Abstract
This chapter highlights the properties of turbulence and mesoscale flow structures in protoplanetary disks and their role in the planet formation process. Here we focus on the formation of planetesimals from a gravitational collapse of a pebble cloud. Large-scale and long-lived flow structures – vortices and zonal flows – are a consequence of weak magneto- and hydrodynamic instabilities in the pressure and entropy stratified quasi-Keplerian shear flow interacting with the fast rotation of the disk. The vortices and zonal flows on the other hand are particle traps tapping into the radial pebble flux of the disk, leading to locally sufficient accumulations to trigger gravitational collapse, directly converting pebbles to many kilometer sized planetesimals. This collapse is moderated by the streaming instability, which is a back-reaction from the particle accumulations onto the gas flow. Without trapping pebbles and increasing thus the local solid-to-gas ratio, this back-reaction would ultimately prevent the formation of planetesimals via turbulent diffusion. The formation of long-lived flow structures is therefore a necessary condition for an efficient and fast formation of planetesimals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alexander R, Pascucci I, Andrews S, Armitage P, Cieza L (2014) The dispersal of protoplanetary disks. In: Beuther H, Klessen RS, Dullemond CP, Henning T (eds) Protostars planets VI. University of Arizona Press, Tucson, pp 475–496
Arlt R, Urpin V (2004) Simulations of vertical shear instability in accretion discs. Astron Astrophy 426(3):755–765. https://doi.org/10.1051/0004-6361:20035896
Armitage P (2013) Astrophysics of planet formation. Cambridge University Press. https://books.google.de/books?id=EFYOngEACAAJ
Avila M (2012) Stability and angular-momentum transport of fluid flows between corotating cylinders. Phys Rev Lett 108(12):124501
Bai XN, Stone JM (2013) Wind-driven accretion in protoplanetary disks. I. Suppression of the magnetorotational instability and launching of the magnetocentrifugal wind. ApJ 769(1):76
Balbus SA, Hawley JF (1991) A powerful local shear instability in weakly magnetized disks. I – linear analysis. II – nonlinear evolution. Astrophys J 376:214–233
Barge P, Sommeria J (1995a) Did planet formation begin inside persistent gaseous vortices? Astron Astrophys 295(1):L1–L4
Béthune W, Lesur G, Ferreira J (2016) Self-organisation in protoplanetary discs. Global, non-stratified Hall-MHD simulations. A&A 589:A87
Béthune W, Lesur G, Ferreira J (2017) Global simulations of protoplanetary disks with net magnetic flux. I. Non-ideal MHD case. A&A 600:A75
Beutel M (2012) An analytical model for the amplification of vortices with baroclinic stratification around young stars. Bachelor Thesis, Max Planck Institute for Astronomy, Heidelberg University
Birnstiel T, Klahr H, Ercolano B (2012) A simple model for the evolution of the dust population in protoplanetary disks. A&A 539:A148
Carrasco-González C, Henning T, Chandler CJ et al (2016) The VLA view of the HL Tau disk: disk mass, grain evolution, and early planet formation. ApJ 821:L16
Carrera D, Johansen A, Davies MB (2015) How to form planetesimals from mm-sized chondrules and chondrule aggregates. A&A 579:A43
Carrera D, Gorti U, Johansen A, Davies MB (2017) Planetesimal formation by the streaming instability in a photoevaporating disk. ApJ 839:16
Clarke C, Carswell B (2014) Principles of astrophysical fluid dynamics. Cambridge University Press, Cambridge
Davis SW, Stone JM, Pessah ME (2010) Sustained magnetorotational turbulence in local simulations of stratified disks with zero net magnetic flux. ApJ 713:52–65
Dittkrist KM, Mordasini C, Klahr H, Alibert Y, Henning T (2014) Impacts of planet migration models on planetary populations. Effects of saturation, cooling and stellar irradiation. A&A 567:A121
