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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Code availability
The code for the numerical simulation is available from the corresponding authors on reasonable request.
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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.
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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.
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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.
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.
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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DOI: https://doi.org/10.1038/s41567-019-0728-9
