Planetary migration

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Planetary migration occurs when a planet or other stellar satellite interacts with a disk of gas or planetesimals, resulting in the alteration of the satellite's orbital parameters, especially its semi-major axis. Planetary migration is the most likely explanation for hot Jupiters, extrasolar planets with jovian masses, but orbits of only a few days. The generally accepted theory of planet formation from a protoplanetary disk predicts 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 Earth masses), if those planets form via the core accretion mechanism.

Types of disk[edit]

Gas disk[edit]

Protoplanetary gas disks around young stars are observed to have lifetimes of a few 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[edit]

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[edit]

Disk migration[edit]

This type of orbital 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 in terms of a torque. This torque alters the angular momentum of the planet's orbit, resulting in a variation of the orbital elements, such as the semi-major axis (but all orbital elements can be affected). 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.

Type I migration[edit]

Planets can drive spiral density waves in the surrounding gas or planetesimal disk, via their perturbing gravitational potential. In the Type I regime, the disk response to this perturbation is linear. An imbalance occurs in the strength of the interaction with the spirals inside and outside the planet's orbit. In most cases, the outer wave exerts a somewhat greater torque on the planet than does the interior wave. This causes the planet to lose orbital angular momentum and the planet then migrates inwards on timescales that are initially short relative to the million-year lifetime of the disk.[1] Torques are also exerted by gas co-rotating with the planet, which shares the same orbit as (or a proximate orbit to) the planet. Co-rotation torques typically raise the angular momentum of the planet, pushing it away from the star. However, in locally isothermal disks and far from steep density gradients, co-rotation torques are generally overpowered by wave, or Lindblad, torques.[2][3] Outward migration in isothermal disks is also possible, but it requires the presence of steep gradients of surface density and/or temperature.[3] Type I migration was shown to be compatible with the formation of some of the observed Kepler planets.[4]

Type II migration[edit]

Planets of more than several tens of Earth's masses start to clear a gap in the disk's density distribution (under typical thermodynamical and viscosity conditions), ending Type I migration. However, material continues to enter the gap on the timescale of the larger accretion disk, moving the planet and gap inward. The timescale of this process (for sufficiently deep gaps) is of the same order of magnitude as the accretion timescale of the disk.[5] This is one hypothesis for how some or most "hot Jupiters" formed. Unless extreme thermal and viscosity conditions are assumed in a disk, there is an ongoing flux of gas through the gap.[6] 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.[5][3] The transition between Type I and Type II migration is generally smooth, but deviations from a smooth transition have also been found.[7][8]

Type III migration[edit]

In this regime of migration, planets interact with large-scale vortices within the disc. But other interpretations exist, which are based on the circulation of co-orbital material during the migration of the planet.[1][5][9] This regime of migration may only apply to planets that can open partial gaps (via tidal interactions) in the gas surface density of the disk. Originally, it was thought to originate from gas streaming across the orbit of the planet, in the opposite direction as the planet's radial motion.[9] More recently, the torques driving this mode of migration were associated to the gas trapped in the libration regions and radially moving with the planet. In this scenario, the torques arise from a density asymmetry between the gas on the leading and the trailing side of the planet, which develops in response to the planet's radial motion.[5][1]

Gravitational scattering[edit]

Another possible mechanism that may move planets over large orbital radii is gravitational scattering by larger planets or, in a protoplantetary disk, gravitational scattering by over-densities in the fluid of the disk.[10] In the case of the Solar System, Uranus and Neptune may have been gravitationally scattered in close encounters with Jupiter and/or Saturn.[11] Planetesimals that were present in the early formation of the Solar System called oligarchs are much smaller than Uranus and Neptune and so are likely to have been scattered much further out and be roaming the space between the Kuiper belt and the Oort cloud. Sedna may be the first known example of such oligarch planets. Even smaller objects would have been scattered even further out to become the Oort cloud.

