Streaming instability

In planetary science a streaming instability is a hypothetical mechanism for the formation of planetesimals in which the drag felt by solid particles orbiting in a gas disk leads to their spontaneous concentration into clumps which can gravitationally collapse.[1]

Background

Planetesimals and larger bodies are traditionally thought to have formed via a hierarchical accretion, the formation of large objects via the collision and mergers of small objects. This process begins with the collision of dust due to Brownian motion producing larger aggregates held together by van der Waals forces. The aggregates settle toward the mid-plane of the disk and collide due to gas turbulence forming pebbles and larger objects. Further collisions and mergers eventually yield planetesimals 1-10 km in diameter held together by self-gravity. The growth of the largest planetesimals then accelerates, as gravitational focusing increases their effective cross-section, resulting in runaway accretion forming the larger asteroids. Later, gravitational scattering by the larger objects excites relative motions, causing a transition to slower oligarchic accretion that ends with the formation of planetary embryos. In the outer Solar System the planetary embryos grow large enough to accrete gas, forming the giant planets. In the inner Solar System the orbits of the planetary embryos become unstable, leading to giant impacts and the formation of the terrestrial planets.[2]

A number of obstacles to this process have been identified: barriers to growth via collisions, the radial drift of larger solids, and the turbulent stirring of planetesimals.[3] As a particle grows the time required for its motion to react to changes in the motion of the gas in turbulent eddies increases. The relative motions of particles, and collision velocities, therefore increases as with the mass of the particles. For silicates the increased collision velocities cause dust aggregates to compact into solid particles that bounce rather than stick, ending growth at the size of chodrules, roughly 1 mm in diameter.[4] Although growth may continue via mass transfers from small to large particles during collisions if a small fraction of particles are able to reach larger sizes, this process is slow relative to radial drift timescales.[5] Icy particles are more likely to stick and to resist compression in collisions which may allow the growth of large porous bodies.[6] However, an increase in impact velocities driven by the relative rates of radial drift of large and small bodies may result in erosion stopping their growth.[7] Objects made up of multiple volatile ices may be sintered as they approach ice lines, reducing the ability to absorb collisions, resulting in bouncing or fragmentation during collisions.[8] Radial drift is the result of the pressure support of the gas, enabling it to orbits at slower velocity than the solids. Solids orbiting through this gas lose angular momentum and spiral toward the central star at rates that increase as they grow. At 1 AU this leads to the loss of meter-sized objects in ~1000 orbits.[9] Turbulence in the protoplanetary disk disk can create density fluctuations which exert torques on planetesimals exciting their relative velocities. Outside the dead zone the higher random velocities can result in the destruction of smaller planetesimals, and the delay of the onset of runaway growth until planetesimals reach radii of 100 km.[10]

Some evidence exists that planetesimal formation may have bypassed these barriers to incremental growth. The size distributions of asteroids has a change in slope at around 100 km which can be reproduced in models if the minimal diameter of the planetesimals was 100 km and the smaller asteroids are debris from collisions.[2] A similar change slope has been observed in the size distribution of the Kuiper belt objects.[11] The low numbers of small craters on Pluto has also been cited as evidence the largest KBO's formed directly.[12] Furthermore, the largest objects in the cold classical Kuiper belt are unlikely to have formed via the traditional mechanism given its current (and likely initial) small mass.[13]

