Planetary migration is the process by which planets or other bodies in orbit around a star change their orbital parameters, especially their semi-major axis, due to interactions with a disk of gas or planetesimals. This phenomenon is important for understanding the formation and evolution of planetary systems, as well as the diversity of exoplanets.
Types of Disk
Planetary migration can occur in different types of disks, depending on the stage of the system's development. In the early phase, when the star is still surrounded by a protoplanetary disk of gas and dust, planets can exchange angular momentum with the surrounding gas and migrate inward or outward. This type of migration is called gas disk migration and is the most likely explanation for the existence of hot Jupiters, which are gas giant planets with very short orbital periods. Gas disk migration can also affect the formation of terrestrial planets, as they may be subject to rapid inward migration if they form while the gas disk is still present.
Gas disk migration is driven by the differential rotation of the gas disk, which creates pressure and density gradients that exert torques on the planet. The magnitude and direction of these torques depend on the location of the planet relative to the disk's inner and outer edges, as well as the disk's temperature, density, and viscosity profiles. For example, if the planet is inside the disk's inner edge, it will experience a positive torque that pushes it outward. If the planet is outside the disk's outer edge, it will experience a negative torque that pulls it inward. If the planet is between the disk's edges, it will experience a combination of positive and negative torques that can cancel out or reinforce each other, depending on the disk's properties and the planet's eccentricity and inclination.
Gas disk migration can explain why some exoplanets have very close orbits to their host stars, such as 51 Pegasi b, the first exoplanet discovered around a main-sequence star in 1995. This planet has a mass of about 0.47 Jupiter masses and an orbital period of only 4.23 days, which implies a very high temperature and a strong tidal interaction with the star. It is unlikely that such a planet formed in situ, as the high temperature and radiation would prevent the accumulation of gas and dust. Instead, it is more plausible that the planet formed farther away from the star and migrated inward due to the gas disk torques.
Gas disk migration can also explain why some exoplanets have very eccentric orbits, such as HD 80606 b, which has a mass of about 3.94 Jupiter masses and an orbital period of 111.8 days, but an eccentricity of 0.93, meaning that its distance from the star varies from 0.03 to 0.83 astronomical units. Such a high eccentricity can result from the interaction of the planet with another massive planet or a stellar companion, which can perturb the planet's orbit and increase its eccentricity. However, this scenario requires a fine-tuning of the initial conditions and the timing of the perturbation. Alternatively, the planet's eccentricity can result from the interaction of the planet with the gas disk, which can induce eccentricity damping or excitation, depending on the disk's properties and the planet's location.
Gas disk migration can also affect the formation of terrestrial planets, as they may be subject to rapid inward migration if they form while the gas disk is still present. This can prevent them from growing to larger sizes and reaching stable orbits, as they may be accreted by the star or collide with other planets. This scenario is known as the migration barrier and poses a challenge for the classical core accretion model of planet formation, which assumes that terrestrial planets form by the gradual accumulation of solid material in the inner regions of the disk. To overcome this challenge, some alternative mechanisms have been proposed, such as the pebble accretion model, which assumes that terrestrial planets form by the rapid accretion of small pebbles that drift inward from the outer regions of the disk.
In the later phase, when the gas disk has dissipated and the system consists of planets and planetesimals, gravitational interactions among these bodies can also cause orbital changes. This type of migration is called planetesimal-driven migration and is responsible for the reshaping of the solar system after its formation. For example, the outward migration of Neptune is believed to have captured Pluto and other objects into resonant orbits, creating the Kuiper belt.
Planetesimal-driven migration is driven by the scattering of planetesimals by the planets, which can transfer angular momentum and energy between them. The net effect of these scattering events depends on the mass ratio and the orbital configuration of the planets and the planetesimals. For example, if the planet is much more massive than the planetesimals, it will tend to scatter them outward and migrate inward. If the planet is comparable in mass to the planetesimals, it will tend to scatter them in both directions and migrate randomly. If the planet is much less massive than the planetesimals, it will tend to scatter them inward and migrate outward.
Planetesimal-driven migration can explain why the giant planets of the solar system have different orbital eccentricities and inclinations than their initial values, as well as why some of them have irregular satellites and rings. For example, the Nice model proposes that the giant planets of the solar system initially formed in a compact and circular configuration, with Jupiter and Saturn in a 3:2 resonance, and Uranus and Neptune closer to the Sun than their current positions. However, as they interacted with a massive disk of planetesimals, they underwent orbital instability and migration, which increased their eccentricities and inclinations, and scattered some of the planetesimals into the inner and outer regions of the solar system, creating the asteroid belt and the Kuiper belt. The migration of the giant planets also affected the orbits of the terrestrial planets and the Moon, and may have triggered the Late Heavy Bombardment, a period of intense cratering on the inner solar system bodies about 3.9 billion years ago.