Tidal migration[edit]

Tides between the star and planet modify the semi-major axis and orbital eccentricity. Disk migration lasts around a million years until the gas dissipates, but tidal migration continues for billions of years. Tidal evolution of close-in planets produces semi-major axes typically half as large as they were at the time that the gas nebula cleared. More massive planets probably undergo much more tidal migration than less massive ones.[12]

In the Solar System[edit]

Main article: Nice model
Simulation showing outer planets and Kuiper belt: a) Before Jupiter/Saturn 2:1 resonance b) Scattering of Kuiper belt objects into the Solar System after the orbital shift of Neptune c) After ejection of Kuiper belt bodies by Jupiter[13]

The migration of the outer planets is necessary to account for the existence and properties of the Solar System's outermost regions.[14] Beyond Neptune, the Solar System continues into the Kuiper belt, the scattered disc, and the Oort cloud, three sparse populations of small icy bodies thought to be the points of origin for most observed comets. At their distance from the Sun, accretion was too slow to allow planets to form before the solar nebula dispersed, and thus the initial disc lacked enough mass density to consolidate into a planet. The Kuiper belt lies between 30 and 55 AU from the Sun, while the farther scattered disc extends to over 100 AU,[14] and the distant Oort cloud begins at about 50,000 AU.[15]

Originally, however, the Kuiper belt was much denser and closer to the Sun: it contained millions of planetesimals, and had an outer edge at approximately 30 AU, the present distance of Neptune.

After the formation of the Solar System, the orbits of all the giant planets continued to change slowly, influenced by their interaction with the large number of remaining planetesimals. After 500–600 million years (about 4 billion years ago) Jupiter and Saturn divergently crossed the 2:1 orbital resonance, in which Saturn orbited the Sun once for every two Jupiter orbits.[14] This resonance created a gravitational push against the outer planets, causing Neptune to surge past Uranus and plough into the dense planetesimal belt. The planets scattered the majority of the small icy bodies inwards, while moving outwards themselves. These planetesimals then scattered off the next planet they encountered in a similar manner, moving the planets' orbits outwards while they moved inwards.[16] This process continued until the planetesimals interacted with Jupiter, whose immense gravity sent them into highly elliptical orbits or even ejected them outright from the Solar System. This caused Jupiter to move slightly inward. This scattering scenario explains the trans-Neptunian populations' present low mass.

The outer two planets of the Solar System, Uranus and Neptune, are believed to have migrated outward in this way from their formation in orbits near Jupiter and Saturn to their current positions, over hundreds of millions of years.[11] Eventually, friction within the planetesimal disc made the orbits of Uranus and Neptune circular again.[14][17]

In contrast to the outer planets, the inner planets are not believed to have migrated significantly over the age of the Solar System, because their orbits have remained stable following the period of giant impacts.[18]

See also[edit]

Notes[edit]