Dittrich K, Klahr H, Johansen A (2013) Gravoturbulent planetesimal formation: the positive effect of long-lived zonal flows. ApJ 763:117
Drazin PG, Reid WH (2004) Hydrodynamic stability, 2nd edn. Cambridge University Press. http://www.ebook.de/de/product/4474346/p_g_drazin_w_h_reid_hydrodynamic_stability.html
Dzyurkevich N, Turner NJ, Henning T, Kley W (2013) Magnetized accretion and dead zones in protostellar disks. Astrophys J 765(2):114
Flaherty KM, Hughes AM, Teague R et al (2018) Turbulence in the TW Hya Disk. ApJ 856:117
Fricke K (1968) Instabilität stationärer rotation in sternen. ZAp 68:317
Fromang S, Lyra W, Masset F (2011) Meridional circulation in turbulent protoplanetary disks. A&A 534:A107
Goldreich P, Schubert G (1967) Differential rotation in stars. ApJ 150:571
Goldreich P, Ward WR (1973) The formation of planetesimals. Astrophys J 183:1051. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=1973ApJ...183.1051G%5Cnpapers2://publication/doi/10.1086/152291
Goldreich P, Goodman J, Narayan R (1986) The stability of accretion tori – I. Long-wavelength modes of slender tori. MNRAS 221(2):339–364
Goodman J, Narayan R, Goldreich P (1987) The stability of accretion tori–II. Non-linear evolution to discrete planets. MNRAS 225(3):695–711
Gressel O, Turner NJ, Nelson RP, McNally CP (2015) Global simulations of protoplanetary disks with ohmic resistivity and ambipolar diffusion. ApJ 801:84
Haisch KE Jr, Lada EA, Lada CJ (2001) Disk frequencies and lifetimes in young clusters. Astrophys J Lett 553(2):L153. http://stacks.iop.org/1538-4357/553/i=2/a=L153
Heimpel M, Aurnou J, Wicht J (2005) Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model. Nature 438:193–196
Jacquet E, Balbus S, Latter H (2011) On linear dust-gas streaming instabilities in protoplanetary discs. MNRAS 415:3591–3598
Ji H, Burin M, Schartman E, Goodman J (2006) Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444:343–346
Johansen A, Youdin AN (2007) Protoplanetary disk turbulence driven by the streaming instability: nonlinear saturation and particle concentration. Astrophys J. http://iopscience.iop.org/0004-637X/662/1/627
Johansen A, Klahr H, Henning T (2006) Gravoturbulent formation of planetesimals. ApJ 636:1121–1134
Johansen A, Oishi JS, Mac Low MM et al (2007) Rapid planetesimal formation in turbulent circumstellar disks. Nature 448:1022–1025
Johansen A, Youdin A, Mac Low MM (2009) Particle clumping and planetesimal formation depend strongly on metallicity. ApJ 704:L75–L79
Johansen A, Jacquet E, Cuzzi JN et al (2010) New paradigms for asteroid formation 5(1972):2–3. http://arxiv.org/abs/1505.02941http://doi.org/10.2458/azu_uapress_9780816532131-ch025
Johansen A, Klahr H, Henning T (2011) High-resolution simulations of planetesimal formation in turbulent protoplanetary discs. A&A 529:A62
Johansen A, Mac Low MM, Lacerda P, Bizzarro M (2015) Growth of asteroids, planetary embryos, and Kuiper belt objects by chondrule accretion. Sci Adv 1(3):e1500109–e1500109. http://doi.org/10.1126/sciadv.1500109
Kaspi Y, Galanti E, Hubbard WB et al (2018) Jupiter’s atmospheric jet streams extend thousands of kilometres deep. Nature 555:223–226
Klahr H (2004) The global baroclinic instability in accretion disks. II. Local linear analysis. ApJ 606(2):1070–1082
Klahr HH, Bodenheimer P (2003) Turbulence in accretion disks: vorticity generation and angular momentum transport via the global baroclinic instability. Astrophys J 582(2):869. http://stacks.iop.org/0004-637X/582/i=2/a=869
Klahr H, Hubbard A (2014) Convective overstability in radially stratified accretion disks under thermal relaxation. Astrophys J 788(1):21. http://stacks.iop.org/0004-637X/788/i=1/a=21
Klahr H, Schreiber A (2015) Linking the origin of asteroids to planetesimal formation in the solar nebula. Proc Int Astron Union 10(S318):1–8. http://www.journals.cambridge.org/abstract_S1743921315010406