Description

Streaming instabilities, first described by Andrew Youdin and Jeremy Goodman,[14] are driven by differences in the motions of the gas and solid particles in the protoplanetary disk. The gas, partially supported by a pressure gradient that offsets some of the gravity from the central star, orbits at about 50 m/s below the Keplerian velocity at its distance. The solid particles orbiting through the gas experience a headwind, causing them to lose momentum to aerodynamic drag and spiral toward the star.[15] The drag also results in a back reaction on the gas, increasing its velocity.[16] When localized clusters of solid particles form, this reduces the headwind and allows them to orbit faster and undergo less inward drift.[17] These clusters can then grow exponentially, forming massive filaments, as they are joined by isolated particles undergoing faster radial drift.[18] The filaments are separated by roughly 0.2 times the scale height of the gas disk[19] and can reach thousands of times the local gas density.[20] These densities are sufficient to trigger gravitational collapse,[18] leading to the formation of planetesimals the size of large asteroids.[20] The collapse into smaller bodies is relatively slow, extending over 1000 years, limiting impact speeds and the fragmentation of particles, resulting in the formation of pebble pile planetesimals with low densities.[21] Larger bodies, in contrast, undergo a more rapid collapse lasting as little as 25 years, resulting in higher impact speeds the formation of denser objects composed of a mixture of dust and pebbles.[21] Collapsing swarms with excess angular momentum can fragment forming binary or in some cases trinary objects resembling those in the Kuiper belt.[22] The initial size distribution of the planetesimals formed via streaming instabilities is more shallow than that of the large asteroids and Kuiper belt objects and has a tail of larger objects.[23] Continued accretion of the chondrules from the disk may shift this size distribution to one resembling the current distribution.[24] In the outer solar system the largest objects can continue to grow via pebble accretion, possibly forming the cores of giant planets.[25]

Requirements

Streaming instabilities form only in the presence of rotation and the radial drift of solids. The formation of a streaming instability begins with a transient region of high pressure within the protoplanetary disk. The elevated pressure alters the local pressure gradient supporting the gas, reducing the gradient on the region's inner edge and increasing the gradient on the region's outer edge. The gas therefore must orbit faster near the inner edge and is able to orbit slower near the outer edge.[18] The Coriolis forces resulting from these relative motions support the elevated pressure, creating a geostropic balance.[26] The motions of the solid near the high pressure regions are also affected: solids at its outer edge face a greater headwind and undergo faster radial drift, solids at its inner edge face a lesser headwind and undergo a slower radial drift.[18] This differential radial drift produces a buildup of solids in higher pressure regions. The drag felt by the solids moving toward the region also creates a back reaction on the gas that reinforces the elevated pressure leading to a runaway process.[26] As more solids are carried toward the region by radial drift this eventually yields a concentration of solids sufficient to drive the increase of the velocity of the gas and reduce the local radial drift of solids seen in streaming instabilities.[18]

Streaming instabilities form when the solid particles are be moderately coupled to the gas, with Stokes numbers of 0.01 - 3; the local solid to gas ratio is near or larger than 1; and the vertically integrated solid to gas ratio is a few times Solar.[27] The Stokes number is a measure of the relative infuences of inertia and gas drag on a particle's motion. In this context it is the product of the timescale for the exponential decay of a particle's velocity due to drag and the angular frequency of its orbit. Small particles like dust are strongly coupled and move with the gas, large bodies such as planetesimals are weakly coupled and orbit largely unaffected by the gas.[3] Moderately coupled solids, sometimes referred to as pebbles, range from roughly cm- to m-sized at asteroid belt distances and from mm- to dm-sized beyond 10 AU.[9] These objects orbit through the gas like planetesimals but are slowed due to the headwind and undergo significant radial drift. The moderately coupled solids that participate in streaming instabilities are those dynamically affected by changes in the motions of gas on scales similar to those of the Coriolis effect, allowing them to be captured by regions of high pressure in a rotating disk.[10] Moderately coupled solids also retain influence on the motion of the gas. If the local solid to gas ratio is near or above 1, this influence is strong enough to reinforce regions of high pressure and to increase the orbital velocity of the gas and slow radial drift.[26] Reaching and maintaining this local solid to gas at the mid-plane requires an average solid to gas ratio in a vertical cross section of the disk that is a few times solar.[28] When the average solid to gas ratio is 0.01, roughly that estimated from measurements of the current Solar System, turbulence at the mid-plane generates a wavelike pattern that puffs up the mid-plane layer of solids. This reduces the solid to gas ratio at the mid-plane to less than 1, suppressing the formation of dense clumps. At higher average solid to gas ratios the mass of solids dampens this turbulence allowing a thin mid-plane layer to form.[29]

