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Electrical charging overcomes the bouncing barrier in planet formation

Abstract

In protoplanetary disks, solid objects (so-called planetesimals) are formed from dust. Micrometre-sized dust grains grow into millimetre-sized aggregates. Once those aggregates have diameters exceeding a few centimetres, they become subject to concentration mechanisms such as the streaming instability, permitting the formation of self-gravitating clusters, which might eventually collapse into kilometre-sized planetesimals. However, for the streaming instability to set in, clumps spanning sizes from centimetres to decimetres are required in the centre of a protoplanetary disk. In the size range between millimetres and centimetres, aggregates bounce off each other rather than sticking together, and growth is stalled. Here we show in microgravity experiments that collisions between millimetre-sized grains lead to sufficient electrical charging for aggregation to bridge this gap between the bouncing barrier and the onset of the streaming instability. We computationally simulate aggregation and find that models agree with the experimental data only if electrical charging is present. We therefore propose that collisional charging may promote early growth in the size gap that current models of planetesimal formation cannot account for.

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Fig. 1: Sketch of the apparatus used in microgravity.
Fig. 2: Aggregates in experiment and simulation.
Fig. 3: Charge distribution of individual grains.
Fig. 4: Size distributions of moderate-sized clusters.

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Data availability

The data represented in Figs. 3 and 4 and in Extended Data Figs. 3 and 8 are available with the online version of this paper. All other data that supports the plots within this paper and other findings of this study are available from the corresponding authors on reasonable request.

Code availability

The code for the numerical simulation is available from the corresponding authors on reasonable request.

References

  1. Testi, L. et al. in Protostars and Planets VI (eds Beuther, H. et al.) 339–362 (Univ. Arizona Press, 2014).

  2. Pohl, A. et al. The circumstellar disk HD 169142: gas, dust, and planets acting in concert? Astrophys. J. 850, 52 (2017).

    ADS  Google Scholar 

  3. Pinilla, P. et al. A multi-wavelength analysis of dust and gas in the SR 24S transition disk. Astrophys. J. 839, 99 (2017).

    ADS  Google Scholar 

  4. Weisberg, M. K., McCoy, T. J. & Krot, A. N. in Meteorites and the Early Solar System II (eds Lauretta, D. S. & McSween, H. Y. Jr) 19–52 (Univ. Arizona Press, 2006).

  5. Friedrich, J. M. et al. Chondrule size and related physical properties: a compilation and evaluation of current data across all meteorite groups. Geochemistry 75, 419–443 (2015).

    Google Scholar 

  6. Dominik, C. & Tielens, A. G. G. M. The physics of dust coagulation and the structure of dust aggregates in space. Astrophys. J. 480, 647–673 (1997).

    ADS  Google Scholar 

  7. Tanaka, H., Wada, K., Suyama, T. & Okuzumi, S. Growth of cosmic dust aggregates and reexamination of particle interaction models. Prog. Theor. Phys. Suppl. 195, 101–113 (2012).

    ADS  MATH  Google Scholar 

  8. Zsom, A., Ormel, C. W., Güttler, C., Blum, J. & Dullemond, C. P. The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier. Astron. Astrophys. 513, A57 (2010).

    ADS  Google Scholar 

  9. Windmark, F. et al. Planetesimal formation by sweep-up: how the bouncing barrier can be beneficial to growth. Astron. Astrophys. 540, A73 (2012).

    Google Scholar 

  10. Booth, R. A., Meru, F., Lee, M. H. & Clarke, C. J. Breakthrough revisited: investigating the requirements for growth of dust beyond the bouncing barrier. Mon. Not. R. Astron. Soc. 475, 167–180 (2018).

    ADS  Google Scholar 

  11. Birnstiel, T., Ormel, C. W. & Dullemond, C. P. Dust size distributions in coagulation/fragmentation equilibrium: numerical solutions and analytical fits. Astron. Astrophys. 525, A11 (2011).

    ADS  Google Scholar 

  12. Youdin, A. N. & Goodman, J. Streaming instabilities in protoplanetary disks. Astrophys. J. 620, 459–469 (2005).

    ADS  Google Scholar 

  13. Johansen, A. et al. in Protostars and Planets VI (eds Beuther, H. et al.) 547–570 (Univ. Arizona Press, 2014).

  14. Simon, J. B., Armitage, P. J., Li, R. & Youdin, A. N. The mass and size distribution of planetesimals formed by the streaming instability. I. the role of self-gravity. Astrophys. J. 822, 55 (2016).