Klahr H, Raettig N, Lyra W (2013) Disk weather. EPJ Web Conf 46:04,001
Latter H (2016) On the convective overstability in protoplanetary discs. Mon Not R Astron Soc 455(3):2608–2618
Lesur GRJ, Latter H (2016) On the survival of zombie vortices in protoplanetary discs. MNRAS 462:4549–4554
Lesur G, Papaloizou JCB (2010) The subcritical baroclinic instability in local accretion disc models. A&A 513:A60
Lesur G, Kunz MW, Fromang S (2014) Thanatology in protoplanetary discs. The combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones. A&A 566:A56
Li ZY, Banerjee R, Pudritz RE et al (2014) The earliest stages of star and planet formation: core collapse, and the formation of disks and outflows. In: Beuther H, Klessen RS, Dullemond CP, Henning T (eds) Protostars and planets VI. University of Arizona Press, Tucson, pp 173–194
Lin MK, Youdin AN (2015) Cooling requirements for the vertical shear instability in protoplanetary disks. ApJ 811:17
Luest R (1952) Die Entwicklung einer um einen Zentralkörper rotierenden Gasmasse. i. Lösungen der hydrodynamischen Gleichungen mit turbulenter Reibung. Zeitschrift Naturforschung Teil A 7:87–98
Lyra W (2014) Convective overstability in accretion disks: three dimensional linear analysis and nonlinear saturation. Astrophys J 789(1):77
Lyra W, Klahr H (2011) The baroclinic instability in the context of layered accretion. Self-sustained vortices and their magnetic stability in local compressible unstratified models of protoplanetary disks. A&A 527:A138
Manger N, Klahr H (2018) Vortex formation and survival in protoplanetary disks subject to vertical shear instability. MNRAS, in press
Marcus PS, Pei S, Jiang CH et al (2015) Zombie Vortex Instability. I. A purely hydrodynamic instability to resurrect the dead zones of protoplanetary disks. ApJ 808:87
Marcus PS, Pei S, Jiang CH, Barranco JA (2016) Zombie vortex instability. II. Thresholds to trigger instability and the properties of zombie turbulence in the dead zones of protoplanetary disks. ApJ 833:148
Meheut H, Keppens R, Casse F, Benz W (2012) Formation and long-term evolution of 3D vortices in protoplanetary discs. A&A 542:A9
Meltzer M (2015) The Cassini-Huygens visit to Saturn. Springer, Cham
Nakagawa Y, Sekiya M, Hayashi C (1986) Settling and growth of dust particles in a laminar phase of a low-mass solar nebula. Icarus 67:375–390
Nelson RP, Gressel O, Umurhan OM (2012) Linear and nonlinear evolution of the vertical shear instability in accretion discs. Mon Not R Astron Soc 435(3):2610–2632
Ogihara M, Ida S, Morbidelli A (2007) Accretion of terrestrial planets from oligarchs in a turbulent disk. Icarus 188:522–534
Ormel CW, Klahr H (2010) The effect of gas drag on the growth of protoplanets. Astron Astrophys 520:A43
Pelletier G, Pudritz RE (1992) Hydromagnetic disk winds in young stellar objects and active galactic nuclei. ApJ 394:117–138
Petersen MR, Julien K, Stewart GR (2007a) Baroclinic vorticity production in protoplanetary disks. I. Vortex formation. ApJ 658(2):1236
Petersen MR, Stewart GR, Julien K (2007b) Baroclinic vorticity production in protoplanetary disks. II. Vortex growth and longevity. ApJ 658(2):1252
Pfeil T (2017) Stability constraints for protoplanetary disks. Bachelor Thesis, Heidelberg University & Max Planck Insititute for Astronomy
Pfeil T, Klahr H (2018) Mapping the conditions for hydrodynamic instability on viscous models of protoplanetary disks. ApJ, submitted
Pringle JE (1981) Accretion discs in astrophysics. Ann Rev Astron Astrophys 19:137–162
Pringle JE, King A (2007) Astrophysical flows. Cambridge University Press. http://www.ebook.de/de/product/5966154/james_e_pringle_andrew_king_astrophysical_flows.html
Pudritz RE, Norman CA (1986) Bipolar hydromagnetic winds from disks around protostellar objects. ApJ 301:571–586