Reaching an average solid to gas ratio across a cross-section of the disk a few times that expected from measurements of the current Solar System requires either a reduced gas column density, possibly due to photo-evaporation, or an initial concentration of solids. One possible mechanism for enhancing the solid concentration is the fragmentation of rapidly drifting large solids into smaller slower drifting solids resulting in a radial pile-up. Inside the water ice line silicate grains may be released as icy bodies sublimates,[30] beyond the water ice line fragmentation due to sintering of solids made up of multiple volatile ices may occur outside other ice lines.[31][32] High initial concentration of solids could also occur at pressure maxima, either radial pressure maxima which result in zonal flows; or local maxima, for example, in anti-cyclonic vortices.[10]

Questions remain regarding the formation of streaming instabilities from particles as small as chondrules in the asteroid belt. In addition to an enhanced solid to gas ratio this may require further growth of the solids beyond the size of chondrules. Slow growth, possible aided by dusty rims that absorb impacts, may occur over a period of 10^5 years if collisions have a distribution of velocities with some slow enough to result in sticking. Or the growth may occur if turbulence and collision velocities is reduced inside initial clumps.[16]

Alternatives

A number of other alternative paths for the formation of planetesimals have been identified. Solids may be concentrated to sufficient densities in the gas disk to collapse due to gravitational instability via a number of mechanisms. On small scales solids may collect between eddies in a turbulent disk. Pressure bumps in the gas disk, which locally reverse the pressure gradient, can result in the gas orbiting at greater than keplerian velocities. The inward radial drift of solids stops at these locations and pile-ups can form as solids drift in from outside the pressure bump. If the aggregates formed from dust or ice grains are able to remain highly porous, impact velocities may remain low enough for very low density objects to grow massive enough for gravitational attraction to drive further accretion.[9]