    ADS  Google Scholar 

  15. Schreiber, A. & Klahr, H. Azimuthal and vertical streaming instability at high dust-to-gas ratios and on the scales of planetesimal formation. Astrophys. J. 861, 47 (2018).

    ADS  Google Scholar 

  16. Squire, J. & Hopkins, P. F. Resonant drag instabilities in protoplanetary discs: the streaming instability and new, faster growing instabilities. Mon. Not. R. Astron. Soc. 477, 5011–5040 (2018).

    ADS  Google Scholar 

  17. Bai, X.-N. & Stone, J. M. Dynamics of solids in the midplane of protoplanetary disks: implications for planetesimal formation. Astrophys. J. 722, 1437–1459 (2010).

    ADS  Google Scholar 

  18. Drazkowska, J. & Dullemond, C. P. Can dust coagulation trigger streaming instability? Astron. Astrophys. 572, A78 (2014).

    ADS  Google Scholar 

  19. Yang, C.-C., Johansen, A. & Carrera, D. Concentrating small particles in protoplanetary disks through the streaming instability. Astron. Astrophys. 606, A80 (2017).

    Google Scholar 

  20. Weidenschilling, S. J. & Cuzzi, J. N. in Protostars and Planets III (eds Levy, E. H. & Lunine, J. I.). 1031–1060 (Univ. Arizona Press, 1993).

  21. Blum, J. & Wurm, G. The growth mechanisms of macroscopic bodies in protoplanetary disks. Annu. Rev. Astron. Astrophys. 46, 21–56 (2008).

    ADS  Google Scholar 

  22. Weidling, R., Güttler, C., Blum, J. & Brauer, F. The physics of protoplanetesimal dust agglomerates. III. Compaction in multiple collisions. Astrophys. J. 696, 2036–2043 (2009).

    ADS  Google Scholar 

  23. Güttler, C., Blum, J., Zsom, A., Ormel, C. W. & Dullemond, C. P. The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments. Astron. Astrophys. 513, A56 (2010).

    ADS  Google Scholar 

  24. Kelling, T., Wurm, G. & Koester, M. Experimental study on bouncing barriers in protoplanetary disks. Astrophys. J. 783, 111 (2014).

    ADS  Google Scholar 

  25. Demirci, T. et al. Is there a temperature limit in planet formation at 1000 K? Astrophys. J. 846, 48 (2017).

    ADS  Google Scholar 

  26. Méndez Harper, J. & Dufek, J. The effects of dynamics on the triboelectrification of volcanic ash. J. Geophys. Res. Atmos. 121, 8209–8228 (2016).

    ADS  Google Scholar 

  27. Waitukaitis, S. R., Lee, V., Pierson, J. M., Forman, S. L. & Jaeger, H. M. Size-dependent same-material tribocharging in insulating grains. Phys. Rev. Lett. 112, 218001 (2014).

    ADS  Google Scholar 

  28. Yoshimatsu, R., Araújo, N. A. M., Wurm, G., Herrmann, H. J. & Shinbrot, T. Self-charging of identical grains in the absence of an external field. Sci. Rep. 7, 39996 (2017).

    ADS  Google Scholar 

  29. Jungmann, F., Steinpilz, T., Teiser, J. & Wurm, G. Sticking and restitution in collisions of charged sub-mm dielectric grains. J. Phys. Commun. 2, 095009 (2018).

    Google Scholar 

  30. Lee, V., James, N. M., Waitukaitis, S. R. & Jaeger, H. M. Collisional charging of individual submillimeter particles: using ultrasonic levitation to initiate and track charge transfer. Phys. Rev. Mater. 2, 035602 (2018).

    Google Scholar 

  31. Lacks, D. J. & Sankaran, R. M. Contact electrification of insulating materials. J. Phys. D 44, 453001 (2011).

    Google Scholar 

  32. Siu, T., Cotton, J., Mattson, G. & Shinbrot, T. Self-sustaining charging of identical colliding particles. Phys. Rev. E 89, 052208 (2014).

