Planetary migration occurs when a planet or other body in orbit around a star interacts with a disk of gas or planetesimals, resulting in the alteration of its orbital parameters, especially its semi-major axis. Planetary migration is the most likely explanation for hot Jupiters (exoplanets with Jovian masses but orbits of only a few days). The generally accepted theory of planet formation from a protoplanetary disk predicts that such planets cannot form so close to their stars, as there is insufficient mass at such small radii and the temperature is too high to allow the formation of rocky or icy planetesimals.
It has also become clear that terrestrial-mass planets may be subject to rapid inward migration if they form while the gas disk is still present. This may affect the formation of the cores of the giant planets (which have masses of the order of 10 to 1000 Earth masses), if those planets form via the core-accretion mechanism.
Types of disk
Gas disk Observations suggest that gas in protoplanetary disks orbiting young stars have lifetimes of a few to several million years. If planets with masses of around an Earth mass or greater form while the gas is still present, the planets can exchange angular momentum with the surrounding gas in the protoplanetary disk so that their orbits change gradually. Although the sense of migration is typically inwards in locally isothermal disks, outward migration may occur in disks that possess entropy gradients.
Planetesimal disk During the late phase of planetary system formation, massive protoplanets and planetesimals gravitationally interact in a chaotic manner causing many planetesimals to be thrown into new orbits. This results in angular-momentum exchange between the planets and the planetesimals, and leads to migration (either inward or outward). Outward migration of Neptune is believed to be responsible for the resonant capture of Pluto and other Plutinos into the 3:2 resonance with Neptune.
Types of migration There are many different mechanisms by which planets' orbits can migrate, which are described below as disk migration (Type I migration, Type II migration, or Type III migration), tidal migration, planetesimal-driven migration, gravitational scattering, and Kozai cycles and tidal friction. This list of types is not exhaustive or definitive: Depending on what is most convenient for any one type of study, different researchers will distinguish mechanisms in somewhat different ways.
Classification of any one mechanism is mainly based on the circumstances in the disk that enable the mechanism to efficiently transfer energy and/or angular momentum to and from planetary orbits. As the loss or relocation of material in the disk changes the circumstances, one migration mechanism will give way to another mechanism, or perhaps none. If there is no follow-on mechanism, migration (largely) stops and the stellar system becomes (mostly) stable.
Disk migration Disk migration arises from the gravitational force exerted by a sufficiently massive body embedded in a disk on the surrounding disk's gas, which perturbs its density distribution. By the reaction principle of classical mechanics, the gas exerts an equal and opposite gravitational force on the body, which can also be expressed as a torque. This torque alters the angular momentum of the planet's orbit, resulting in a variation of the semi-major axis and other orbital elements. An increase over time of the semi-major axis leads to outward migration, i.e., away from the star, whereas the opposite behavior leads to inward migration.
Three sub-types of disk migration are distinguished as Types I, II, and III. The numbering is not intended to suggest a sequence or stages.
Type I migration Small planets undergo Type I disk migration driven by torques arising from Lindblad and co-rotation resonances. Lindblad resonances excite spiral density waves in the surrounding gas, both interior and exterior of the planet's orbit. In most cases, the outer spiral wave exerts a greater torque than does the inner wave, causing the planet to lose angular momentum, and hence migrate toward the star. The migration rate due to these torques is proportional to the mass of the planet and to the local gas density, and results in a migration timescale that tends to be short relative to the million-year lifetime of the gaseous disk. Additional co-rotation torques are also exerted by gas orbiting with a period similar to that of the planet. In a reference frame attached to the planet, this gas follows horseshoe orbits, reversing direction when it approaches the planet from ahead or from behind. The gas reversing course ahead of the planet originates from a larger semi-major axis and may be cooler and denser than the gas reversing course behind the planet. This may result in a region of excess density ahead of the planet and of lesser density behind the planet, causing the planet to gain angular momentum.
The planet mass for which migration can be approximated to Type I depends on the local gas pressure scale height and, to a lesser extent, the kinematic viscosity of the gas. In warm and viscous disks, Type I migration may apply to larger mass planets. In locally isothermal disks and far from steep density and temperature gradients, co-rotation torques are generally overpowered by the Lindblad torques. Regions of outward migration may exist for some planetary mass ranges and disk conditions in both local isothermal and non-isothermal disks. The locations of these regions may vary during the evolution of the disk, and in the local-isothermal case are restricted to regions with large density and/or temperature radial gradients over several pressure scale-heights. Type I migration in a local isothermal disk was shown to be compatible with the formation and long-term evolution of some of the observed Kepler planets. The rapid accretion of solid material by the planet may also produce a "heating torque" that causes the planet to gain angular momentum.