External links

Numerical Simulation of 3D Streaming Instability

References

  1. ↑ "Planetesimal formation". Lund University. Retrieved 16 December 2015.
  2. 1 2 Morbidelli, Alessandro; Bottke, William F.; Nesvorný, David; Levison, Harold F. (2009). "Asteroids were born big". Icarus 204 (2): 558–573. arXiv:0907.2512. Bibcode:2009Icar..204..558M. doi:10.1016/j.icarus.2009.07.011.
  3. 1 2 Birnstiel, T.; Fang, M.; Johansen, A. "Dust Evolution and the Formation of Planetesimals". arXiv:1604.02952.
  4. ↑ Zsom, A.; Ormel, C. W.; Güttler, C.; Blum, J.; Dullemond, C. P. (2010). "The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier". Astronomy and Astrophysics 513: A57. arXiv:1001.0488. Bibcode:2010A&A...513A..57Z. doi:10.1051/0004-6361/200912976.
  5. ↑ Windmark, F.; Birnstiel, T.; Güttler, C.; Blum, J.; Dullemond, C. P.; Henning, Th. (2012). "Planetesimal formation by sweep-up: how the bouncing barrier can be beneficial to growth". Astronomy & Astrophysics 540: A73. arXiv:1201.4282. Bibcode:2012A&A...540A..73W. doi:10.1051/0004-6361/201118475.
  6. ↑ Okuzumi, Satoshi; Tanaka, Hidekazu; Kobayashi, Hiroshi; Wada, Koji (2012). "Rapid Coagulation of Porous Dust Aggregates outside the Snow Line: A Pathway to Successful Icy Planetesimal Formation". The Astrophysical Journal 752 (2): 106. arXiv:1204.5035. Bibcode:2012ApJ...752..106O. doi:10.1088/0004-637X/752/2/106.
  7. ↑ Krijt, S.; Ormel, C. W.; Dominik, C.; Tielens, A. G. G. M. (2015). "Erosion and the limits to planetesimal growth". Astronomy & Astrophysics 574: A83. arXiv:1412.3593. Bibcode:2015A&A...574A..83K. doi:10.1051/0004-6361/201425222.
  8. ↑ Sirono, Sin-iti (2011). "The Sintering Region of Icy Dust Aggregates in a Protoplanetary Nebula". The Astrophysical Journal 735 (2): 131. Bibcode:2011ApJ...735..131S. doi:10.1088/0004-637X/735/2/131.
  9. 1 2 3 Johansen, A.; Blum, J.; Tanaka, H.; Ormel, C.; Bizzarro, M.; Rickman, H. (2014). "The Multifaceted Planetesimal Formation Process". In Beuther, H.; Klessen, R. S.; Dullemond, C. P.; Henning, T. Protostars and Planets VI. University of Arizona Press. pp. 547–570. arXiv:1402.1344. Bibcode:2014prpl.conf..547J. doi:10.2458/azu_uapress_9780816531240-ch024. ISBN 978-0-8165-3124-0.
  10. 1 2 3 Johansen, A.; Jacquet, E.; Cuzzi, J. N.; Morbidelli, A.; Gounelle, M. (2015). "New Paradigms For Asteroid Formation". In Michel, P.; DeMeo, F.; Bottke, W. Asteroids IV. Space Science Series. University of Arizona Press. p. 471. arXiv:1505.02941. Bibcode:2015arXiv150502941J. ISBN 978-0-8165-3213-1.
  11. ↑ Fraser, Wesley C.; Brown,, Michael E.; Morbidelli,, Alessandro; Parker, Alex; Batygin, Konstantin (2014). "he Absolute Magnitude Distribution of Kuiper Belt Objects". The Astrophysical Journal 782 (2): 100. arXiv:1401.2157. Bibcode:2014ApJ...782..100F. doi:10.1088/0004-637X/782/2/100.
  12. ↑ "At Pluto, New Horizons Finds Geology of All Ages, Possible Ice Volcanoes, Insight into Planetary Origins". The Johns Hopkins University Applied Physics Laboratory LLC. Retrieved 3 January 2016.
  13. ↑ Nesvorny, D. (2015). "Jumping Neptune Can Explain the Kuiper Belt Kernel". The Astronomical Journal 150 (3): 68. arXiv:1506.06019. Bibcode:2015AJ....150...68N. doi:10.1088/0004-6256/150/3/68.
  14. ↑ Youdin, Andrew; Goodman, Jeremy (2005). "Streaming Instabilities in Protoplanetary Disks". The Astrophysical Journal. 620 (1): 459–469. arXiv:astro-ph/0409263. Bibcode:2005ApJ...620..459Y. doi:10.1086/426895.
  15. ↑ Pfalzner, S.; Davies, M. B.; Gournelle, M.; Johansen, A.; Münker, C.; Lacerda, P.; Portegies Zwart, S.; Testi, L.; Trieloff, M.; Veras, D. (2015). "The formation of the solar system". Physica Scripta 90 (6): 068001. arXiv:1501.03101. doi:10.1088/0031-8949/90/6/068001.
  16. 1 2 Carrera, D.; Johansen, A.; Davies, M. B. (2015). "How to form planetesimals from mm-sized chondrules and chondrule aggregates". Astronomy and Astrophysics 579: A43. arXiv:1501.05314. Bibcode:2015A&A...579A..43C. doi:10.1051/0004-6361/201425120.
