major axis to shrink (inward migration), while net addition causes it to grow (outward migration); eccentricity and inclination may also be modified as a consequence of the same disk–body torques. Disk-driven migration is categorized into three dynamical regimes — Types I, II and III — labels that distinguish different torque/response behaviours and mass regimes, but that do not imply a temporal or evolutionary ordering among stages of planetary growth.
Type I migration
Type I migration describes the orbital evolution of low-mass planets embedded in a gaseous protoplanetary disk, driven primarily by gravitational torques arising at Lindblad and co-rotation resonances. Lindblad resonances excite spiral density waves on both sides of the planet’s orbit; the outer wave typically exerts the stronger torque, extracting angular momentum from the planet and producing the usual tendency for inward migration. The characteristic migration speed increases with the planet’s mass and with the local gas surface density, so Type I timescales are often short compared with the multi‑million‑year lifetimes of protoplanetary disks.
Co-rotation torques originate from disk gas that corotates with the planet and follows horseshoe-shaped streamlines in the planet’s rotating frame. Because gas executing a horseshoe U‑turn ahead of the planet often comes from larger orbital radii and can be cooler or denser than the gas coming from behind, an asymmetric density distribution can develop (excess ahead, deficit behind), producing a net positive co-rotation torque that can transfer angular momentum to the planet. Whether this positive contribution outweighs the Lindblad torque depends sensitively on local disk structure.
The range of planet masses for which the Type I description applies is set chiefly by the disk’s pressure scale height (a measure of its thermal thickness) and, to a lesser extent, by its kinematic viscosity; hotter and more viscous disks tend to maintain Type I behavior up to larger planet masses. In locally isothermal disks, and in regions without strong radial gradients of density or temperature, Lindblad torques usually dominate so net inward migration is the norm. Nevertheless, both locally isothermal and thermally stratified (non‑isothermal) disk models admit limited zones where the total torque is positive and outward migration can occur for particular planet masses; in the strictly local‑isothermal case such outward zones require strong radial variations in density or temperature extending over several pressure scale heights and therefore depend sensitively on the disk’s radial profile.
Additional processes can modify or reverse Type I migration. Rapid accretion of solids can produce an accretional heating asymmetry (a “heating torque”) that supplies positive angular momentum, and time‑dependent changes in disk structure shift the locations and strengths of inward versus outward migration zones. Population‑synthesis studies and comparisons with Kepler detections indicate that Type I processes, including their modified forms, can play a central role in shaping the architectures of observed planetary systems.
Type II migration
Type II migration arises once a planet is massive enough to carve an annular depression in a gaseous protoplanetary disk: the planet’s tidal forces transfer angular momentum outward and remove it from the inner disk, and when these torques exceed the disk’s local viscous stresses a persistent low–surface-density gap forms. The ease and depth of gap opening depend on the disk’s thermodynamic and transport properties (temperature and viscosity) together with planet mass; in typical disk models partial clearing appears near Saturn masses, while a Jupiter-mass object is expected to enter the nominal Type II regime. In contrast to Type I, where viscous diffusion continually replenishes the planet’s vicinity and smooths density contrasts, Type II begins when tidal torques dominate viscous resupply and maintain a sustained surface-density depression.
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In the idealized limit of a perfect, impenetrable gap the planet’s orbital evolution is tied to the viscous evolution of the disk: a planet in the inner, accreting disk migrates inward on the viscous timescale, generally more slowly than a comparable Type I migration rate, whereas in a viscously expanding outer disk the same coupling can drive outward motion. Real disks, however, typically allow some gas to flow across the gap; this leakage makes the net torques on the planet sensitive to local surface density, temperature and viscosity, so that Type II behaviour is best understood as Type I–like torques modified by the planet‑induced alteration of the disk profile. The transition from Type I to Type II is therefore usually continuous as mass increases and the density perturbation grows, although numerical and analytic work reveals circumstances in which the progression is non‑monotonic or punctuated.
Finally, disk eccentricity excited by the planet can substantially change this picture: an eccentric gaseous response can retard or stall migration and, in some parameter regimes, reverse its direction. Physically and in models both Type I and Type II phenomena are produced by the same classes of gravitational resonances (Lindblad and corotation); conceptually they form a single migration regime in which the classical Type I torques are altered by the planet’s modification of the disk’s surface density.
