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.
Subscribe to Journal
Get full journal access for 1 year
only $15.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The code for the numerical simulation is available from the corresponding authors on reasonable request.
Testi, L. et al. in Protostars and Planets VI (eds Beuther, H. et al.) 339–362 (Univ. Arizona Press, 2014).
Pohl, A. et al. The circumstellar disk HD 169142: gas, dust, and planets acting in concert? Astrophys. J. 850, 52 (2017).
Pinilla, P. et al. A multi-wavelength analysis of dust and gas in the SR 24S transition disk. Astrophys. J. 839, 99 (2017).
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).
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).
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).
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).
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).
Windmark, F. et al. Planetesimal formation by sweep-up: how the bouncing barrier can be beneficial to growth. Astron. Astrophys. 540, A73 (2012).
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).
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).
Youdin, A. N. & Goodman, J. Streaming instabilities in protoplanetary disks. Astrophys. J. 620, 459–469 (2005).
Johansen, A. et al. in Protostars and Planets VI (eds Beuther, H. et al.) 547–570 (Univ. Arizona Press, 2014).
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).
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).
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).
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).
Drazkowska, J. & Dullemond, C. P. Can dust coagulation trigger streaming instability? Astron. Astrophys. 572, A78 (2014).
Yang, C.-C., Johansen, A. & Carrera, D. Concentrating small particles in protoplanetary disks through the streaming instability. Astron. Astrophys. 606, A80 (2017).
Weidenschilling, S. J. & Cuzzi, J. N. in Protostars and Planets III (eds Levy, E. H. & Lunine, J. I.). 1031–1060 (Univ. Arizona Press, 1993).
Blum, J. & Wurm, G. The growth mechanisms of macroscopic bodies in protoplanetary disks. Annu. Rev. Astron. Astrophys. 46, 21–56 (2008).
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).
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).
Kelling, T., Wurm, G. & Koester, M. Experimental study on bouncing barriers in protoplanetary disks. Astrophys. J. 783, 111 (2014).
Demirci, T. et al. Is there a temperature limit in planet formation at 1000 K? Astrophys. J. 846, 48 (2017).
Méndez Harper, J. & Dufek, J. The effects of dynamics on the triboelectrification of volcanic ash. J. Geophys. Res. Atmos. 121, 8209–8228 (2016).
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).
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).
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).
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).
Lacks, D. J. & Sankaran, R. M. Contact electrification of insulating materials. J. Phys. D 44, 453001 (2011).
Siu, T., Cotton, J., Mattson, G. & Shinbrot, T. Self-sustaining charging of identical colliding particles. Phys. Rev. E 89, 052208 (2014).
Desch, S. J. & Cuzzi, J. N. The generation of lightning in the solar nebula. Icarus 143, 87–105 (2000).
Muranushi, T. Dust-dust collisional charging and lightning in protoplanetary discs. Mon. Not. R. Astron. Soc. 401, 2641–2664 (2010).
Pähtz, T., Herrmann, H. J. & Shinbrot, T. Why do particle clouds generate electric charges? Nat. Phys. 6, 364–368 (2010).
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).
Konopka, U. et al. Charge-induced gelation of microparticles. New J. Phys. 7, 227 (2005).
Feng, J. Q. Electrostatic interaction between two charged dielectric spheres in contact. Phys. Rev. E 62, 2891–2897 (2000).
Matias, A. F. V., Shinbrot, T. & Araújo, N. A. M. Mechanical equilibrium of aggregates of dielectric spheres. Phys. Rev. E 98, 062903 (2018).
Haeberle, J., Schella, A., Sperl, M., Schröter, M. & Born, P. Double origin of stochastic granular tribocharging. Soft Matter 14, 4987–4995 (2018).
Corral, Á. & González, Á. Power law size distributions in geoscience revisited. Earth Space Sci. 6, 673–697 (2019).
Lin, M. Y. et al. Universality in colloid aggregation. Nature 339, 466–469 (1989).
Meakin, P. & Family, F. Structure and dynamics of reaction-limited aggregation. Phys. Rev. A 36, 5498–5501 (1987).
Meakin, P. Aggregation kinetics. Phys. Scripta 46, 295–331 (1992).
Ball, R. C., Weitz, D. A., Witten, T. A. & Leyvraz, F. Universal kinetics in reaction-limited aggregation. Phys. Rev. Lett. 58, 274–277 (1987).
Okuzumi, S. Electric charging of dust aggregates and its effect on dust coagulation in protoplanetary disks. Astrophys. J. 698, 1122–1135 (2009).
Matthews, L. S., Shotorban, B. & Hyde, T. W. Cosmic dust aggregation with stochastic charging. Astrophys. J. 776, 103 (2013).
Johansen, A. & Okuzumi, S. Harvesting the decay energy of 26Al to drive lightning discharge in protoplanetary discs. Astron. Astrophys. 609, A31 (2018).
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).
Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 9, 671–675 (2012).
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).
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).
Kuwabara, G. & Kono, K. Restitution coefficient in a collision between two spheres. Japan. J. Appl. Phys. 26, 1230–1233 (1987).
Demirci, T. et al. Are pebble pile planetesimals doomed? Mon. Not. R. Astron. Soc. 484, 2779–2785 (2019).
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).
Kataoka, R. & Sato, T. Ionization of protoplanetary disks by galactic cosmic rays, solar protons, and supernova remnants. Geosci. Front. 8, 247–252 (2017).
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.
The authors declare no competing interests.
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.
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.
This image shows the glass particles of 434 µm diameter used in the experiments.
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
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.
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.
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.
Marked by the arrow, an individual grain impacts a charged cluster at 0.13 m s−1. The cluster only deforms but stays intact.
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
Datapoints of the measured grain charges.
Datapoints and errors of the measured and simulated cluster sizes.
Datapoints of the measured grain sizes.
Raw datapoints of the measures cluster sizes in the experiments, used for Fig. 4 and Ext. Dat. Fig. 8.
About this article
Cite this article
Steinpilz, T., Joeris, K., Jungmann, F. et al. Electrical charging overcomes the bouncing barrier in planet formation. Nat. Phys. (2019). https://doi.org/10.1038/s41567-019-0728-9