    ADS  Google Scholar 

  33. Desch, S. J. & Cuzzi, J. N. The generation of lightning in the solar nebula. Icarus 143, 87–105 (2000).

    ADS  Google Scholar 

  34. Muranushi, T. Dust-dust collisional charging and lightning in protoplanetary discs. Mon. Not. R. Astron. Soc. 401, 2641–2664 (2010).

    ADS  Google Scholar 

  35. Pähtz, T., Herrmann, H. J. & Shinbrot, T. Why do particle clouds generate electric charges? Nat. Phys. 6, 364–368 (2010).

    Google Scholar 

  36. Wurm, G., Schmidt, L., Steinpilz, T., Boden, L. & Teiser, J. A challenge for Martian lightning: limits of collisional charging at low pressure. Icarus 331, 103–109 (2019).

    ADS  Google Scholar 

  37. Konopka, U. et al. Charge-induced gelation of microparticles. New J. Phys. 7, 227 (2005).

    ADS  Google Scholar 

  38. Feng, J. Q. Electrostatic interaction between two charged dielectric spheres in contact. Phys. Rev. E 62, 2891–2897 (2000).

    ADS  Google Scholar 

  39. Matias, A. F. V., Shinbrot, T. & Araújo, N. A. M. Mechanical equilibrium of aggregates of dielectric spheres. Phys. Rev. E 98, 062903 (2018).

    ADS  Google Scholar 

  40. Haeberle, J., Schella, A., Sperl, M., Schröter, M. & Born, P. Double origin of stochastic granular tribocharging. Soft Matter 14, 4987–4995 (2018).

    ADS  Google Scholar 

  41. Corral, Á. & González, Á. Power law size distributions in geoscience revisited. Earth Space Sci. 6, 673–697 (2019).

    ADS  Google Scholar 

  42. Lin, M. Y. et al. Universality in colloid aggregation. Nature 339, 466–469 (1989).

    Google Scholar 

  43. Meakin, P. & Family, F. Structure and dynamics of reaction-limited aggregation. Phys. Rev. A 36, 5498–5501 (1987).

    ADS  Google Scholar 

  44. Meakin, P. Aggregation kinetics. Phys. Scripta 46, 295–331 (1992).

    ADS  Google Scholar 

  45. Ball, R. C., Weitz, D. A., Witten, T. A. & Leyvraz, F. Universal kinetics in reaction-limited aggregation. Phys. Rev. Lett. 58, 274–277 (1987).

    ADS  Google Scholar 

  46. Okuzumi, S. Electric charging of dust aggregates and its effect on dust coagulation in protoplanetary disks. Astrophys. J. 698, 1122–1135 (2009).

    ADS  Google Scholar 

  47. Matthews, L. S., Shotorban, B. & Hyde, T. W. Cosmic dust aggregation with stochastic charging. Astrophys. J. 776, 103 (2013).

    ADS  Google Scholar 

  48. Johansen, A. & Okuzumi, S. Harvesting the decay energy of 26Al to drive lightning discharge in protoplanetary discs. Astron. Astrophys. 609, A31 (2018).

    ADS  Google Scholar 

  49. Bergin, E. A., Aikawa, Y., Blake, G. A. & van Dishoeck, E. F. in Protostars and Planets V (eds Reipurth, B. et al.) 751–766 (Univ. Arizona Press, 2007).

  50. Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 9, 671–675 (2012).

    Google Scholar 

  51. Lee, V., Waitukaitis, S. R., Miskin, M. Z. & Jaeger, H. M. Direct observation of particle interactions and clustering in charged granular streams. Nat. Phys. 11, 733–737 (2015).

    Google Scholar 

  52. Kloss, C., Goniva, C., Hager, A., Amberger, S. & Pirker, S. Models, algorithms and validation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dynam. 12, 140–152 (2012).

    MathSciNet  Google Scholar 

  53. Kuwabara, G. & Kono, K. Restitution coefficient in a collision between two spheres. Japan. J. Appl. Phys. 26, 1230–1233 (1987).

    ADS  Google Scholar 

  54. Demirci, T. et al. Are pebble pile planetesimals doomed? Mon. Not. R. Astron. Soc. 484, 2779–2785 (2019).

    ADS  Google Scholar 

  55. Cleeves, L. I., Adams, F. C. & Bergin, E. A. Exclusion of cosmic rays in protoplanetary disks: stellar and magnetic effects. Astrophys. J. 772, 5 (2013).