Type III disk migration
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Type III disk migration is a rapid mode of planet–disk interaction that arises in relatively extreme combinations of planet mass and disk properties and yields radial migration rates far shorter than those of the standard Type I and Type II regimes. Although sometimes labeled “runaway migration,” the term is misleading: the defining characteristic is very short migration timescales rather than a guaranteed time‑increasing rate. The dominant torque in this regime derives from gas retained within the planet’s co‑orbital (libration) region; because the planet does not clear this region completely, the trapped co‑orbital gas can exert large, asymmetric forces on the planet. A necessary ingredient is an initial, relatively rapid radial displacement of the planet through the disk, which perturbs and redistributes co‑orbital material and establishes a density contrast between the leading and trailing sides of the planet. It is this density asymmetry — not merely streaming flow across the orbit — that produces the strong net co‑orbital torque responsible for the rapid migration. Consequently, Type III migration requires comparatively massive disks and planets that open only partial gaps so that substantial gas remains in the libration region; without that retained gas the co‑orbital torque mechanism cannot operate. Modern interpretations thus emphasize trapped co‑orbital gas and the density imbalance set up by the planet’s motion, in contrast to earlier views that invoked a positive feedback between cross‑orbit streaming and displacement. Temporally, Type III episodes can drive either very fast inward movement or transient outward excursions and do not always exhibit monotonic acceleration. Such transient outward movements offer a plausible pathway for delivering giant planets to large orbital radii on short timescales, particularly if subsequent gap opening and Type II evolution fail to return the planet inward, and therefore Type III behavior can be important for explaining some observed wide‑orbit giant planets.
Gravitational scattering—whether through close encounters with more massive planets or interactions with localized overdensities in a protoplanetary disk—provides an efficient route for relocating planets to substantially larger orbital radii than their formation locations. In the Solar System, for example, scattering by Jupiter and Saturn offers a natural explanation for the outward displacement of Uranus and Neptune onto their present wide orbits. Once the gaseous component of the disk has cleared, multi-planet systems are susceptible to dynamical instabilities that can dramatically reconfigure orbital architectures, producing outcomes that include planet–planet ejections or collisions with the host star. Strong scattering events also pump up orbital eccentricities and inclinations, accounting plausibly for the relatively large eccentricities observed among many exoplanets and often leaving systems close to dynamical stability boundaries. Planets thrown onto very eccentric trajectories can acquire small perihelion distances, allowing dissipation by stellar tides to modify semimajor axes and eccentricities and thereby alter long-term orbital evolution. In systems with an exterior planetesimal reservoir, interactions between planets and that disk can drive planetesimal-driven migration and resonance crossings that trigger further instabilities—the Nice model of the Solar System provides a paradigmatic example. Finally, dynamical friction exerted by a massive planetesimal swarm can partially reverse the excitation produced by scattering, damping eccentricities and inclinations on a timescale and to an extent that depend on the mass ratio between the planetesimal disk and the scattered planets.
Tidal migration
Tidal interactions between a star and a close-in planet redistribute orbital energy and angular momentum, driving secular changes in the planet’s semi-major axis and eccentricity. When a planet orbits inside the stellar corotation radius (i.e., faster than the star’s rotation), the planet raises a tidal bulge on the star that lags the planet’s instantaneous position; the resulting gravitational torque extracts angular momentum from the planetary orbit and causes gradual orbital decay.
For eccentric orbits the tidal forcing is strongly phase dependent and peaks near perihelion. Because tidal dissipation decelerates the planet most effectively at closest approach, the orbit’s aphelion is reduced more rapidly than the perihelion, producing net eccentricity damping alongside inward migration.
Unlike migration driven by interactions with a protoplanetary gas disk, which operates only during the short-lived nebular phase (a few million years), tidal migration persists on stellar evolutionary timescales and can continue to reshape orbits for billions of years. As a result, many close-in planets experience substantial inward modification after disk dispersal; their present-day semi-major axes are often substantially smaller—commonly about half—than at the epoch when the gas nebula cleared.
