Pebble accretion

In pebble accretion the accretion of objects ranging from cm's up to meters in diameter onto planetesimals in a protoplanetary disk is enhanced by aerodynamic drag. The rapid growth of the planetesimals via pebble accretion allows for the formation of giant planet cores in the outer Solar System before the dispersal of the gas disk. A reduction in the size of pebbles as they lose water ice after crossing the ice line and a declining density of gas with distance from the sun slow the rates of pebble accretion in the inner Solar System resulting in smaller terrestrial planets, a small mass of Mars and a low mass asteroid belt.

Description

Pebbles ranging in size from cm's up to a meter in size are accreted at an enhanced rate in a protoplanetary disk. A protoplanetary disk is made up of a mix of gas and solids including dust, pebbles, planetesimals, and protoplanets.[1] Gas in a protoplanetary disk is pressure supported and as a result orbits at a velocity slower than large objects.[2] The gas affects the motions of the solids in varying ways depending on their size, with dust moving with the gas and the largest planetesimals orbiting largely unaffected by the gas.[3] Pebbles are an intermediate case, aerodynamic drag causes them to settle toward the central plane of the disk and to orbit at a sub-keplerian velocity resulting in radial drift toward the central star.[4] The pebbles frequently encounter planetesimals as a result of their lower velocities and inward drift. If their motions were unaffected by the gas only a small fraction, determined by gravitational focusing and the cross-section of the planetesimals, would be accreted by the planetesimals. The remainder would follow hyperbolic paths, accelerating toward the planetesimal on their approach and decelerating as they recede. However, the drag the pebbles experience grows as their velocities increase, slowing some enough that they collide with the planetesimal.[5] Others become gravitationally bound, and are eventually accreted after spiraling toward the planetesimal.[6] Pebble accretion primarily affects the accretion rates of the largest planetesimals, those larger than Ceres in the inner Solar System and Pluto in the outer Solar System.[7] These objects are massive enough that the duration of encounters is sufficient for gas drag to significantly reduce the relative velocities of the pebbles.

Outer Solar System

If the formation of pebbles is slow, pebble accretion leads to the formation of a few gas giants in the outer Solar System. The formation of the gas giants is a long-standing problem in planetary science.[8] The accretion of the cores of giant planets via the collision and mergers of planetesimals is slow and is unlikely to be completed before the gas disk dissipates.[1] The largest planetesimals can grow much faster via pebble accretion,[9] but if the formation of pebbles is rapid many planetesimals are formed via streaming instabilities or other mechanisms and grow into numerous Earth-mass planets instead of giant planet cores.[10] As the largest objects approach Earth-mass the radius from which pebbles are accreted is limited by the Hill radius.[2] This slows their growth relative to their neighbors and allows many objects to accrete similar masses of pebbles. However, if pebble formation is slow, the initial formation of planetesimals is limited.[11] As the masses of the first planetesimals grow via pebble accretion they become large enough to gravitationally stir the planetesimals which formed later, increasing the inclinations of these smaller planetesimals.[11] Their inclined orbits keep small planetesimals outside of the narrow disk of pebbles during most of their orbits, limiting their growth.[10] As a result, most of mass is accreted by the few large objects which grow into giant planet cores.[12] A few of these cores eventually grow massive enough to create a gap in the pebble disk. Accretion of pebbles is then halted and the gas envelope surrounding the core cools and collapses allowing for the rapid accretion of gas and the formation of a gas giant. Cores that do not grow massive enough to clear gaps in the pebble disk are only able to accrete small gas envelopes and instead become ice giants.[3] However, dedicated formation models indicate that it is difficult to reconcile growth via pebble accretion with the final mass and composition of the solar system ice giants Uranus and Neptune.[13]

Inner Solar System

The terrestrial planets may be much smaller than the giant planets due to sublimation of water ice as pebbles crossed the ice line. Upon crossing the water ice line the water ice in pebbles sublimates and the pebbles break up into smaller silicate grains. The smaller grains are dispersed into a thicker disk by the turbulence in the gas disk. The mass flow of solids drifting through the terrestrial region is also reduced by half by the loss of water ice. In combination these two factors significantly reduce the rate at which mass is accreted by planetesimals in the inner Solar System relative to the outer Solar System. As a result, planetary embryos in the inner Solar System are able to grow only to around Mars-mass, unlike in the outer Solar System where they grow more than 10x Earth-mass forming the cores of giant planets.[14]

