Planetary migration

• 1. Defining Planetary Migration

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  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. This process changes the semi-major axis and other orbital elements over time. The phenomenon explains why hot Jupiters exist despite theoretical constraints on their formation near stars. Observations suggest that gas in protoplanetary disks has lifetimes of only a few to several million years. If planets form while this gas is still present, they exchange angular momentum with the surrounding material. This exchange gradually shifts their orbits inward or outward depending on local conditions. In locally isothermal disks, migration typically moves planets toward the star. However, outward migration may occur in disks possessing entropy gradients. The sense of migration depends on the balance between different torques acting on the planet.

• 2. Gas Disk Interactions

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  Three sub-types of disk migration are distinguished as Types I, II, and III based on planetary mass and local gas density. Type I migration affects small planets through Lindblad and co-rotation resonances. These resonances excite spiral density waves in the surrounding gas both interior and exterior to the planet's orbit. In most cases, the outer spiral wave exerts a greater torque than does the inner wave. Consequently, the planet loses angular momentum and migrates toward the star. The migration rate due to these torques is proportional to the mass of the planet and to the local gas density. A Jupiter-mass planet in a typical protoplanetary disk undergoes migration at approximately the Type II rate. When a planet opens a gap in a gaseous disk, it enters the Type II regime. The depth of this gap depends on the temperature and viscosity of the gas. In simple scenarios where no gas crosses the gap, the planet follows the viscous evolution of the disk's gas. This process can be slower than Type I migration but still significant over millions of years.

• 3. Planetesimal Dynamics

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  During the late phase of planetary system formation, massive protoplanets and planetesimals gravitationally interact in a chaotic manner. Many planetesimals get thrown into new orbits as a result of these interactions. This results in angular-momentum exchange between the planets and the planetesimals, leading 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. Gravitational scattering by larger planets moves planets over large orbital radii. Systems of exoplanets can undergo similar dynamical instabilities following the dissipation of the gas disk. These events alter their orbits and sometimes eject planets entirely from the system. Planets scattered gravitationally often end up on highly eccentric orbits with perihelia close to the star. Their eccentricities and inclinations are excited during these encounters, providing an explanation for observed distributions among closely orbiting exoplanets. The resulting systems frequently sit near the limits of stability.

• 4. Tidal Evolution Cycles

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  Tides between the star and planet modify the semi-major axis and orbital eccentricity of the planet. If the planet orbits very near its star, it raises a bulge on the stellar surface. When the star's rotational period exceeds the planet's orbital period, the bulge lags behind the line connecting them. This creates a torque that causes the planet to lose angular momentum and decrease its semi-major axis over time. Unlike disk migration which lasts only a few million years until gas dissipates, tidal migration continues for billions of years. Tidal evolution produces semi-major axes typically half as large as they were when the gas nebula cleared. Kozai cycles occur in planetary orbits inclined relative to binary stars. Interactions with the more distant star cause the planet's orbit to exchange eccentricity and inclination. This process increases eccentricity enough to create strong tides when the planet approaches the star. The planet loses angular momentum causing its orbit to shrink further. Eventually, if the orbit shrinks enough to remove it from the distant star's influence, the Kozai cycles end and the orbit tidally circularizes rapidly.

• 5. Solar System History

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  Beyond Neptune, the Solar System extends into the Kuiper belt, scattered disc, and Oort cloud. These sparse populations contain small icy bodies thought to be the origin points for most observed comets. According to the Nice model scenario, the Kuiper belt was originally much denser and closer to the Sun. It contained millions of planetesimals and had an outer edge at approximately 30 AU. After 500, 600 million years, Jupiter and Saturn divergently crossed the 2:1 orbital resonance. This crossing increased the eccentricities of both planets and destabilized Uranus and Neptune. Encounters between these giants caused Neptune to surge past Uranus and plough into the dense planetesimal belt. The planets scattered the majority of small icy bodies inward while moving outward themselves. This scattering continued until planetesimals interacted with Jupiter, whose gravity sent them into highly elliptical orbits or ejected them outright. This process explains the trans-Neptunian populations' present low mass compared to their original state.

• 6. Exoplanet Formation Paradoxes

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  Hot Jupiters are exoplanets with Jovian masses but orbits of only a few days. Their existence contradicts standard theories predicting such planets cannot form so close to stars due to insufficient mass and high temperatures. Planetary migration offers the most likely explanation for these distant-formed giants now orbiting near their host stars. Observations suggest that gas in protoplanetary disks has lifetimes of only a few to several million years. If massive planets form while this gas remains, they can migrate rapidly toward the star. Type II migration is one specific mechanism explaining how hot Jupiters reach their current positions. In more realistic situations, unless extreme thermal conditions occur, there is an ongoing flux of gas through gaps created by migrating planets. Torques acting on these planets become susceptible to local disk properties similar to those during Type I migration. Systems of exoplanets can undergo dynamical instabilities following resonance crossings during planetesimal-driven migration. These events alter orbital configurations and sometimes result in ejection or collision with the central star.