  17. ↑ Johansen, A.; Youdin, A. N.; Lithwick, Y. (2011). "Rapid Accretion of Large Planetesimals by Gravitational Instabilities" (PDF). Workshop on Formation of the First Solids in the Solar System 1639. p. 9080. Bibcode:2011LPICo1639.9080J.
  18. 1 2 3 4 5 Johansen, A.; Oishi, J. S.; Mac Low, M.-M.; Klahr, H.; Henning, T.; Youdin, A. (2007). "Rapid planetesimal formation in turbulent circumstellar disks". Nature 448 (7157): 1022–1025. arXiv:0708.3890. Bibcode:2007Natur.448.1022J. doi:10.1038/nature06086.
  19. ↑ Yang, C.-C.; Johansen, A. (2014). "On the Feeding Zone of Planetesimal Formation by the Streaming Instability". The Astrophysical Journal 792 (2): 86. arXiv:1407.5995. Bibcode:2014ApJ...792...86Y. doi:10.1088/0004-637X/792/2/86.
  20. 1 2 Johansen, A.; Youdin, A. N.; Lithwick, Y. (2012). "Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities" (PDF). Astronomy and Astrophysics 537: A125. arXiv:1111.0221. Bibcode:2012A&A...537A.125J. doi:10.1051/0004-6361/201117701.
  21. 1 2 Wahlberg Jansson, K.; Johansen, A. (2014). "Formation of pebble-pile planetesimals" (PDF). Astronomy and Astrophysics 570: A47. arXiv:1408.2535. Bibcode:2014A&A...570A..47W. doi:10.1051/0004-6361/201424369.
  22. ↑ Nesvorný, D.; Youdin, A. N.; Richardson, D. C. (2010). "Formation of Kuiper Belt Binaries by Gravitational Collapse". The Astronomical Journal 140 (3): 785–793. arXiv:1007.1465. Bibcode:2010AJ....140..785N. doi:10.1088/0004-6256/140/3/785.
  23. ↑ Simon, J. B.; Armitage, P. J.; Li, R.; Youdin, A. N. (2015). "The Initial Mass and Size Distribution of Planetesimals. I. The Effect of Resolution, Gravity, and Initial Conditions in Streaming Instability Calculations". arXiv:1512.00009 [astro-ph.EP].
  24. ↑ Johansen, Anders; Mac Low, Mordecai-Mark; Lacerda, Pedro; Bizzarro, Martin (2015). "Growth of asteroids, planetary embryos, and Kuiper belt objects by chondrule accretion". Science Advances 1 (3): 1500109. arXiv:1503.07347. Bibcode:2015SciA....115109J. doi:10.1126/sciadv.1500109.
  25. ↑ Lambrechts, M.; Johansen, A. (2012). "Rapid growth of gas-giant cores by pebble accretion". Astronomy & Astrophysics 544: A32. arXiv:1205.3030. Bibcode:2012A&A...544A..32L. doi:10.1051/0004-6361/201219127.
  26. 1 2 3 Jacquet, Emmanuel; Balbus, Steven; Latter, Henrik (2011). "On linear dust-gas streaming instabilities in protoplanetary discs". Monthly Notices of the Royal Astronomical Society 415 (4): 3591–3598. arXiv:1104.5396. Bibcode:2011MNRAS.415.3591J. doi:10.1111/j.1365-2966.2011.18971.x.
  27. ↑ Krijt, S.; Ormel, C. W.; Dominik, C.; Tielens, A. G. G. M. (2016). "A panoptic model for planetesimal formation and pebble delivery". Astronomy and Astrophysics 586: A20. arXiv:1511.07762. Bibcode:2016A&A...586A..20K. doi:10.1051/0004-6361/201527533.
  28. ↑ Drążkowska, J.; Dullemond, C. P. (2014). "Can dust coagulation trigger streaming instability?" (PDF). Astronomy and Astrophysics 572: A78. arXiv:1410.3832. Bibcode:2014A&A...572A..78D. doi:10.1051/0004-6361/201424809.
  29. ↑ Johansen, Anders; Youdin, Andrew; Mac Low, Mordecai-Mark (2009). "Particle Clumping and Planetesimal Formation Depend Strongly on Metallicity". The Astrophysical Journal Letters 704 (2): L75–L79. arXiv:0909.0259. doi:10.1088/0004-637X/704/2/L75.
  30. ↑ Saito, Etsuko; Sirono, Sin-iti (2011). "Planetesimal Formation by Sublimation". The Astrophysical Journal 728 (1): 20. doi:10.1088/0004-637X/728/1/20.
  31. ↑ Sirono, Sin-iti (2011). "Planetesimal Formation Induced by Sintering". The Astrophysical Journal Letters 733 (2): L41. doi:10.1088/2041-8205/733/2/L41.
  32. ↑ Okuzumi, Satoshi; Momose, Munetake; Sirono, Sin-iti; Kobayashi, Hiroshi; Tanaka, Hidekazu (2016). "Sintering-induced Dust Ring Formation in Protoplanetary Disks: Application to the HL Tau Disk". The Astrophysical Journal 821 (2): 82. arXiv:1510.03556. doi:10.3847/0004-637X/821/2/82.
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