    ADS  Google Scholar 

  56. Kataoka, R. & Sato, T. Ionization of protoplanetary disks by galactic cosmic rays, solar protons, and supernova remnants. Geosci. Front. 8, 247–252 (2017).

    Google Scholar 

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Acknowledgements

This project is supported by DLR Space Administration with funds provided by the Federal Ministry of Economic Affairs and Energy (BMWi) under grant number DLR 50 WM 1542 and DLR 50 WM 1762. T.Shinbrot acknowledges support from the US NSF, CBET award 1804286.

Author information

Authors and Affiliations

Authors

Contributions

T.Steinpilz and F.J. designed and performed experiments and analysed the data. K.J. and L.B. wrote the code and performed the simulations. G.W., D.W. and J.T. conceived the research. T.Shinbrot contributed to the conception of research into electrostatic contributions to particle aggregation and to data analysis. All authors discussed the results and wrote the manuscript.

Corresponding authors

Correspondence to Tobias Steinpilz or Gerhard Wurm.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Katherine Follette and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Particle tracks in the electrical field.

Tracks of individual charged grains between capacitor plates in microgravity. Particles enter from the shaker at the right. Tracks are made visible by superimposing a stack of 180 frames (consuming 1 s). Note rebounds are visible at the capacitor walls (top and bottom). For experiment parameters see Table 1.

Extended Data Fig. 2 Scanning electron microscope (SEM) image of sample particles.

This image shows the glass particles of 434 µm diameter used in the experiments.

Extended Data Fig. 3 Size distribution of the sample particles.

The black dots show a histogram of the measured grain sizes of the glass particles used. The uncertainties in size determination of individual grains are 2 %. The blue line is a normal distribution fitted to the experimental data. From the fit we get an average grain diameter of 434 µm with the standard deviation of ± 17 µm.

Source Data

Extended Data Fig. 4 Disintegration of charged aggregates.

a: An aggregate below the white arrow collides with the top capacitor wall and fragments into individual grains. The image shows trajectories of the individual grains following disintegration and an overlay of the original aggregate. The acceleration of each particle in the capacitor field is used to determine the charges of all individual grain within the aggregate. b: Example of charges reconstructed from a disintegration event. Charges are expressed in 105 e. Unlabeled particles do not fragment adequately to establish their charge. The uncertainties due to the error of the trajectory fit, the mass distribution and the unknown position perpendicular to the observation plane are estimated to be 20 % of the net charge (experiment parameters in Table 1). c: Same as b but showing an aggregate that only consists of positive charges.

Extended Data Fig. 5 Snapshots from the simulations.

a: Initial configuration of the simulation. b: Simulated aggregates at a later time. Color is used to distinguish individual aggregates. All grains sticking to each other share the same color.

Extended Data Fig. 6 Collision between two charged grains.

Example of two 434 µm glass particles colliding at 5.4 mm s−1. They collide, bounce off each other but collide a second time due to attractive Coulomb forces. They stick together, eventually.

Extended Data Fig. 7 Impact of individual grain into larger cluster.

Marked by the arrow, an individual grain impacts a charged cluster at 0.13 m s−1. The cluster only deforms but stays intact.

Extended Data Fig. 8 Experimental raw data.

Data of the 3 experimental trials added to generate the experimental data in Fig. 4. Shown are the measured numbers of clusters with a given particle number per cluster. The data are direct counts of grains and clusters and therefore have no error. Also added are power law fits to each data set. The slopes are -1.3, -0.9 and -1.1 for C3A1, C3A3 and C3A6, respectively.

Source Data

Supplementary information

Supplementary Video 1

Video for Extended Data Fig. 6.

Supplementary Video 2

Video for Extended Data Fig. 7.

Supplementary Video 3

Video for Extended Data Fig. 4a.

Source data

Source Data Fig. 3

Datapoints of the measured grain charges.

Source Data Fig. 4

Datapoints and errors of the measured and simulated cluster sizes.

Source Data Extended Data Fig. 3

Datapoints of the measured grain sizes.

Source Data Extended Data Fig. 8

Raw datapoints of the measures cluster sizes in the experiments, used for Fig. 4 and Ext. Dat. Fig. 8.

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Steinpilz, T., Joeris, K., Jungmann, F. et al. Electrical charging overcomes the bouncing barrier in planet formation. Nat. Phys. 16, 225–229 (2020). https://doi.org/10.1038/s41567-019-0728-9

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