Pudritz RE, Ouyed R, Fendt C Brandenburg A (2007) Disk winds, jets, and outflows: theoretical and computational foundations. In: Reipurth B, Jewitt D, Keil K (eds) Protostars planets V. University of Arizona Press, Tucson, pp. 277–294, 951pp
Raettig N, Klahr H, Lyra W (2015) Particle trapping and streaming instability in vortices in protoplanetary disks. ApJ 804:35
Rayleigh L (1917) On the dynamics of revolving fluids. R Soc Lond Proc Ser A 93:148–154
Rüdiger G, Arlt R, Shalybkov D (2002) Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification. Astron Astrophys 391(2): 781–787
Ryan BR, Gammie CF, Fromang S, Kestener P (2017) Resolution dependence of magnetorotational turbulence in the isothermal stratified shearing box. ApJ 840:6
Safronov V (1972) Evolution of the protoplanetary cloud and formation of the earth and the planets. Israel program for scientific translations, Jerusalem, p 11. http://www.getcited.org/pub/101392020
Schäfer U, Yang CC, Johansen A (2017) Initial mass function of planetesimals formed by the streaming instability. A&A 597:A69
Shakura NI, Sunyaev RA (1973) Black holes in binary systems. Observational appearance. Astron Astrophys 24:337–355
Shore SN (2007) Astrophysical hydrodynamics. Wiley VCH Verlag GmbH. http://www.ebook.de/de/product/5489098/steven_n_shore_astrophysical_hydrodynamics.html
Simon JB, Armitage PJ, Li R, Youdin AN (2016) The mass and size distribution of planetesimals formed by the streaming instability. I. The role of self-gravity. Astrophys J 822(1):55
Squire J, Hopkins PF (2018a) Resonant drag instabilities in protoplanetary disks: the streaming instability and new, faster-growing instabilities. MNRAS 477:5011–5040
Squire J, Hopkins PF (2018b) Resonant drag instability of grains streaming in fluids. ApJ 856:L15
Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. R Soc Lond Philos Trans Ser A 223:289–343
Testi L, Birnstiel T, Ricci L et al (2014) Dust evolution in protoplanetary disks. In: Beuther H, Klessen RS, Dullemond CP, Henning T (eds) Protostars and planets VI. University of Arizona Press, Tucson, pp 339–361
Turner NJ, Fromang S, Gammie C et al (2014) Transport and accretion in planet-forming disks. In: Protostars and planets VI. University of Arizona Press. https://doi.org/10.2458/azu_uapress_9780816531240-ch018
Urpin V, Brandenburg A (1998) Magnetic and vertical shear instabilities in accretion discs. MNRAS 294:399
van der Marel N, van Dishoeck EF, Bruderer S et al (2013) A major asymmetric dust trap in a transition disk. Science 340:1199–1202
Weidenschilling SJ (1977) Aerodynamics of solid bodies in the solar nebula. MNRAS 180:57–70
Weidenschilling SJ (1980) Dust to planetesimals – settling and coagulation in the solar nebula. Icarus 44:172–189
Whipple FL (1964) The history of the solar system. Proc Nat Acad Sci 52:565–594
Yang CC, Johansen A, Carrera D (2017) Concentrating small particles in protoplanetary disks through the streaming instability. A&A 606:A80
Youdin AN, Goodman J (2005) Streaming instabilities in protoplanetary disks. ApJ 620:459–469
Youdin AN, Johansen A (2007) Protoplanetary disk turbulence driven by the streaming instability: linear evolution and numerical methods. Astrophys J 662(1):613–626. http://arxiv.org/abs/astro-ph/0702625
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this entry
Cite this entry
Klahr, H., Pfeil, T., Schreiber, A. (2018). Instabilities and Flow Structures in Protoplanetary Disks: Setting the Stage for Planetesimal Formation. In: Deeg, H., Belmonte, J. (eds) Handbook of Exoplanets . Springer, Cham. https://doi.org/10.1007/978-3-319-55333-7_138
Download citation
DOI: https://doi.org/10.1007/978-3-319-55333-7_138
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-55332-0
Online ISBN: 978-3-319-55333-7
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics