Skip to main content
SpringerLink
Log in

Streaming Instability in the Gas-Dust Medium of the Protoplanetary Disc and the Formation of Fractal Dust Clusters

  • Published:
Solar System Research Aims and scope Submit manuscript

Abstract

The sequence of evolution of the protoplanetary gas-and-dust disk around the parent star includes, according to modern concepts, its compression in the central plane and decay into separate dust condensations (clusters) due to the occurrence of various types of instabilities. The interaction of dust clusters of a fractal structure during their collisions is considered as a key mechanism for the formation and growth of primary solids, which serve as the basis for the subsequent formation of planetesimals and embryos of planets. Among the mechanisms contributing to the formation of planetesimals, an important place belongs, along with gravitational instability, hydrodynamic instabilities, in particular, the socalled streaming instability of the two-phase gas-dust layer due to its ability to concentrate dispersed particles in dense clots. In contrast to a number of existing models of streaming instability, in which dust particles are considered structurally compact and monodisperse, this paper proposes a more realistic model of polydisperse particles of fractal nature, forming dust clusters as a result of coagulation. The instability of the dust layer in the central plane of the protoplanetary disk under linear axisymmetric perturbations of its parameters is considered. A preliminary conclusion can be drawn that the proposed model of dust fractal aggregates of different scales increases the efficiency of linear growth of hydrodynamic instabilities, including the streaming instabilities associated with the difference between the velocities of the dust and gas phases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Armitage, P.J., Lecture notes on the formation and early evolution of planetary systems, 2007. https://doi.org/abs/astro-ph/0701485.

    Google Scholar 

  • Armitage, P.J., Dynamics of protoplanetary disks, Ann. Rev. Astron. Astrophys., 2011, vol. 49, pp. 195–236.

    Article  ADS  Google Scholar 

  • Armitage, P.J., Physical processes in protoplanetary disks, 45th Saas-Fee Advanced Course of the Swiss Society for Astrophysics and Astronomy “From Protoplanetary Disks to Planet Formation,” Les Diablerets, Switzerland, Geneva: Swiss Soc. Astrophys. Astron., 2015, pp. 1–127.

    Google Scholar 

  • Bai, X.-N. and Stone, J.M., Dynamics of solids in the mid-plane of protoplanetary disks: Implications for planetesimal formation, Astrophys. J., 2010a, vol. 722no. 2, pp. 1437–1459.

    Article  ADS  Google Scholar 

  • Bai, X.-N. and Stone, J.M., The effect of the radial pressure gradient in protoplanetary disks on planetesimal formation, Astrophys. J., 2010b, vol. 722no. 2, pp. L220–L223.

    Article  ADS  Google Scholar 

  • Bai, X.-N. and Stone, J.M., Particle-gas dynamics with Athena: Method and convergence, Astrophys. J. Suppl., 2010c, vol. 190no. 2, pp. 297–310.

    Article  ADS  Google Scholar 

  • Bertini, I., Gutierrez, P.J., and Sabolo, W., The influence of the monomer shape in the first stage of dust growth in the protoplanetary disk, Astron. Astrophys., 2009, vol. 504, pp. 625–633.

    Article  ADS  Google Scholar 

  • Blum, J. and Wurm, G., The growth mechanisms of macroscopic bodies in protoplanetary disks, Ann. Rev. Astron. Astrophys., 2008, vol. 46, pp. 21–56.

    Article  ADS  Google Scholar 

  • Carrera, D., Johansen, A., and Davies, M., How to form planetesimals from mm-sized chondrules and chondrule aggregates, Astron. Astrophys., 2015, vol. 579, art. ID A43.

  • Carrera, D., Gorti, U., Johansen, A., and Davies, M., Planetesimal formation by the streaming instability in a photoevaporating disk, Astrophys. J., 2017, vol. 839no. 1, art. ID 16.

    Google Scholar 

  • Chapman, S. and Cowling, T.G., The Mathematical Theory of Non-Uniform Gases, Cambridge: Cambridge Univ. Press, 1960.

    MATH  Google Scholar 

  • Chavanis, P.H., Trapping of dust by coherent vortices in the solar nebula, Astron. Astrophys., 2000, vol. 356, pp. 1089–1111.

    ADS  Google Scholar 

  • Chen, Z.-Y., Meakin, P., and Deutch, J.M., Comment on “Hydrodinamic behavior of fractal aggregates,” Phys. Rev. Lett., 1987. 59,no. 18, p. 2121.

    Article  ADS  Google Scholar 

  • Chiang, E. and Youdin, A.N., Forming planetesimals in solar and extrasolar nebulae, Ann. Rev. Earth Planet. Sci., 2010, vol. 38, pp. 493–522.

    Article  ADS  Google Scholar 

  • Cuzzi, J.N., Dobrovolskis, A.R., and Champney, J.M., Particlegas dynamics in the midplane of a protoplanetary nebulae, Icarus, 1993, vol. 106, pp. 102–134.

    Article  ADS  Google Scholar 

  • Cuzzi, J.N., Hogan, R.C., and Shariff, K., Toward planetesimals: dense chondrule clumps in the protoplanetary nebula, Astrophys. J., 2008, vol. 687, pp. 1432–1447.

    Article  ADS  Google Scholar 

  • Hodgson, L.S. and Brandenburg, A., Turbulence effects in planetesimal formation, Astron. Astrophys., 1998, vol. 330, pp. 1169–1174.

    ADS  Google Scholar 

  • Jacquet, E., Balbus, S., and Latter, H., On linear dustgas streaming instabilities in protoplanetary discs, Mon. Not. R. Astron. Soc., 2011, vol. 415, pp. 3591–3598.

    Article  ADS  Google Scholar 

  • Johansen, A., Henning, T., and Klahr, H., Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk midplanes, Astrophys. J., 2006, vol. 643, pp. 1219–1232.

    Article  ADS  Google Scholar 

  • Johansen, A., Oishi, J.S., MacLow, M.-M., Klahr, H., Henning, T., and Youdin, A., Rapid planetesimal formation in turbulent circumstellar disks, Nature, 2007, vol. 448, pp. 1022–1025.

    Article  ADS  Google Scholar 

  • Johansen, A., Youdin, A., and Klahr, H., Zonal flows and long-lived axisymmetric pressure bumps in magnetorotational turbulence, Astrophys. J., 2009, vol. 697, pp. 1269–1289.

    Article  ADS  Google Scholar 

  • Dominik, C. and Tielens, A.G., The physics of dust coagulation and the structure of dust aggregates in space, Astrophys. J., 1997, vol. 480, pp. 647–673.

    Article  ADS  Google Scholar 

  • Drążkowska, J. and Dullemond, C.P., Can dust coagulation trigger streaming instability? Astron. Astrophys., 2014, vol. 572, art. ID A78.

  • Garaud, P. and Lin, D.N.C., On the evolution and stability of a protoplanetary disk dust layer, Astrophys. J., 2004, vol. 608,no. 2, pp. 1050–1075.

    Article  ADS  Google Scholar 

  • Goldreich, P. and Lynden-Bell, D.I., Gravitational stability of uniformly rotating disks, Mon. Not. R. Astron. Soc., 1965, vol. 130, pp. 97–124.

    Article  ADS  Google Scholar 

  • Goldreich, P. and Ward, W.R., The formation of planetesimals, Astrophys. J., 1973, vol. 183,no. 3, pp. 1051–1061.

    Article  ADS  Google Scholar 

  • Kataoka, A., Tanaka, H., Okuzumi, S., and Wada, K., Fluffy dust forms icy planetesimals by static compression, Astron. Astrophys., 2013, vol. 557, art. ID L4.

  • Kolesnichenko, A.V., Synergetic mechanism of the development of coherent structures in the continual theory of developed turbulence, Sol. Syst. Res., 2004, vol. 38,no. 5, pp. 351–371.

    Article  ADS  Google Scholar 

  • Kolesnichenko, A.V., The theory of the inverse energy cascade in the helical turbulence of an astrophysical disk, Preprint of Keldysh Inst. of Applied Mathematics, Russ. Acad. Sci., Moscow, 2014, no. 70.

  • Kolesnichenko, A.V., Nekotorye problemy konstruirovaniya kosmicheskikh sploshnykh sred. Modelirovanie akkretsionnykh protoplanetnykh diskov (Simulation of Space Continuous Media. Modeling of Accretionary Proto-planetary Disks), Moscow: Inst. Prikl. Matem. im. M.V. Keldysha, 2017.

    Google Scholar 

  • Kolesnichenko, A.V. and Marov, M.Ya., Fundamentals of the mechanics of heterogeneous media in the circumsolar protoplanetary cloud: The effects of solid particles on disk turbulence, Sol. Syst. Res., 2006, vol. 40,no. 1, pp. 1–56.

    Article  ADS  Google Scholar 

  • Kolesnichenko, A.V. and Marov, M.Ya., The effect of spirality on the evolution of turbulence in the solar protoplanetary cloud, Sol. Syst. Res., 2007, vol. 41,no. 1, pp. 1–18.

    Article  ADS  Google Scholar 

  • Kolesnichenko, A.V. and Marov, M.Ya., Turbulentnost' i samoorganizatsiya. Problemy modelirovaniya kosmicheskikh i prirodnykh sred (Turbulence and Self-Organization: Modeling of Space and Natural Media), Moscow: BINOM. Laboratoriya Znanii, 2009.

    Google Scholar 

  • Kolesnichenko, A.V. and Marov, M.Ya., Modeling of aggregation of fractal dust clusters in a laminar protoplanetary disk, Sol. Syst. Res., 2013, vol. 47,no. 2, pp. 80–98.

    Article  ADS  Google Scholar 

  • Kolesnichenko, A.V. and Marov, M.Ya., Modeling the formation of dust fractal clusters as the basis for loose protoplanethesimals in the solar preplanetary cloud, Preprint of Keldysh Inst. of Applied Mathematics, Russ. Acad. Sci., Moscow, 2014, no. 75.

  • Kolesnichenko, A.V. and Marov, M.Ya., Modification of the jeans instability criterion for fractal-structure astrophysical objects in the framework of non-extensive statistics, Sol. Syst. Res., 2014b, vol. 48no. 5, pp. 354–365.

    Article  ADS  Google Scholar 

  • Lissauer, J.J. and de Pater, I., Fundamental Planetary Science: Physics, Chemistry and Habitability, New York: Cambridge Univ. Press, 2013.

    Book  Google Scholar 

  • Makalkin, A.B. and Ziglina, I.N., Gravitational instability in the dust layer of a protoplanetary disk with interaction between the layer and the surrounding gas, Sol. Syst. Res., 2018, vol. 52,no. 6, pp. 518–533.

    Article  ADS  Google Scholar 

  • Marov, M.Ya., Small bodies in the Solar system and some problems in cosmogony, Phys.-Usp., 2005, vol. 48,no. 6, pp. 638–647.

    Article  ADS  Google Scholar 

  • Marov, M.Ya. and Kolesnichenko, A.V., Turbulence and Self-Organizing: Problems Modeling of Space and Environments, Berlin: Springer-Verlag, 2013.

    Book  Google Scholar 

  • Marov, M.Ya. and Rusol, A.V., Estimating the parameters of collisions between fractal dust clusters in a gas-dust protoplanetary disk, Astron. Lett., 2018, vol. 44,no. 7, pp. 474–481.

    Article  ADS  Google Scholar 

  • Marov, M.Ya. and Shevchenko, I.I., Ekzoplanety. Ekzo-planetologiya (Exoplanets. Exoplanetology), Moscow: Inst. Komp'yut. Issled., 2017.

    Google Scholar 

  • Mikhailov, E.F. and Vlasenko, S.S., The generation of fractal structures in gaseous phase, Phys.-Usp., 1995, vol. 38,no. 3, pp. 253–271.

    Article  ADS  Google Scholar 

  • Mizuno, H., Grain growth in the turbulent accretion disk solar nebula, Icarus, 1989, vol. 80, pp. 189–201.

    Article  ADS  Google Scholar 

  • Morbidelli, A. and Raymond, S.N., Challenges in planet formation, J. Geophys. Res.: Planets, 2016, vol. 121,no. 10, pp. 1962–1980.

    Article  ADS  Google Scholar 

  • Nakagawa, Y., Sekiya, M., and Hayashi, C., Settling and growth of dust particles in a laminar phase of a low-mass solar nebula, Icarus, 1986, vol. 67, pp. 375–390.

    Article  ADS  Google Scholar 

  • Nakamoto, T. and Nakagawa, Y., Formation, early evolution, and gravitational stability of protoplanetary disks, Astrophys. J., 1994, vol. 421, pp. 640–651.

    Article  ADS  Google Scholar 

  • Nigmatulin, R.I., Dinamika mnogofaznykh sred (Dynamics of Multiphase Media), Moscow: Nauka, 1987, part 1.

    Google Scholar 

  • Okuzumi, S., Tanaka, H., and Sakagami, M.-A., Numerical modeling of the coagulation and porosity evolution of dust aggregates, Astrophys. J., 2009, vol. 707. P 1247–1264.

    Article  ADS  Google Scholar 

  • Pan, L., Padoan, P., Scalo, J., Kritsuk, A.G., and Norman, M.L., Turbulent clustering of protoplanetary dust and planetesimal formation, Astrophys. J., 2011, vol. 740no. 1, art. ID 6.

    Google Scholar 

  • Perets, H.B. and Murray-Clay, R., Windshearing in gaseous protoplanetary disks, Proc. Int. Astron. Union, 2011, vol. 276, pp. 453–454.

    Google Scholar 

  • Pinte, C., Dent, W.R.F., Ménard, F., Hales, A., Hill, T., Cortes, P., and de Gregorio-Monsalvo, I., Dust and gas in the disk of HL Tauri: Surface density, dust settling, and dust-to-gas ratio, Astrophys. J., 2016, vol. 816no. 1, art. ID 25.

    Google Scholar 

  • Roy, N. and Ray, A.K., Fractal features in accretion discs, Mon. Not. R. Astron. Soc., 2009, vol. 397,no. 3, pp. 1374–1385.

    Article  ADS  Google Scholar 

  • Safronov, V.S., Evolution of dust component in near-Sun pre-planetary disk, Astron. Vestn., 1987, vol. 21,no. 3, pp. 216–220.

    ADS  Google Scholar 

  • Samko, S.G., Kilbas, A.A., and Marichev, O.I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya (Integrals and Derivatives of fractional Order and Their Application), Minsk: Nauka i Tekhnika, 1987.

    MATH  Google Scholar 

  • Shakura, N.I. and Sunyaev, R.A., Black holes in binary systems. Observational appearance, Astron. Astrophys., 1973, vol. 24, pp. 337–355.

    ADS  Google Scholar 

  • Shariff, K. and Cuzzi, J.N., Gravitational instability of solid assisted by gas drag: slowing by turbulent mass diffusivity, Astrophys. J., 2011, vol. 738no. 1, art. ID 73.

    Google Scholar 

  • Shu, F.H., Waves in planetary rings, in Planetary Rings (A85-3440115-88), Tucson, Az: Univ. Arizona Press, 1984, pp. 513–561.

    Google Scholar 

  • Smirnov, B.M., Fizika fraktal'nykh klasterov (Physics of Fractal Clusters), Moscow: Nauka, 1991.

    Google Scholar 

  • Smirnov, B.M., Processes involving clusters and small particles in a buffer gas, Phys.-Usp., Phys.-Usp., 2011, vol. 54,no. 7, pp. 691–721.

    Article  ADS  Google Scholar 

  • Squire, J. and Hopkins, P.F., Resonant drag instabilities in protoplanetary discs: the streaming instability and new, faster growing instabilities, Mon. Not. R. Astron. Soc., 2018a, vol. 477no. 4, pp. 5011–5040.

    Article  ADS  Google Scholar 

  • Squire, J. and Hopkins, P.F., Resonant drag instability of grains streaming in fluids, Astrophys. J. Lett., 2018b, vol. 856no. 1, art. ID L15.

    Google Scholar 

  • Takahashi, S.Z. and Inutsuka, S., Two-component secular gravitational instability in a protoplanetary disk: A possible mechanism for creating ring-like structures, Astrophys. J., 2014, vol. 794no. 1, art. ID 55.

    Google Scholar 

  • Takahashi, S.Z. and Inutsuka, S., An origin of multiple ring structure and hidden planets in HL Tau: a unified picture by secular gravitational instability, Astron. J., 2016, vol. 152no. 6, art. ID 184.

    Google Scholar 

  • Tarasov, V.E., Fractional hydrodynamic equations for fractal media, Ann. Phys., 2005, vol. 318,no. 2, pp. 286–307.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Tarasov, V.E., Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, New York: Springer-Verlag, 2010.

    Book  MATH  Google Scholar 

  • Toomre, A., On the gravitational stability of a disk of stars, Astrophys. J., 1964, vol. 139, pp. 1217–1238.

    Article  ADS  Google Scholar 

  • Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 1988, vol. 52, pp. 479–487.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ward, W.R., On planetesimal formation: Tire role of collective particle behavior, in Origin of the Earth and Moon, Canup, R.M., Righter, K., Eds., Tucson: Univ. Arizona Press, 2000, pp. 75–84.

    Google Scholar 

  • Weidenschilling, S.J., Formation of planetesimals and accretion of the terrestrial planets, Space Sci. Rev., 2000, vol. 92, pp. 295–310.

    Article  ADS  Google Scholar 

  • Wetherill, G.W. and Stewart, G.R., Accumulation of a swarm of small planetesimals, Icarus, 1989, vol. 77, pp. 330–357.

    Article  ADS  Google Scholar 

  • Wiltzius, P., Hydrodynamic behavior of fractal aggregates, Phys. Rev. Lett., 1987, vol. 58,no. 7, pp. 710–713.

    Article  ADS  Google Scholar 

  • Umurhan, O.M., Estrada, P.R., Cuzzi, J.N., and Hartlep, T., Streaming instability in turbulent protoplanetary disks: theoretical predictions, Proc. 49th Lunar and Planetary Science Conf., LPI Contributions no. 2083, Houston: Lunar Planet. Inst., 2018.

    Google Scholar 

  • Yang, C.-C. and Johansen, A., On the feeding zone of planetesimal formation by the streaming instability, Astrophys. J., 2014, vol. 792,no. 2, p. 86.

    Article  ADS  Google Scholar 

  • Yang, C.-C., Johansen, A., and Carrera, D., Concentrating small particles in protoplanetary disks through the streaming instability, Astron. Astrophys., 2017, vol. 606, art. ID A80.

  • Youdin, A.N., Planetesimal formation without thresholds. I. Dissipative gravitational instabilities and particle stirring by turbulence, 2005a. https://doi.org/abs/astroph/0508659.

    Google Scholar 

  • Youdin, A.N., Planetesimal formation without thresholds. II. Gravitational instability of solids in turbulent protoplanetary disks, 2005b. https://doi.org/abs/astroph/0508662.

    Google Scholar 

  • Youdin, A.N., On the formation of planetesimals via secular gravitational instabilities with turbulent stirring, Astrophys. J., 2011, vol. 731, pp. 99–117.

    Article  ADS  Google Scholar 

  • Youdin, A.N. and Goodman, J., Streaming instabilities in protoplanetary disks, Astrophys. J., 2005, vol. 620, pp. 459–469.

    Article  ADS  Google Scholar 

  • Youdin, A.N. and Lithwick, Y., Particle stirring in turbulent gas disks: including orbital oscillations, Icarus, 2007, vol. 192, pp. 588–604.

    Article  ADS  Google Scholar 

  • Youdin, A.N. and Shu, F., Planetesimal formation by gravitational instability, Astrophys. J., 2002, vol. 580, pp. 494–505.

    Article  ADS  Google Scholar 

  • Ziglina, I.N. and Makalkin, A.B., Gravitational instability in the dust layer of a protoplanetary disk: Interaction of solid particles with turbulent gas in the layer, Sol. Syst. Res., 2016, vol. 50,no. 6, pp. 408–425.

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The work was performed in the framework of the State Task of Keldysh Institute of Applied Mathematics and Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy of Sciences with partial support by the Russian Foundation for Basic Research, project nos. 17-02-00507 and 18-01-00064, and by the Presidium of the Russian Academy of Sciences, program no. 12.

Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia

    A. V. Kolesnichenko

  2. Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow, 119334, Russia

    M. Ya. Marov

Authors
  1. A. V. Kolesnichenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Ya. Marov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. V. Kolesnichenko or M. Ya. Marov.

Additional information

Russian Text © The Author(s), 2019, published in Astronomicheskii Vestnik, 2019, Vol. 53, No. 3, pp. 195–213.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kolesnichenko, A.V., Marov, M.Y. Streaming Instability in the Gas-Dust Medium of the Protoplanetary Disc and the Formation of Fractal Dust Clusters. Sol Syst Res 53, 181–198 (2019). https://doi.org/10.1134/S003809461903002X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S003809461903002X

Keywords

Search

Navigation