Planetesimal-driven migration can also explain why some exoplanets have very large semi-major axes, such as HR 8799 b, which has a mass of about 7 Jupiter masses and an orbital distance of about 68 astronomical units from its host star. Such a large distance is difficult to explain by gas disk migration, as the gas disk would be too thin and weak to exert significant torques on the planet. Instead, it is more plausible that the planet formed closer to the star and migrated outward due to the scattering of planetesimals by another massive planet or a stellar companion.
Types of Migration
There are many different mechanisms by which planets' orbits can migrate, depending on the mass of the planet, the structure of the disk, and the presence of other planets. Some of the most common types of migration are:
Type I migration: This occurs when a low-mass planet (less than a few Earth masses) interacts with the gas disk through Lindblad and corotation torques. These torques can cause the planet to lose or gain angular momentum and migrate inward or outward. The direction and rate of migration depend on the disk's temperature, density, and viscosity profiles, as well as the planet's eccentricity and inclination. Typically, Type I migration is inward and fast, unless the disk has a positive entropy gradient or a large surface density gradient, which can reverse the direction or slow down the migration.
Type I migration is the dominant mode of migration for low-mass planets in the gas disk, and can have a significant impact on their formation and survival. For example, Type I migration can explain why some exoplanets have very small orbital periods, such as Kepler-10b, which has a mass of about 3.33 Earth masses and an orbital period of only 0.84 days. This planet is likely to have formed farther away from the star and migrated inward due to the gas disk torques, reaching a very close orbit where the tidal forces of the star prevent further migration.
Type I migration can also explain why some exoplanets have very large orbital periods, such as Kepler-1649c, which has a mass of about 1.06 Earth masses and an orbital period of 19.5 days, placing it in the habitable zone of its host star. This planet is likely to have formed closer to the star and migrated outward due to the gas disk torques, reaching a more distant orbit where the disk's pressure gradient prevents further migration.
Type I migration can also affect the formation of terrestrial planets in the solar system, as they may be subject to rapid inward migration if they form while the gas disk is still present. This can prevent them from growing to larger sizes and reaching stable orbits, as they may be accreted by the star or collide with other planets. This scenario is known as the migration barrier and poses a challenge for the classical core accretion model of planet formation, which assumes that terrestrial planets form by the gradual accumulation of solid material in the inner regions of the disk. To overcome this challenge, some alternative mechanisms have been proposed, such as the pebble accretion model, which assumes that terrestrial planets form by the rapid accretion of small pebbles that drift inward from the outer regions of the disk.
Type II migration: This occurs when a high-mass planet (more than a few Earth masses) opens a gap in the gas disk due to its gravitational influence. The planet then migrates along with the viscous evolution of the disk, which tends to transport angular momentum outward and mass inward. The rate of migration depends on the disk's viscosity and the planet's mass. Type II migration is usually inward and slower than Type I migration, unless the disk is very massive or the planet is very low-mass, in which case the migration can be outward or faster.
Type II migration is the dominant mode of migration for high-mass planets in the gas disk, and can have a significant impact on their orbital stability and diversity. For example, Type II migration can explain why some exoplanets have very large masses and radii, such as WASP-17b, which has a mass of about 0.49 Jupiter masses and a radius of about 1.99 Jupiter radii, making it the largest known exoplanet. This planet is likely to have formed farther away from the star and migrated inward due to the gas disk torques, reaching a very close orbit where the tidal forces of the star inflate its radius.
Type II migration can also explain why some exoplanets have very small masses and radii, such as Kepler-37b, which has a mass of about 0.01 Earth masses and a radius of about 0.3 Earth radii, making it the smallest known exoplanet. This planet is likely to have formed closer to the star and migrated outward due to the gas disk torques, reaching a more distant orbit where the disk's pressure gradient prevents further migration.
Type II migration can also affect the formation of giant planets in the solar system, as they may be subject to rapid inward migration if they form while the gas disk is still present. This can prevent them from reaching their current positions and masses, as they may be accreted by the star or collide with other planets. This scenario is known as the core accretion catastrophe and poses a challenge for the classical core accretion model of planet formation, which assumes that giant planets form by the gradual accumulation of gas onto a solid core. To overcome this challenge, some alternative mechanisms have been proposed, such as the disk instability model, which assumes that giant planets form by the rapid collapse of a dense and massive region of the gas disk.
Type III migration: This occurs when a moderately massive planet (a few Earth masses) interacts with the gas disk through co-orbital torques. These torques can cause the planet to undergo runaway migration, either inward or outward, depending on the disk's vortensity gradient and the planet's mass. Type III migration is very fast and can result in large orbital changes in a short time.
Type III migration is a rare but dramatic mode of migration for intermediate-mass planets in the gas disk, and can have a significant impact on their orbital dynamics and diversity. For example, Type III migration can explain why some exoplanets have very high orbital inclinations, such as XO-3b, which has a mass of about 11.79 Jupiter masses and an orbital inclination of about 37.3 degrees, meaning that its orbit is highly tilted with respect to the star's equator. This planet is likely to have formed in a coplanar orbit with the star and migrated inward or outward due to the co-orbital torques, reaching a very eccentric orbit where the tidal forces of the star or another planet perturb its inclination.
Type III migration can also explain why some exoplanets have very low orbital inclinations, such as Kepler-419b, which has a mass of about 2.5 Jupiter masses and an orbital inclination of about 0.2 degrees, meaning that its orbit is nearly aligned with the star's equator. This planet is likely to have formed in a highly inclined orbit with the star and migrated inward or outward due to the co-orbital torques, reaching a very circular orbit where the tidal forces of the star or another planet dampen its inclination.
Type III migration can also affect the formation of intermediate-mass planets in the solar system, as they may be subject to rapid inward or outward migration if they form while the gas disk is still present. This can prevent them from reaching their current positions and masses, as they may be accreted by the star or collide with other planets. This scenario is known as the oligarchic growth barrier and poses a challenge for the classical core accretion model of planet formation, which assumes that intermediate-mass planets form by the gradual accumulation of solid material in the outer regions of the disk. To overcome this challenge, some alternative mechanisms have been proposed, such as the planetesimal isolation model, which assumes that intermediate-mass planets form by the rapid accretion of planetesimals that are trapped in a pressure maximum of the gas disk.
Resonance Capture
The migration of planets can also affect the orbits of other planets in the system, especially if they are in or near mean motion resonances. A mean motion resonance occurs when two planets have orbital periods that are in a simple ratio, such as 2:1 or 3:2. This causes them to experience periodic gravitational perturbations that can alter their eccentricities and inclinations. If the planets migrate at different rates, they can become locked in a resonance, which can stabilize or destabilize their orbits, depending on the resonance and the migration direction.
Resonance capture is a common outcome of planetary migration and can explain many features of the solar system and exoplanetary systems. For example, the orbital configuration of the four Galilean moons of Jupiter is a result of resonance capture during their inward migration in the gas disk. The moons are in a 4:2:1 resonance, meaning that for every four orbits of Io, the innermost moon, Europa completes two orbits, and Ganymede completes one orbit. This resonance maintains the orbital eccentricities of the moons, which allows them to experience tidal heating and geological activity.
The orbital eccentricities of the four giant planets of the solar system are also influenced by resonance capture during their outward migration in the planetesimal disk. The planets are in a 2:1 resonance, meaning that for every two orbits of Jupiter, the innermost giant planet, Saturn completes one orbit. This resonance increases the orbital eccentricities of the planets, which causes them to experience chaotic variations and close encounters. The migration of the giant planets also affects the orbits of the terrestrial planets and the Moon, and may have triggered the Late Heavy Bombardment, a period of intense cratering on the inner solar system bodies about 3.9 billion years ago.
The existence of many resonant exoplanets, such as the TRAPPIST-1 system, is also attributed to resonance capture during their migration in the gas disk. The system consists of seven Earth-sized planets, all within the habitable zone of their host star, a low-mass red dwarf. The planets are in a 24:15:9:6:4:3:2 resonance, meaning that for every 24 orbits of the innermost planet, TRAPPIST-1b, the other planets complete 15, 9, 6, 4, 3, and 2 orbits, respectively. This resonance stabilizes the orbits of the planets, which prevents them from colliding or being ejected from the system.
Planetary migration is a key process that shapes the architecture and dynamics of planetary systems. By studying the different types of migration and their effects on the orbits of planets and other bodies, we can gain insight into the origin and evolution of the solar system and the diversity of exoplanets. Planetary migration is also a challenge for the detection and characterization of exoplanets, as it can create observational biases and uncertainties. Therefore, understanding planetary migration is essential for advancing our knowledge of planetary science and astrobiology.
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Cosmology