Type II migration A planet massive enough to open a gap in a gaseous disk undergoes a regime referred to as Type II disk migration. When the mass of a perturbing planet is large enough, the tidal torque it exerts on the gas transfers angular momentum to the gas exterior of the planet's orbit, and does the opposite interior to the planet, thereby repelling gas from around the orbit. In a Type I regime, viscous torques can efficiently counter this effect by resupplying gas and smoothing out sharp density gradients. But when the torques become strong enough to overcome the viscous torques in the vicinity of the planet's orbit, a lower density annular gap is created. The depth of this gap depends on the temperature and viscosity of the gas and on the planet mass. In the simple scenario in which no gas crosses the gap, the migration of the planet follows the viscous evolution of the disk's gas. In the inner disk, the planet spirals inward on the viscous timescale, following the accretion of gas onto the star. In this case, the migration rate is typically slower than would be the migration of the planet in the Type I regime. In the outer disk, however, migration can be outward if the disk is viscously expanding. A Jupiter-mass planet in a typical protoplanetary disk is expected to undergo migration at approximately the Type II rate, with the transition from Type I to Type II occurring at roughly the mass of Saturn, as a partial gap is opened.
Type II migration is one explanation for the formation of hot Jupiters. In more realistic situations, unless extreme thermal and viscosity conditions occur in a disk, there is an ongoing flux of gas through the gap. As a consequence of this mass flux, torques acting on a planet can be susceptible to local disk properties, akin to torques at work during Type I migration. Therefore, in viscous disks, Type II migration can be typically described as a modified form of Type I migration, in a unified formalism. The transition between Type I and Type II migration is generally smooth, but deviations from a smooth transition have also been found. In some situations, when planets induce eccentric perturbation in the surrounding disk's gas, Type II migration may slow down, stall, or reverse.
From a physical viewpoint, Type I and Type II migration are driven by the same type of torques (at Lindblad and co-rotation resonances). In fact, they can be interpreted and modeled as a single regime of migration, that of Type I appropriately modified by the perturbed gas surface density of the disk.
Type III disk migration Type III disk migration applies to fairly extreme disk / planet cases and is characterized by extremely short migration timescales. Although sometimes referred to as "runaway migration", the migration rate does not necessarily increase over time. Type III migration is driven by the co-orbital torques from gas trapped in the planet's libration regions and from an initial, relatively fast, planetary radial motion. The planet's radial motion displaces gas in its co-orbital region, creating a density asymmetry between the gas on the leading and the trailing side of the planet. Type III migration applies to disks that are relatively massive and to planets that can only open partial gaps in the gas disk. Previous interpretations linked Type III migration to gas streaming across the orbit of the planet in the opposite direction as the planet's radial motion, creating a positive feedback loop. Fast outward migration may also occur temporarily, delivering giant planets to distant orbits, if later Type II migration is ineffective at driving the planets back.
Gravitational scattering
Another possible mechanism that may move planets over large orbital radii is gravitational scattering by larger planets or, in a protoplanetary disk, gravitational scattering by over-densities in the fluid of the disk. In the case of the Solar System, Uranus and Neptune may have been gravitationally scattered onto larger orbits by close encounters with Jupiter and/or Saturn. Systems of exoplanets can undergo similar dynamical instabilities following the dissipation of the gas disk that alter their orbits and in some cases result in planets being ejected or colliding with the star.
Planets scattered gravitationally can end on highly eccentric orbits with perihelia close to the star, enabling their orbits to be altered by the tides they raise on the star. The eccentricities and inclinations of these planets are also excited during these encounters, providing one possible explanation for the observed eccentricity distribution of the closely orbiting exoplanets. The resulting systems are often near the limits of stability. As in the Nice model, systems of exoplanets with an outer disk of planetesimals can also undergo dynamical instabilities following resonance crossings during planetesimal-driven migration. The eccentricities and inclinations of the planets on distant orbits can be damped by dynamical friction with the planetesimals with the final values depending on the relative masses of the disk and the planets that had gravitational encounters.
Tidal migration Tides between the star and planet modify the semi-major axis and orbital eccentricity of the planet. If the planet is orbiting very near to its star, the tide of the planet raises a bulge on the star. If the star's rotational period is longer than the planet's orbital period the location of the bulge lags behind a line between the planet and the center of the star creating a torque between the planet and the star. As a result, the planet loses angular momentum and its semi-major axis decreases with time.