In hierarchical binary systems a planet whose orbital plane is significantly tilted with respect to the binary orbit is subject to long-term, secular perturbations from the distant stellar companion that exchange orbital inclination and eccentricity — the Kozai mechanism. These Kozai cycles drive periodic, coupled oscillations in eccentricity and inclination: when inclination falls, eccentricity can rise to very large values, producing brief but extreme reductions in perihelion distance that bring the planet much closer to its host star at periastron.
During these high-eccentricity passages tidal forces between planet and star become strong and dissipate orbital energy and angular momentum. Because dissipation is concentrated near periastron, each high-eccentricity episode extracts some angular momentum and gradually reduces the planet’s semi‑major axis, producing inward migration through the combined action of Kozai excitation and tidal friction. The episodic nature of the Kozai cycles slows this secular shrinkage relative to continuous dissipation, since tides act efficiently only during the peaks of eccentricity.
If tidal decay reduces the semi‑major axis enough that the distant companion no longer imposes significant perturbations, the Kozai oscillations are quenched; thereafter tides operate continuously to circularize the orbit and complete the inward migration. This Kozai-plus-tides pathway can also alter orbital orientation substantially, including the generation of retrograde orbits through angular‑momentum exchanges during the high‑eccentricity phase. Similar behaviour can arise in compact planetary systems without a stellar companion: planet–planet scattering can produce mutual inclinations that trigger Kozai‑like oscillations, leading likewise to high eccentricities, tidal shrinkage and circularization, and in some cases orbital flips.
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Planetesimal-driven migration
Planetesimal-driven migration arises from the cumulative effect of many gravitational encounters between a planet and a population of small bodies. Each close approach transfers angular momentum between planet and planetesimal; while the outcome of any single encounter depends sensitively on geometry (approach direction, impact parameter and orbital phase), the planet’s long-term orbital drift is set by the statistical average of these exchanges across the entire encounter ensemble.
The sign and magnitude of the net migration are determined by the specific angular-momentum distribution of the interacting planetesimals relative to the planet. Populations with higher mean specific angular momentum than the planet (for example, a disk concentrated outside the planet’s orbit) tend to push the planet outward, whereas populations with lower mean specific angular momentum drive inward motion. When the planet and its surrounding disk have comparable angular momentum, the evolution becomes controlled by the balance between sinks (loss channels) and sources (supply channels) that alter the pool of bodies available for scattering.
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In an isolated single-planet system the dominant sink is typically ejection of planetesimals from the system. Because ejection can preferentially remove planetesimals carrying higher angular momentum, the planet tends to lose angular momentum and migrate inward. By contrast, in multi-planet systems neighbouring planets act as both sinks and sources: planetesimals scattered into an adjacent planet’s domain may be removed from the original scattering population or be captured and transferred, thereby changing the local angular-momentum budget. Such interplanetary exchanges generally segregate angular-momentum transfer—an outer planet preferentially removes or delivers material with larger specific angular momentum relative to an inner planet—producing divergent orbital evolution of the planetary pair.
Dynamical mechanisms that replenish the scattering population also matter. Mean-motion resonances excite planetesimal eccentricities until their orbits cross a planet’s path, injecting fresh scattering bodies and modifying both the rate and the sign of angular-momentum transfer. Because the planet’s motion concurrently reshapes the local planetesimal reservoir, migration acts simultaneously as a source and a sink: this self-alteration yields positive feedback that tends to prolong migration in its initial direction unless removal processes outpace resupply. Migration is therefore damped when sinks remove planetesimals faster than they are replenished, and sustained when the inflow rate exceeds losses.
Two distinct sustained regimes are commonly identified. Runaway migration occurs when a planet’s motion continuously sweeps up new planetesimals faster than they are lost, amplifying its drift. Forced migration describes sustained evolution that primarily results from planetesimals being transferred into another planet’s influence, which shifts the angular-momentum balance and drives systematic orbital change.
The intrinsic frequency of encounters also biases migration. For a single planet in a planetesimal disk, inner (shorter-period, lower–specific-angular-momentum) bodies have shorter synodic times and are encountered more often, producing a bias toward loss of planetary angular momentum and inward migration. In the presence of gas, however, aerodynamic drag can preferentially remove these shortest-period small bodies from the scattering population; for certain size ranges this selective depletion reverses the encounter bias and can enable outward planetesimal-driven migration.
Resonance capture
Convergent orbital migration—when outer planets migrate inward faster than inner ones or when an inner planet’s inward drift is arrested—naturally drives pairs and chains of planets toward simple period ratios and thus into mean‑motion resonances. Two common migration‑halt configurations favor such convergent capture: an inner planet stopped at the gas‑disk inner edge, producing compact systems of close‑in planets, and stalls at disk “convergence zones” where Type I torques cancel (for example near compositional transitions such as the ice line), which concentrate embryos at larger orbital radii and generate more widely spaced resonant chains. In this way spatial variations of Type I torques organize the disk, gathering migrating bodies at radii where the net torque vanishes and promoting resonant locking among multiple objects.
Resonant capture can also occur through strong gravitational encounters, particularly when planets attain non‑negligible eccentricities; such impulsive captures differ from smooth torque‑driven locking because they commonly trap bodies with significant eccentricity and inclination. Solar System examples illustrate both modes: the “grand tack” scenario invokes Jupiter’s inward migration and subsequent capture with Saturn into an exterior mean‑motion resonance, a sequence that reversed Jupiter’s motion and, together with later resonant captures of Uranus and Neptune, plausibly prevented formation of a compact super‑Earth system. Similarly, outward migration of a massive planet can shepherd planetesimals into long‑lived resonant populations—the resonant trans‑Neptunian objects in the Kuiper belt are a clear manifestation of this process.
Despite the efficiency of resonance formation during the gas‑disk phase, most observed exoplanets are not locked in exact resonances, indicating substantial post‑disk dynamical evolution. After gas dispersal, the loss of damping allows mutual perturbations to grow, leading to gravitational instabilities, orbit crossing and scattering that break resonance chains. A variety of additional mechanisms can erode or prevent resonant capture: interactions with remnant planetesimal disks, tidal evolution with the host star, stochastic turbulent torques in the gas, and perturbations from another planet’s density wake; each operates most effectively in particular mass and orbital regimes. Resonance capture is also intrinsically more difficult for sub‑Neptune bodies on eccentric orbits, so low‑mass, eccentric planets frequently end up in near‑resonant or non‑resonant configurations, contributing to the observed diversity of planetary system architectures.
In the Solar System
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Beyond Neptune the small-body reservoir is partitioned into three sparsely populated, icy regions—the Kuiper belt (∼30–55 AU), the scattered disc (extending beyond 100 AU), and the distant Oort cloud (beginning near 50,000 AU)—which together supply most observed comets. Planet formation at these distances was hindered by the low surface density and slow accretion rates of the outer protoplanetary disc, so no additional planets formed there. Dynamical reconstructions and numerical models indicate, however, that the Kuiper belt was originally far more massive and located closer to the Sun, containing millions of planetesimals with an original outer edge near ≈30 AU (the present orbital radius of Neptune).
After the giant planets formed, their orbits continued to evolve through repeated gravitational encounters with the abundant leftover planetesimals beyond them. Roughly 500–600 million years after formation (around 4 Ga) Jupiter and Saturn crossed their mutual 2:1 mean-motion resonance in a divergent manner; this resonance crossing amplified their eccentricities and destabilized the orbits of Uranus and Neptune. The ensuing close encounters scattered Neptune inward past Uranus and into the formerly dense planetesimal belt, triggering a cascade of scattering events that redistributed small icy bodies throughout the Solar System.
The cascade operated through systematic exchange of angular momentum: when a planet scattered a planetesimal inward, the planet typically gained angular momentum and migrated outward; that inward-scattered planetesimal was then deflected by the next inner giant, repeating the process and progressively shifting the giants’ semimajor axes while transporting planetesimals toward the inner system. The chain ended when planetesimals reached Jupiter, whose strong gravity either placed them on long-period, comet-like orbits or expelled them from the Sun’s gravitational domain; these outcomes produced only a small inward adjustment of Jupiter’s orbit. This planetesimal-driven migration and scattering naturally explains the present low mass of the trans‑Neptunian populations and the broad, dynamically excited structure of the Kuiper belt and scattered disc.
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By contrast, the terrestrial planets experienced little subsequent orbital displacement after their formation epoch of giant impacts and early dynamical excitation; their orbits remained largely stable and did not undergo the extensive migration observed among the giant planets.