  1. ^ a b c Lubow, S. H.; Ida, S. (2011). "Planet Migration". In S. Seager. Exoplanets. University of Arizona Press, Tucson, AZ. pp. 347–371. arXiv:1004.4137Freely accessible. Bibcode:2011exop.book..347L. 
  2. ^ Tanaka, H.; Takeuchi, T.; Ward, W. R. (2002). "Three-Dimensional Interaction between a Planet and an Isothermal Gaseous Disk. I. Corotation and Lindblad Torques and Planet Migration". The Astrophysical Journal. 565 (2): 1257–1274. Bibcode:2002ApJ...565.1257T. doi:10.1086/324713. 
  3. ^ a b c D'Angelo, G.; Lubow, S. H. (2010). "Three-dimensional Disk-Planet Torques in a Locally Isothermal Disk". The Astrophysical Journal. 724 (1): 730–747. arXiv:1009.4148Freely accessible. Bibcode:2010ApJ...724..730D. doi:10.1088/0004-637X/724/1/730. 
  4. ^ D'Angelo, G.; Bodenheimer, P. (2016). "In Situ and Ex Situ Formation Models of Kepler 11 Planets". The Astrophysical Journal. 828 (1): id. 33 (32 pp.). arXiv:1606.08088Freely accessible. Bibcode:2016ApJ...828...33D. doi:10.3847/0004-637X/828/1/33. 
  5. ^ a b c d D'Angelo, G.; Lubow, S. H. (2008). "Evolution of Migrating Planets Undergoing Gas Accretion". The Astrophysical Journal. 685 (1): 560–583. arXiv:0806.1771Freely accessible. Bibcode:2008ApJ...685..560D. doi:10.1086/590904. 
  6. ^ Lubow, S.; D'Angelo, G. (2006). "Gas Flow across Gaps in Protoplanetary Disks". The Astrophysical Journal. 641 (1): 526–533. arXiv:astro-ph/0512292Freely accessible. Bibcode:2006ApJ...641..526L. doi:10.1086/500356. 
  7. ^ D'Angelo, G.; Kley, W.; Henning T. (2003). "Orbital Migration and Mass Accretion of Protoplanets in Three-dimensional Global Computations with Nested Grids". The Astrophysical Journal. 586 (1): 540–561. arXiv:astro-ph/0308055Freely accessible. Bibcode:2003ApJ...586..540D. doi:10.1086/367555. 
  8. ^ Masset, F. S.; D'Angelo, G.; Kley, W. (2006). "On the Migration of Protogiant Solid Cores". The Astrophysical Journal. 652 (1): 730–745. arXiv:astro-ph/0607155Freely accessible. Bibcode:2006ApJ...652..730M. doi:10.1086/507515. 
  9. ^ a b Masset, F. S.; Papaloizou, J. C. B. (2003). "Runaway Migration and the Formation of Hot Jupiters". The Astrophysical Journal. 588 (1): 494–508. arXiv:astro-ph/0301171Freely accessible. Bibcode:2003ApJ...588..494M. doi:10.1086/373892. 
  10. ^ R. Cloutier; M-K. Lin (2013). "Orbital migration of giant planets induced by gravitationally unstable gaps: the effect of planet mass". arXiv:1306.2514Freely accessible. Bibcode:2013MNRAS.434..621C. doi:10.1093/mnras/stt1047. 
  11. ^ a b E. W. Thommes; M. J. Duncan; H. F. Levison (2002). "The Formation of Uranus and Neptune among Jupiter and Saturn". Astronomical Journal. 123 (5): 2862. arXiv:astro-ph/0111290Freely accessible. Bibcode:2002AJ....123.2862T. doi:10.1086/339975. 
  12. ^ Tidal Evolution of Close-in Extra-Solar Planets, Brian Jackson, Richard Greenberg, Rory Barnes, (Submitted on 4 Jan 2008)
  13. ^ R. Gomes; H. F. Levison; K. Tsiganis; A. Morbidelli (2005). "Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets" (PDF). Nature. 435 (7041): 466–9. Bibcode:2005Natur.435..466G. doi:10.1038/nature03676. PMID 15917802. 
  14. ^ a b c d Harold F. Levison; Alessandro Morbidelli; Christa Van Laerhoven; et al. (2007). "Origin of the Structure of the Kuiper Belt during a Dynamical Instability in the Orbits of Uranus and Neptune". Icarus. 196 (1): 258. arXiv:0712.0553Freely accessible. Bibcode:2008Icar..196..258L. doi:10.1016/j.icarus.2007.11.035. 
  15. ^ Alessandro Morbidelli (2005). "Origin and dynamical evolution of comets and their reservoirs". arXiv:astro-ph/0512256Freely accessible [astro-ph]. 
  16. ^ G. Jeffrey Taylor (21 August 2001). "Uranus, Neptune, and the Mountains of the Moon". Planetary Science Research Discoveries. Hawaii Institute of Geophysics & Planetology. Retrieved 2008-02-01. 
  17. ^ M. J. Fogg; R. P. Nelson (2007). "On the formation of terrestrial planets in hot-Jupiter systems". Astronomy & Astrophysics. 461 (3): 1195. arXiv:astro-ph/0610314Freely accessible. Bibcode:2007A&A...461.1195F. doi:10.1051/0004-6361:20066171. 
  18. ^ Douglas N. C. Lin (May 2008). "The Genesis of Planets". Scientific American. 298 (5): 50–59. doi:10.1038/scientificamerican0508-50. PMID 18444325. (subscription required (help)). 

References[edit]