Pebble accretion becomes less efficient as the density of gas in the protoplanetary disk decreases resulting in small mass of Mars and a low mass asteroid belt. The protoplanetary disk from which the Solar System formed is believed to have had a surface density that decreased with distance from the Sun and have been flared, with an increasing thickness with distance from the Sun.[15] As a result, the density of the gas and the aerodynamic drag felt by pebbles embedded in the disk decreased significantly with distance. This caused the efficiency of pebble accretion to fall rapidly with distance as the aerodynamic drag becomes too weak for the pebbles to be captured during encounters with the largest objects. An object that grows rapidly at Earth's orbital distance would only grow slowly in Mars's orbit and very little in the asteroid belt.[6] In addition, the inward drift of the pebbles which form in the asteroid belt but are not accreted there further depletes its final mass.[15]

References

  1. 1 2 Lewin, Sarah. "To Build a Gas Giant Planet, Just Add Pebbles". Space.com. Retrieved 22 November 2015.
  2. 1 2 Kretke, K. A.; Levison, H. F. (2014). "Challenges in Forming the Solar System's Giant Planet Cores via Pebble Accretion". The Astronomical Journal 148 (6): 109. arXiv:1409.4430. doi:10.1088/0004-6256/148/6/109.
  3. 1 2 Lambrechts, M.; Johansen, A.; Morbidelli, A. (2014). "Separating gas-giant and ice-giant planets by halting pebble accretion". Astronomy & Astrophysics 572: A35. arXiv:1408.6087. doi:10.1051/0004-6361/201423814.
  4. ↑ Lambrechts, M.; Johansen, A. (2014). "Forming the cores of giant planets from the radial pebble flux in protoplanetary discs". Astronomy & Astrophysics 572: A107. arXiv:1408.6094. doi:10.1051/0004-6361/201424343.
  5. ↑ Ormel, C. W.; Klahr, H. H. (2010). "The effect of gas drag on the growth of protoplanets. Analytical expressions for the accretion of small bodies in laminar disks". Astronomy and Astrophysics 520: A43. arXiv:1007.0916. doi:10.1051/0004-6361/201014903.
  6. 1 2 "Scientists predict that rocky planets formed from "pebbles"". Southwest Research Institute. Retrieved 22 November 2015.
  7. ↑ Morbidelli, A.; Nesvorny, D. (2012). "Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations". Astronomy & Astrophysics 546: A18. arXiv:1208.4687. doi:10.1051/0004-6361/201219824.
  8. ↑ "Scientists think 'planetary pebbles' were the building blocks for the largest planets". Phys.org. Retrieved 22 November 2015.
  9. ↑ Lambrechts, M.; Johansen, A. (2012). "Rapid growth of gas-giant cores by pebble accretion". Astronomy & Astrophysics 544: A32. arXiv:1205.3030. doi:10.1051/0004-6361/201219127.
  10. 1 2 Hand, Eric. "How Jupiter and Saturn were born from pebbles". Science. Retrieved 22 November 2015.
  11. 1 2 Levison, Harold F.; Kretke, Katherine A.; Duncan, Martin J. (2015). "Growing the gas-giant planets by the gradual accumulation of pebbles". Nature 524 (7565): 322–324. arXiv:1510.02094. doi:10.1038/nature14675.
  12. ↑ Witze, Alexandra. "Small rocks build big planets". Nature.com. Retrieved 22 November 2015.
  13. ↑ Helled, R.; Bodenheimer, P. (2014). "The Formation of Uranus and Neptune: Challenges and Implications for Intermediate-mass Exoplanets" (PDF). The Astrophysical Journal 789 (1): id. 69 (11 pp.). arXiv:1404.5018. Bibcode:2014ApJ...789...69H. doi:10.1088/0004-637X/789/1/69.
  14. ↑ Morbidelli, A.; Lambrechts, M.; Jacobson, S.; Bitsch, B. (2015). "The great dichotomy of the Solar System: Small terrestrial embryos and massive giant planet cores". Icarus 258: 418–429. arXiv:1506.01666. doi:10.1016/j.icarus.2015.06.003.
  15. 1 2 Levison, Harold F.; Kretke, Katherine A.; Walsh, Kevin; Bottke, William (2015). "Growing the terrestrial planets from the gradual accumulation of sub-meter sized objects" (PDF). PNAS 112 (46): 14180–14185. arXiv:1510.02095. doi:10.1073/pnas.1513364112.
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